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CHAPTER 14—SIMPLE LINEAR REGRESSION MULTIPLE CHOICE 1. value of a. b. c. d. ANS: A 2. a. b. c. d. ANS: A 3. correlation a. b. c. d. ANS: C 4. a. b. c. d. ANS: D 5. The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = ? 0 + ? 1x, is known as a. regression equation b. correlation equation c. estimated regression equation d. regression model ANS: A 6. a. b. c. d. ANS: C 7. a. b. c. d.

In regression analysis, the unbiased estimate of the variance is coefficient of correlation coefficient of determination mean square error slope of the regression equation The model developed from sample data that has the form of is known as regression equation correlation equation estimated regression equation regression model In regression analysis, the model in the form is called regression equation correlation equation estimated regression equation regression model If the coefficient of determination is a positive value, then the coefficient of must also be positive must be zero can be either negative or positive must be larger than 1 The coefficient of determination cannot be negative is the square root of the coefficient of correlation is the same as the coefficient of correlation can be negative or positive In a regression analysis, the error term ?

is a random variable with a mean or expected zero one any positive value any value a.

b. c. d. ANS: C 8. a. b. c. d. ANS: B 9. a. b. c. d. ANS: A 10. a. b. c. d. ANS: D 11. a. b. c. d. ANS: C 12. error term ?? a. b. c. d. ANS: A The standard error is the coefficient of correlation coefficient of determination mean square error slope of the regression equation The interval estimate of the mean value of y for a given value of x is prediction interval estimate confidence interval estimate average regression x versus y correlation interval The interval estimate of an individual value of y for a given value of x is prediction interval estimate confidence interval estimate average regression x versus y correlation interval

t-statistic squared square root of SSE square root of SST square root of MSE If MSE is known, you can compute the r square coefficient of determination standard error all of these alternatives are correct In regression analysis, which of the following is not a required assumption about the The expected value of the error term is one. The variance of the error term is the same for all values of X. The values of the error term are independent. The error term is normally distributed. 13. A regression analysis between sales (Y in $1000) and advertising (X in dollars) resulted in the following equation = 30,000 + 4 X The above equation implies that an a. b. c. d.

increase of $4 in advertising is associated with an increase of $4,000 in sales increase of $1 in advertising is associated with an increase of $4 in sales increase of $1 in advertising is associated with an increase of $34,000 in sales increase of $1 in advertising is associated with a. b. c. d. ANS: D increase of $4 in advertising is associated with an increase of $4,000 in sales increase of $1 in advertising is associated with an increase of $4 in sales increase of $1 in advertising is associated with an increase of $34,000 in sales increase of $1 in advertising is associated with an increase of $4,000 in sales 14. Regression analysis is a statistical procedure for developing a mathematical equation that describes how a. one independent and one or more dependent variables are related b.

several independent and several dependent variables are related c. one dependent and one or more independent variables are related d. None of these alternatives is correct. ANS: C 15. In a simple regression analysis (where Y is a dependent and X an independent variable), if the Y intercept is positive, then a. there is a positive correlation between X and Y b. if X is increased, Y must also increase c. if Y is increased, X must also increase d. None of these alternatives is correct. ANS: D 16. a. b. c. d. ANS: A 17. The equation that describes how the dependent variable (y) is related to the independent variable (x) is called a. the correlation model b. the regression model c.

correlation analysis d. None of these alternatives is correct. ANS: B 18. a. b. c. d. ANS: B 19. a. b. c. d. Larger values of r2 imply that the observations are more closely grouped about the average value of the independent variables average value of the dependent variable least squares line origin In regression analysis, the independent variable is used to predict other independent variables used to predict the dependent variable called the intervening variable the variable that is being predicted In regression analysis, the variable that is being predicted is the dependent variable independent variable intervening variable is usually x a. b. c. d.

ANS: C 20. value of a. b. c. d. ANS: A 21. a. b. c. d. ANS: B 22. a. b. c. d. ANS: B 23. a. b. c. d. ANS: B 24. a. b. c. d. ANS: D average value of the independent variables average value of the dependent variable least squares line origin In a regression analysis, the error term ? is a random variable with a mean or expected zero one any positive value any value In simple linear regression analysis, which of the following is not true? The F test and the t test yield the same conclusion. The F test and the t test may or may not yield the same conclusion. The relationship between X and Y is represented by means of a straight line. The value of F = t2.

Correlation analysis is used to determine the equation of the regression line the strength of the relationship between the dependent and the independent variables a specific value of the dependent variable for a given value of the independent variable None of these alternatives is correct. In a regression and correlation analysis if r2 = 1, then SSE must also be equal to one SSE must be equal to zero SSE can be any positive value SSE must be negative In a regression and correlation analysis if r2 = 1, then SSE = SST SSE = 1 SSR = SSE SSR = SST 25. In a regression analysis, the regression equation is given by y = 12 – 6x. If SSE = 510 and SST = 1000, then the coefficient of correlation is a. -0. 7 b. +0.

7 c. 0. 49 d. -0. 49 ANS: A 26. In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination is a. 0. 6667 b. 0. 6000 c. 0. 4000 d. 1. 5000 ANS: B 27. a. b. c. d. ANS: B 28. a. b. c. d. ANS: C 29. Regression analysis was applied between demand for a product (Y) and the price of the product (X), and the following estimated regression equation was obtained. = 120 – 10 X Based on the above estimated regression equation, if price is increased by 2 units, then demand is expected to a. increase by 120 units b. increase by 100 units c. increase by 20 units d. decease by 20 units ANS: D 30. a. b. c. d. ANS: B 31. a. b. c. d.

ANS: C If the coefficient of determination is a positive value, then the regression equation must have a positive slope must have a negative slope could have either a positive or a negative slope must have a positive y intercept The coefficient of correlation is the square of the coefficient of determination is the square root of the coefficient of determination is the same as r-square can never be negative In a regression analysis, the variable that is being predicted must have the same units as the variable doing the predicting is the independent variable is the dependent variable usually is denoted by x If the coefficient of determination is equal to 1, then the coefficient of correlation must also be equal to 1 can be either -1 or +1 can be any value between -1 to +1 must be -1 32. If the coefficient of correlation is 0. 8, the percentage of variation in the dependent variable explained by the variation in the independent variable is a. 0. 80% b. 80% c. 0. 64% d. 64% ANS: D 33. In regression and correlation analysis, if SSE and SST are known, then with this information the a. coefficient of determination can be computed b.

slope of the line can be computed c. Y intercept can be computed d. x intercept can be computed ANS: A 34. In regression analysis, if the independent variable is measured in pounds, the dependent variable a. must also be in pounds b. must be in some unit of weight c. cannot be in pounds d. can be any units ANS: D 35. If there is a very weak correlation between two variables, then the coefficient of determination must be a. much larger than 1, if the correlation is positive b. much smaller than 1, if the correlation is negative c. much larger than one d. None of these alternatives is correct. ANS: D 36. a. b. c. d. ANS: A 37. a. b. c. d. ANS: A 38.

If the coefficient of correlation is a negative value, then the coefficient of determination a. must also be negative b. must be zero c. can be either negative or positive d. must be positive If the coefficient of correlation is a positive value, then the slope of the regression line must also be positive can be either negative or positive can be zero cannot be zero SSE can never be larger than SST smaller than SST equal to 1 equal to zero a. b. c. d. ANS: D 39. a. b. c. d. ANS: B 40. a. b. c. d. ANS: A 41. a. b. c. d. ANS: B 42. a. b. c. d. ANS: A A least squares regression line must also be negative must be zero can be either negative or positive must be positive

It is possible for the coefficient of determination to be larger than 1 less than one less than -1 None of these alternatives is correct. If two variables, x and y, have a good linear relationship, then there may or may not be any causal relationship between x and y x causes y to happen y causes x to happen None of these alternatives is correct. If the coefficient of determination is 0. 81, the coefficient of correlation is 0. 6561 could be either + 0. 9 or – 0. 9 must be positive must be negative may be used to predict a value of y if the corresponding x value is given implies a cause-effect relationship between x and y can only be determined if a good linear relationship exists between x and y None of these alternatives is correct. 43.

If all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on this data is a. 0 b. 1 c. either 1 or -1, depending upon whether the relationship is positive or negative d. could be any value between -1 and 1 ANS: B 44. a. b. c. d. ANS: D If a data set has SSR = 400 and SSE = 100, then the coefficient of determination is 0. 10 0. 25 0. 40 0. 80 45. Compared to the confidence interval estimate for a particular value of y (in a linear regression model), the interval estimate for an average value of y will be a. narrower b. wider c. the same d. None of these alternatives is correct. ANS: A 46.

A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation = 50,000 – 8X The above equation implies that an a. b. c. d. ANS: D 47. In a regression analysis if SST = 500 and SSE = 300, then the coefficient of determination is a. 0. 20 b. 1. 67 c. 0. 60 d. 0. 40 ANS: D 48. Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained. = 500 + 4 X Based on the above estimated regression line if advertising is $10,000, then the point estimate for sales (in dollars) is a. $900 b. $900,000 c. $40,500 d. $505,000 ANS: B 49. a. b. c. d.

ANS: B The coefficient of correlation is the square of the coefficient of determination is the square root of the coefficient of determination is the same as r-square can never be negative increase of $1 in price is associated with a decrease of $8 in sales increase of $8 in price is associated with an increase of $8,000 in sales increase of $1 in price is associated with a decrease of $42,000 in sales increase of $1 in price is associated with a decrease of $8000 in sales 50. If the coefficient of correlation is 0. 4, the percentage of variation in the dependent variable explained by the variation in the independent variable a. is 40% b. is 16%. c. is 4% d. can be any positive value ANS: B variable a. b. c. d. 51.

In regression analysis if the dependent variable is measured in dollars, the independent must also be in dollars must be in some units of currency can be any units cannot be in dollars ANS: C 52. If there is a very weak correlation between two variables then the coefficient of correlation must be a. much larger than 1, if the correlation is positive b. much smaller than 1, if the correlation is negative c. any value larger than 1 d. None of these alternatives is correct. ANS: D 53. If the coefficient of correlation is a negative value, then the coefficient of determination a. must also be negative b. must be zero c. can be either negative or positive d. must be positive ANS: D 54.

A regression analysis between demand (Y in 1000 units) and price (X in dollars) resulted in the following equation = 9 – 3X The above equation implies that if the price is increased by $1, the demand is expected to a. increase by 6 units b. decrease by 3 units c. decrease by 6,000 units d. decrease by 3,000 units ANS: D 55. In a regression analysis if SST = 4500 and SSE = 1575, then the coefficient of determination is a. 0. 35 b. 0. 65 c. 2. 85 d. 0. 45 ANS: B 56. Regression analysis was applied between sales (in $10,000) and advertising (in $100) and the following regression function was obtained. = 50 + 8 X Based on the above estimated regression line if advertising is $1,000, then the point estimate for sales (in dollars) is a. $8,050 b. $130 c. $130,000 d. $1,300,000 ANS: D 57. a. b. c. d. ANS: D 58.

If the coefficient of determination is 0. 9, the percentage of variation in the dependent variable explained by the variation in the independent variable a. is 0. 90% b. is 90%. c. is 81% d. 0. 81% ANS: B 59. Regression analysis was applied between sales (Y in $1,000) and advertising (X in $100), and the following estimated regression equation was obtained. = 80 + 6. 2 X Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is a. $62,080 b. $142,000 c. $700 d. $700,000 ANS: D Exhibit 14-1 The following information regarding a dependent variable (Y) and an independent variable (X) is provided.

Y 4 3 4 6 8 X 2 1 4 3 5 If the coefficient of correlation is a positive value, then the intercept must also be positive the coefficient of determination can be either negative or positive, depending on the value of the slope the regression equation could have either a positive or a negative slope the slope of the line must be positive Y 4 3 4 6 8 SSE = 6 SST = 16 60. a. b. c. d. ANS: B 61. a. b. c. d. ANS: A 62. a. b. c. d. ANS: C 63. a. b. c. d. ANS: A 64. a. b. c. d. ANS: B Exhibit 14-2 You are given the following information about y and x. y Dependent Variable 5 4 3 2 1 Refer to Exhibit 14-1. The MSE is 1 2 3 4 Refer to Exhibit 14-1. The coefficient of correlation is 0. 7906 – 0. 7906 0. 625 0. 375 Refer to Exhibit 14-1. The coefficient of determination is 0. 7096 – 0. 7906 0. 625 0. 375 X 2 1 4 3 5 Refer to Exhibit 14-1.

The least squares estimate of the Y intercept is 1 2 3 4 Refer to Exhibit 14-1. The least squares estimate of the slope is 1 2 3 4 x Independent Variable 1 2 3 4 5 65. a. b. c. d. ANS: B 66. a. b. c. d. ANS: C 67. a. b. c. d. ANS: C 68. a. b. c. d. ANS: C 69. a. b. c. d. ANS: C Refer to Exhibit 14-2. The least squares estimate of b1 (slope) equals 1 -1 6 5 Refer to Exhibit 14-2. The least squares estimate of b0 (intercept)equals 1 -1 6 5 Refer to Exhibit 14-2. The point estimate of y when x = 10 is -10 10 -4 4 Refer to Exhibit 14-2. The sample correlation coefficient equals 0 +1 -1 -0. 5 Refer to Exhibit 14-2. The coefficient of determination equals 0 -1 +1 -0. 5

Exhibit 14-3 You are given the following information about y and x. y Dependent Variable 12 3 7 6 70. a. b. c. d. x Independent Variable 4 6 2 4 Refer to Exhibit 14-3. The least squares estimate of b1 equals 1 -1 -11 11 ANS: B 71. a. b. c. d. ANS: D 72. a. b. c. d. ANS: A 73. a. b. c. d. ANS: D Exhibit 14-4 Regression analysis was applied between sales data (Y in $1,000s) and advertising data (x in $100s) and the following information was obtained. = 12 + 1. 8 x n = 17 SSR = 225 SSE = 75 Sb1 = 0. 2683 74. Refer to Exhibit 14-4. Based on the above estimated regression equation, if advertising is $3,000, then the point estimate for sales (in dollars) is a. $66,000 b.

$5,412 c. $66 d. $17,400 ANS: A 75. a. b. c. d. ANS: B 76. a. b. c. d. Refer to Exhibit 14-4. To perform an F test, the p-value is less than . 01 between . 01 and . 025 between . 025 and . 05 between . 05 and 0. 1 Refer to Exhibit 14-4. The F statistic computed from the above data is 3 45 48 50 Refer to Exhibit 14-3. The coefficient of determination equals -0. 4364 0. 4364 -0. 1905 0. 1905 Refer to Exhibit 14-3. The sample correlation coefficient equals -0. 4364 0. 4364 -0. 1905 0. 1905 Refer to Exhibit 14-3. The least squares estimate of b0 equals 1 -1 -11 11 a. b. c. d. ANS: D 77. a. b. c. d. ANS: C less than . 01 between . 01 and . 025 between .

025 and . 05 between . 05 and 0. 1 Refer to Exhibit 14-4. The t statistic for testing the significance of the slope is 1. 80 1. 96 6. 708 0. 555 78. Refer to Exhibit 14-4. The critical t value for testing the significance of the slope at 95% confidence is a. 1. 753 b. 2. 131 c. 1. 746 d. 2. 120 ANS: B Exhibit 14-5 The following information regarding a dependent variable (Y) and an independent variable (X) is provided. Y 1 2 3 4 5 79. a. b. c. d. ANS: B 80. a. b. c. d. ANS: A 81. a. b. c. d. ANS: D 82. Refer to Exhibit 14-5. The coefficient of determination is Refer to Exhibit 14-5. The coefficient of correlation is 0 -1 0. 5 1 Refer to Exhibit 14-5.

The least squares estimate of the slope is 1 -1 0 3 X 1 2 3 4 5 Refer to Exhibit 14-5. The least squares estimate of the Y intercept is 1 0 -1 3 a. b. c. d. ANS: D 83. a. b. c. d. ANS: A Exhibit 14-6 For the following data the value of SSE = 0. 4130. y Dependent Variable 15 17 23 17 84. a. b. c. d. ANS: D 85. a. b. c. d. ANS: B 86. a. b. c. d. ANS: A 87. a. b. c. d. ANS: C Refer to Exhibit 14-5. The MSE is 0 -1 0. 5 1 0 -1 1 0. 5 x Independent Variable 4 6 2 4 Refer to Exhibit 14-6. The slope of the regression equation is 18 24 0. 707 -1. 5 Refer to Exhibit 14-6. The y intercept is -1. 5 24 0. 50 -0. 707 Refer to Exhibit 14-6. The total sum of squares (SST) equals 36 18 9 1296

Refer to Exhibit 14-6. The coefficient of determination (r2) equals 0. 7071 -0. 7071 0. 5 -0. 5 Exhibit 14-7 You are given the following information about y and x. y Dependent Variable 5 7 9 11 88. a. b. c. d. ANS: D 89. a. b. c. d. ANS: B 90. a. b. c. d. ANS: B 91. a. b. c. d. ANS: C Exhibit 14-8 The following information regarding a dependent variable Y and an independent variable X is provided ? X = 90 ? Y = 340 n=4 SSR = 104 92. a. b. c. d. Refer to Exhibit 14-8. The total sum of squares (SST) is -156 234 1870 1974 ? (Y – )(X – ) = -156 ? (X – )2 = 234 ? (Y – )2 = 1974 Refer to Exhibit 14-7. The coefficient of determination equals 0. 3162 -0.

3162 0. 10 -0. 10 Refer to Exhibit 14-7. The sample correlation coefficient equals 0. 3162 -0. 3162 0. 10 -0. 10 Refer to Exhibit 14-7. The least squares estimate of b0 (intercept) equals -10 10 0. 5 -0. 5 x Independent Variable 4 6 2 4 Refer to Exhibit 14-7. The least squares estimate of b1 (slope) equals -10 10 0. 5 -0. 5 a. b. c. d. ANS: D 93. a. b. c. d. ANS: C 94. a. b. c. d. ANS: D 95. a. b. c. d. ANS: A 96. a. b. c. d. ANS: C 97. a. b. c. d. ANS: A -156 234 1870 1974 Refer to Exhibit 14-8. The sum of squares due to error (SSE) is -156 234 1870 1974 Refer to Exhibit 14-8. The mean square error (MSE) is 1870 13 1974 935 Refer to Exhibit 14-8.

The slope of the regression equation is -0. 667 0. 667 100 -100 Refer to Exhibit 14-8. The Y intercept is -0. 667 0. 667 100 -100 Refer to Exhibit 14-8. The coefficient of correlation is -0. 2295 0. 2295 0. 0527 -0. 0572 Exhibit 14-9 A regression and correlation analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x). ?X = 90 ? Y = 170 n = 10 SSE = 505. 98 98. a. b. c. d. Refer to Exhibit 14-9. The least squares estimate of b1 equals 0. 923 1. 991 -1. 991 -0. 923 ? (Y – )(X – ) = 466 ? (X – )2 = 234 ? (Y – )2 = 1434 a. b. c. d. ANS: B 99. a. b. c. d. ANS: D 100. a. b. c. d. ANS: D 101. a. b. c. d. ANS: A 102. a. b.

c. d. ANS: A 0. 923 1. 991 -1. 991 -0. 923 Refer to Exhibit 14-9. The least squares estimate of b0 equals 0. 923 1. 991 -1. 991 -0. 923 Refer to Exhibit 14-9. The sum of squares due to regression (SSR) is 1434 505. 98 50. 598 928. 02 Refer to Exhibit 14-9. The sample correlation coefficient equals 0. 8045 -0. 8045 0 1 Refer to Exhibit 14-9. The coefficient of determination equals 0. 6472 -0. 6472 0 1 Exhibit 14-10 The following information regarding a dependent variable Y and an independent variable X is provided. ?X = 16 ? Y = 28 n=4 SSE = 34 103. a. b. c. d. ANS: A 104. a. b. c. d. Refer to Exhibit 14-10. The Y intercept is -1 1. 0 11 0. 0 ?

(X – )(Y – ) = -8 ? (X – )2 = 8 SST = 42 Refer to Exhibit 14-10. The slope of the regression function is -1 1. 0 11 0. 0 a. b. c. d. ANS: C 105. a. b. c. d. ANS: A 106. a. b. c. d. ANS: D 107. a. b. c. d. ANS: A 108. a. b. c. d. ANS: C 109. a. b. c. d. ANS: B PROBLEM Refer to Exhibit 14-10. The MSE is -1 1. 0 11 0. 0 Refer to Exhibit 14-10. The coefficient of determination is 0. 1905 -0. 1905 0. 4364 -0. 4364 Refer to Exhibit 14-10. The coefficient of correlation is 0. 1905 -0. 1905 0. 4364 -0. 4364 17 8 34 42 Refer to Exhibit 14-10. The point estimate of Y when X = 3 is 11 14 8 0 Refer to Exhibit 14-10. The point estimate of Y when X = -3 is 11 14 8 0 1.

Assume you have noted the following prices for books and the number of pages that each book contains. Book A B C D E F G Pages (x) 500 700 750 590 540 650 480 Price (y) $7. 00 7. 50 9. 00 6. 50 7. 50 7. 00 4. 50 A B C D E F G a. b. c. 500 700 750 590 540 650 480 $7. 00 7. 50 9. 00 6. 50 7. 50 7. 00 4. 50 Develop a least-squares estimated regression line. Compute the coefficient of determination and explain its meaning. Compute the correlation coefficient between the price and the number of pages. Test to see if x and y are related. Use ? = 0. 10. = 1. 0416 + 0. 0099x r 2 = . 5629; the regression equation has ANS: a. b. c. accounted for 56. 29% of the total sum of squares rxy = 0. 75 t = 2. 54 > 2.

015 (df = 5); p-value is between . 05 and 0. 1; (Excel’s results: p-value of 0. 052); reject Ho, and conclude x and y are related 2. Assume you have noted the following prices for books and the number of pages that each book contains. Book A B C D E F G a. b. c. d. ANS: a. Pages (x) 500 700 750 590 540 650 480 Price (y) $7. 00 7. 50 9. 00 6. 50 7. 50 7. 00 4. 50 Perform an F test and determine if the price and the number of pages of the books are related. Let ? = 0. 01. Perform a t test and determine if the price and the number of pages of the books are related. Let ? = 0. 01. Develop a 90% confidence interval for estimating the average price of books that contain 800 pages.

Develop a 90% confidence interval to estimate the price of a specific book that has 800 pages. F = 6. 439 < 16. 26; p-value is between 0. 1 and 0. 2 (Excel’s result: p-value = . 052); do not reject Ho; conclude x and y are not related t = 2. 5376 < 4. 032; p-value is between 0. 1 and 0. 2. (Excel’s result: p-value = . 052); do not reject Ho; conclude x and y are not related $7. 29 to $10. 63 (rounded) $5. 62 to $12. 31 (rounded) b. c. d. 3. The following data represent the number of flash drives sold per day at a local computer shop and their prices. Price (x) $34 36 32 35 30 38 40 a. b. c. Units Sold (y) 3 4 6 5 9 2 1 Develop a least-squares regression line and explain what the slope of the line indicates.

Compute the coefficient of determination and comment on the strength of relationship between x and y. Compute the sample correlation coefficient between the price and the number of flash drives sold. Use ? = 0. 01 to test the relationship between x and y. = 29. 7857 – 0. 7286x The slope indicates that as the price goes up by $1, the number of units sold goes down by 0. 7286 units. r 2 = . 8556; the regression equation has ANS: a. b. c. accounted for 85. 56% of the total sum of squares rxy = -0. 92 t = -5. 44 < -4. 032 (df = 5); p-value < . 01; (Excel’s result: p-value = . 0028); reject Ho, and conclude x and y are related 4. The following data represent the number of flash drives sold per day at a local computer shop and their prices.

Price (x) $34 36 32 35 30 38 40 a. b. Units Sold (y) 3 4 6 5 9 2 1 Perform an F test and determine if the price and the number of flash drives sold are related. Let ? = 0. 01. Perform a t test and determine if the price and the number of flash drives sold are related. Let ? = 0. 01. ANS: a. b. F = 29. 624 > 16. 26; p-value < . 01; (Excel’s result: p-value = . 0028); reject Ho, x and y are related t = -5. 4428 < -4. 032; p-value < . 01; (Excel’s result: p-value = . 0028); reject Ho, x and y are related 5. Shown below is a portion of an Excel output for regression analysis relating Y (dependent variable) and X (independent variable).

ANOVA Regression Residual Total Intercept x a. b. c. d. e. df 1 8 9 Coefficients 39. 222 -0. 5556 SS 110 74 184 Standard Error 5. 943 0. 1611 What has been the sample size for the above? Perform a t test and determine whether or not X and Y are related. Let ? = 0. 05. Perform an F test and determine whether or not X and Y are related. Let ? = 0. 05. Compute the coefficient of determination. Interpret the meaning of the value of the coefficient of determination that you found in d. Be very specific. ANS: a through d Summary Output Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA df Regression Residual Total Intercept x 1 8 9 Coefficients 39.

222 -0. 556 SS 110 74 184 MS 110 9. 25 F 11. 892 Significance F 0. 009 0. 7732 0. 5978 0. 5476 3. 0414 10 Standard Error 5. 942 0. 161 t Stat 6. 600 -3. 448 P-value 0. 000 0. 009 e. 59. 783% of the variability in Y is explained by the variability in X. 6. Shown below is a portion of a computer output for regression analysis relating Y (dependent variable) and X (independent variable). ANOVA Regression Residual Intercept x a. b. c. d. e. df 1 8 Coefficients 11. 065 -0. 511 SS 24. 011 67. 989 Standard Error 2. 043 0. 304 What has been the sample size for the above? Perform a t test and determine whether or not X and Y are related. Let ? = 0. 05.

Perform an F test and determine whether or not X and Y are related. Let ? = 0. 05. Compute the coefficient of determination. Interpret the meaning of the value of the coefficient of determination that you found in d. Be very specific. ANS: a through d Summary Output Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA df Regression Residual Total Intercept x e. 1 8 9 Coefficients 11. 065 -0. 511 SS 24. 011 67. 989 92 MS 24. 011 8. 499 F 2. 825 Significance F 0. 131 0. 511 0. 261 0. 169 2. 915 10 Standard Error 2. 043 0. 304 t Stat 5. 415 -1. 681 P-value 0. 001 0. 131 26. 1% of the variability in Y is explained by the variability in X. 7.

Part of an Excel output relating X (independent variable) and Y (dependent variable) is shown below. Fill in all the blanks marked with “? “. Summary Output Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA df Regression Residual Total Intercept x ANS: Summary Output Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA df Regression Residual Total Intercept x 1 13 14 Coefficients 8. 6 0. 25 SS 2. 750 148. 850 151. 600 MS 2. 75 11. 45 F 0. 2402 Significance F 0. 6322 0. 1347 0. 0181 -0. 0574 3. 384 15 ? ? 14 Coefficients 8. 6 0. 25 SS 2. 7500 ? ? MS ? 11. 45 t Stat ? ? F ?

Significance F 0. 632 0. 1347 ? ? 3. 3838 ? Standard Error 2. 2197 0. 5101 P-value 0. 0019 0. 632 Standard Error 2. 2197 0. 5101 t Stat 3. 8744 0. 4901 p-value 0. 0019 0. 6322 8. Shown below is a portion of a computer output for a regression analysis relating Y (dependent variable) and X (independent variable). ANOVA Regression Residual Total Intercept x df 1 13 Coefficients 15. 532 -1. 106 SS 115. 064 82. 936 Standard Error 1. 457 0. 261 a. b. c. ANS: a and b Summary Output Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA df Regression Residual Total Intercept x c. 1 13 14 Coefficients 15. 532 -1.

106 SS 115. 064 82. 936 198 Perform a t test using the p-value approach and determine whether or not Y and X are related. Let ? = 0. 05. Using the p-value approach, perform an F test and determine whether or not X and Y are related. Compute the coefficient of determination and fully interpret its meaning. Be very specific. 0. 7623 0. 5811 0. 5489 2. 5258 15 MS 115. 064 6. 380 F 18. 036 Significance F 0. 001 Standard Error 1. 457 0. 261 t Stat 10. 662 -4. 247 P-value 0. 000 0. 001 58. 11% of the variability in Y is explained by the variability in X. 9. Part of an Excel output relating X (independent variable) and Y (dependent variable) is shown below.

Fill in all the blanks marked with “? “. Summary Output Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA df Regression Residual Total ? ? ? SS ? ? 1000. 0000 MS ? ? F ? Significance F 0. 0129 ? 0. 5149 ? 7. 3413 11 Intercept x ANS: Summary Output Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Coefficients ? ? Standard Error 29. 4818 0. 7000 t Stat 3. 7946 -3. 0911 P-value 0. 0043 0. 0129 0. 7176 0. 5149 0. 4611 7. 3413 11 df SS 514. 9455 485. 0545 1000. 0000 MS 514. 9455 53. 8949 F 9. 5546 Significance F 0. 0129 Regression Residual Total Intercept x 1 9 10 Coefficients 111.

8727 -2. 1636 Standard Error 29. 4818 0. 7000 t Stat 3. 7946 -3. 0911 P-value 0. 0043 0. 0129 10. Shown below is a portion of a computer output for a regression analysis relating Y (demand) and X (unit price). ANOVA Regression Residual Total Intercept X a. b. c. d. df 1 46 47 Coefficients 80. 390 -2. 137 SS 5048. 818 3132. 661 8181. 479 Standard Error 3. 102 0. 248 Perform a t test and determine whether or not demand and unit price are related. Let ? = 0. 05. Perform an F test and determine whether or not demand and unit price are related. Let ? = 0. 05. Compute the coefficient of determination and fully interpret its meaning. Be very specific.

Compute the coefficient of correlation and explain the relationship between demand and unit price. ANS: a and b Summary Output Regression Statistics Multiple R R Square Adjusted R Square 0. 786 0. 617 0. 609 Summary Output Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA df Regression Residual Total Intercept X c. d. 1 46 47 Coefficients 80. 390 -2. 137 SS 5048. 818 3132. 661 8181. 479 MS 5048. 818 68. 101 F 74. 137 Significance F 0. 000 0. 786 0. 617 0. 609 8. 252 48 Standard Error 3. 102 0. 248 t Stat 25. 916 -8. 610 P-value 0. 000 0. 000 R2 = 0. 617; 61. 7% of the variability in demand is explained by the variability in price. R = -0.

786; since the slope is negative, the coefficient of correlation is also negative, indicating that as unit price increases demand decreases. 11. Shown below is a portion of a computer output for a regression analysis relating supply (Y in thousands of units) and unit price (X in thousands of dollars). ANOVA Regression Residual Intercept X a. b. c. d. e. f. ANS: a through c Regression Statistics Multiple R R Square Adjusted R Square Standard Error 0. 219 0. 048 0. 024 13. 431 df 1 39 Coefficients 54. 076 0. 029 SS 354. 689 7035. 262 Standard Error 2. 358 0. 021 What has been the sample size for this problem? Perform a t test and determine whether or not supply and unit price are related. Let ? = 0. 05.

Perform and F test and determine whether or not supply and unit price are related. Let ? = 0. 05. Compute the coefficient of determination and fully interpret its meaning. Be very specific. Compute the coefficient of correlation and explain the relationship between supply and unit price. Predict the supply (in units) when the unit price is $50,000. Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA df Regression Residual Total Intercept X d. e. f. 1 39 40 Coefficients 54. 076 0. 029 SS 354. 689 7035. 262 7389. 951 MS 354. 689 180. 391 F 1. 966 0. 219 0. 048 0. 024 13. 431 41 Significance F 0. 169 Standard Error 2. 358 0. 021 t Stat 22. 938 1. 402 P-value 0. 000 0. 169 R2 = 0.

048; 4. 8% of the variability in supply is explained by the variability in price. R = 0. 219; since the slope is positive, as unit price increases so does supply. supply = 54. 076 + . 029(50) = 55. 526 (55,526 units) 12. Given below are four observations collected in a regression study on two variables x (independent variable) and y (dependent variable). x 2 6 9 9 a. b. c. d. ANS: Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA df Regression Residual Total 1 2 3 SS 13. 364 0. 636 14 MS 13. 364 0. 318 F 42. 000 Significance F 0. 023 y 4 7 8 9 Develop the least squares estimated regression equation.

At 95% confidence, perform a t test and determine whether or not the slope is significantly different from zero. Perform an F test to determine whether or not the model is significant. Let ? = 0. 05. Compute the coefficient of determination. 0. 977 0. 955 0. 932 0. 564 4 ANOVA df Regression Residual Total 1 2 3 Coefficients Intercept X a. b. c. d. 2. 864 0. 636 SS 13. 364 0. 636 14 Standard Error 0. 698 0. 098 MS 13. 364 0. 318 t Stat 4. 104 6. 481 F 42. 000 Significance F 0. 023 P-value 0. 055 0. 023 = 2. 864 + 0. 636x p-value < . 05; reject Ho p-value < . 05; reject Ho 0. 955 13. Given below are five observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). x 2 3 4 5 6 a. b. c. d. e.

ANS: Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA df Regression Residual Total 1 3 4 Coefficients Intercept X a. b. c. d. 6. 000 -0. 800 SS 6. 4 0. 4 6. 8 Standard Error 0. 490 0. 115 MS 6. 400 0. 133 t Stat 12. 247 -6. 928 F 48. 000 Significance F 0. 006 y 4 4 3 2 1 Develop the least squares estimated regression equation. At 95% confidence, perform a t test and determine whether or not the slope is significantly different from zero. Perform an F test to determine whether or not the model is significant. Let ? = 0. 05. Compute the coefficient of determination. Compute the coefficient of correlation. 0. 970 0. 941 0. 922 0. 365 5 P-value 0. 001 0. 006 = 6 – 0. 8 x p-value < . 05; reject Ho p-value < . 05; reject Ho 0. 941 a. b.

c. d. e. = 6 – 0. 8 x p-value < . 05; reject Ho p-value < . 05; reject Ho 0. 941 -0. 970 14. Below you are given a partial computer output based on a sample of 8 observations, relating an independent variable (x) and a dependent variable (y). Intercept X Analysis of Variance SOURCE Regression Error (Residual) Total a. b. c. d. ANS: a. b. c. d. SS 41. 674 71. 875 Develop the estimated regression line. At ? = 0. 05, test for the significance of the slope. At ? = 0. 05, perform an F test. Determine the coefficient of determination. = 13. 251 + 0. 803x t = 2. 086; p-value is between . 05 and . 1 (critical t = 2. 447); do not reject Ho F = 4.

348; p-value is between . 05 and . 1 (critical F = 5. 99); do not reject Ho 0. 42 Coefficient 13. 251 0. 803 Standard Error 10. 77 0. 385 15. Below you are given a partial computer output based on a sample of 8 observations, relating an independent variable (x) and a dependent variable (y). Intercept x Analysis of Variance SOURCE Regression Error (Residual) a. b. c. d. ANS: SS 400 138 Develop the estimated regression line. At ? = 0. 05, test for the significance of the slope. At ? = 0. 05, perform an F test. Determine the coefficient of determination. Coefficient -9. 462 0. 769 Standard Error 7. 032 0. 184 a. b. c. d. = -9. 462 + 0. 769x t = 4.

17; p-value (actual p-value using Excel = 0. 0059) < . 05; reject Ho F = 17. 39; p-value (actual p-value using Excel = 0. 0059) < . 05; reject Ho 0. 743 16. The following data represent a company’s yearly sales volume and its advertising expenditure over a period of 8 years. (Y) Sales in Millions of Dollars 15 16 18 17 16 19 19 24 a. b. c. d. e. f. g. h. i. ANS: a. The scatter diagram shows a positive relation between sales and advertising. b. c. d. e. f. = -10. 42 + 0. 7895X $21,160,000 As advertising is increased by $10,000, sales are expected to increase by $789,500. 0. 8459; 84. 59% of variation in sales is explained by variation in advertising F = 32.

93; p-value (actual p-value using Excel = (X) Advertising in ($10,000) 32 33 35 34 36 37 39 42 Develop a scatter diagram of sales versus advertising and explain what it shows regarding the relationship between sales and advertising. Use the method of least squares to compute an estimated regression line between sales and advertising. If the company’s advertising expenditure is $400,000, what are the predicted sales? Give the answer in dollars. What does the slope of the estimated regression line indicate? Compute the coefficient of determination and fully interpret its meaning. Use the F test to determine whether or not the regression model is significant at ? = 0. 05. Use the t test to determine whether the slope of the regression model is significant at ? = 0. 05.

Develop a 95% confidence interval for predicting the average sales for the years when $400,000 was spent on advertising. Compute the correlation coefficient. between sales and advertising. b. c. d. e. f. = -10. 42 + 0. 7895X $21,160,000 As advertising is increased by $10,000, sales are expected to increase by $789,500. 0. 8459; 84. 59% of variation in sales is explained by variation in advertising F = 32. 93; p-value (actual p-value using Excel = 0. 0012) < . 05; reject Ho; it is significant (critical F = 5. 99) t = 5. 74; p-value (actual p-value using Excel = 0. 0012) < . 05; reject Ho; significant (critical t = 2. 447) $19,460,000 to $22,860,000 0. 9197 g. h. i. 17.

Given below are five observations collected in a regression study on two variables x (independent variable) and y (dependent variable). x 10 20 30 40 50 a. b. c. d. e. ANS: a. b. c. d. e. y 7 5 4 2 1 Develop the least squares estimated regression equation At 95% confidence, perform a t test and determine whether or not the slope is significantly different from zero. Perform an F test to determine whether or not the model is significant. Let ? = 0. 05. Compute the coefficient of determination. Compute the coefficient of correlation. = 8. 3 – 0. 15x t = -15; p-value (actual p-value using Excel = 0. 0001) < . 05; reject Ho (critical t = 3. 18) F = 225; p-value (actual p-value using Excel = 0. 0001) < . 05; reject Ho (critical F = 10. 13) 0. 9868 0. 9934 18.

Below you are given a partial computer output based on a sample of 14 observations, relating an independent variable (x) and a dependent variable (y). Predictor Constant X Analysis of Variance SOURCE Regression Error (Residual) Total SS 958. 584 1021. 429 Coefficient 6. 428 0. 470 Standard Error 1. 202 0. 035 a. b. c. d. e. ANS: a. b. c. d. e. Develop the estimated regression line. At ? = 0. 05, test for the significance of the slope. At ? = 0. 05, perform an F test. Determine the coefficient of determination. Determine the coefficient of correlation. = 6. 428 + 0. 47x t = 13. 529; p-value (actual p-value using Excel = 0. 0000) < . 05; reject Ho (critical t = 2. 179) F = 183. 04; p-value (actual p-value using Excel = 0. 0000) < . 05; reject Ho (critical F = 4. 75) 0. 938 0. 968 19.

Below you are given a partial computer output based on a sample of 21 observations, relating an independent variable (x) and a dependent variable (y). Predictor Constant X Analysis of Variance SOURCE Regression Error a. b. c. d. e. ANS: a. b. c. d. e. SS 1,759. 481 259. 186 Develop the estimated regression line. At ? = 0. 05, test for the significance of the slope. At ? = 0. 05, perform an F test. Determine the coefficient of determination. Determine the coefficient of correlation. = 30. 139 – 0. 252X t = -11. 357; p-value (almost zero) < ? = . 05; reject Ho (critical t = 2. 093) F = 128. 982; p-value (almost zero) < ? = . 05; reject Ho (critical F = 4. 38) 0. 872 -0. 934 Coefficient 30. 139 -0.

252 Standard Error 1. 181 0. 022 20. An automobile dealer wants to see if there is a relationship between monthly sales and the interest rate. A random sample of 4 months was taken. The results of the sample are presented below. The estimated least squares regression equation is = 75. 061 – 6. 254X Y Monthly Sales 22 20 X Interest Rate (In Percent) 9. 2 7. 6 Y Monthly Sales 22 20 10 45 a. b. X Interest Rate (In Percent) 9. 2 7. 6 10. 4 5. 3 Obtain a measure of how well the estimated regression line fits the data. You want to test to see if there is a significant relationship between the interest rate and monthly sales at the 1% level of significance.

State the null and alternative hypotheses. At 99% confidence, test the hypotheses. Construct a 99% confidence interval for the average monthly sales for all months with a 10% interest rate. Construct a 99% confidence interval for the monthly sales of one month with a 10% interest rate. R2 = 0. 8687 H0: ? 1 = 0 Ha: ? 1 0 test statistic t = -3. 64; p-value is between . 05 and . 10 (critical t = 9. 925); do not reject H0 -33. 151 to 58. 199; therefore, 0 to 58. 199 -67. 068 to 92. 116; therefore, 0 to 92. 116 c. d. e. ANS: a. b. c. d. e. 21. Jason believes that the sales of coffee at his coffee shop depend upon the weather. He has taken a sample of 6 days.

Below you are given the results of the sample. Cups of Coffee Sold 350 200 210 100 60 40 a. b. c. d. Temperature 50 60 70 80 90 100 Which variable is the dependent variable? Compute the least squares estimated line. Compute the correlation coefficient between temperature and the sales of coffee. Is there a significant relationship between the sales of coffee and temperature? Use a . 05 level of significance. Be sure to state the null and alternative hypotheses. Predict sales of a 90 degree day. Cups of coffee sold = 605. 714 – 5. 943X 0. 95197 H0: ? 1 = 0 Ha: ? 1 0 e. ANS: a. b. c. d. a. b. c. d. Cups of coffee sold = 605. 714 – 5. 943X 0. 95197 H0: ? 1 = 0 Ha: ? 1 0 t = -6.

218; p-value (actual p-value using Excel = 0. 0034) < ? = . 05; reject Ho (critical t = 2. 776) e. 70. 8 or 71 cups 22. Researchers have collected data on the hours of television watched in a day and the age of a person. You are given the data below. Hours of Television 1 3 4 3 6 a. b. c. Age 45 30 22 25 5 Determine which variable is the dependent variable. Compute the least squares estimated line. Is there a significant relationship between the two variables? Use a . 05 level of significance. Be sure to state the null and alternative hypotheses. Compute the coefficient of determination. How would you interpret this value? Hours of Television = 6. 564 – 0. 1246X H0: ? 1 = 0 Ha: ?

1 0 t = -12. 018; p-value (actual p-value using Excel = 0. 0002) < ? = . 05; reject H0 (critical t = 3. 18) d. 0. 98 (rounded); 98 % of variation in hours of watching television is explained by variation in age. d. ANS: a. b. c. 23. Given below are seven observations collected in a regression study on two variables, X (independent variable) and Y (dependent variable). X 2 3 6 7 8 7 9 a. b. c. Y 12 9 8 7 6 5 2 Develop the least squares estimated regression equation. At 95% confidence, perform a t test and determine whether or not the slope is significantly different from zero. Perform an F test to determine whether or not a. b. c. d. ANS: a. b. c. d.

Develop the least squares estimated regression equation. At 95% confidence, perform a t test and determine whether or not the slope is significantly different from zero. Perform an F test to determine whether or not the model is significant. Let ? = 0. 05. Compute the coefficient of determination. = 13. 75 -1. 125X t = -5. 196; p-value (actual p-value using Excel = 0. 0001) < ? = . 05; reject Ho (critical t = 2. 571) F = 27; p-value (actual p-value using Excel = 0. 0001) < ? = . 05; reject Ho (critical F = 6. 61) 0. 844 24. The owner of a retail store randomly selected the following weekly data on profits and advertising cost. Week 1 2 3 4 5 a.

Advertising Cost ($) 0 50 250 150 125 Profit ($) 200 270 420 300 325 b. c. d. e. ANS: a. b. c. d. Write down the appropriate linear relationship between advertising cost and profits. Which is the dependent variable? Which is the independent variable? Calculate the least squares estimated regression line. Predict the profits for a week when $200 is spent on advertising. At 95% confidence, test to determine if the relationship between advertising costs and profits is statistically significant. Calculate the coefficient of determination. E(Y) = ? 0 + ? 1X, where Y is profit and X is advertising cost = 210. 0676 + 0. 80811X $371. 69 t = 6. 496; p-value (actual p-value using Excel = 0. 0013) < ? = .

05; reject Ho; relationship is significant (critical t = 3. 182) 0. 9336 e. 25. The owner of a bakery wants to analyze the relationship between the expenditure of a customer and the customer’s income. A sample of 5 customers is taken and the following information was obtained. Y Expenditure . 45 10. 75 5. 40 X Income (In Thousands) 20 19 22 Y Expenditure . 45 10. 75 5. 40 7. 80 5. 60 X Income (In Thousands) 20 19 22 25 14 The least squares estimated line is = 4. 348 + 0. 0826 X. a. Obtain a measure of how well the estimated regression line fits the data. b. You want to test to see if there is a significant relationship between expenditure and income at the 5% level of significance.

Be sure to state the null and alternative hypotheses. c. Construct a 95% confidence interval estimate for the average expenditure for all customers with an income of $20,000. d. Construct a 95% confidence interval estimate for the expenditure of one customer whose income is $20,000. ANS: a. b. R2 = 0. 0079 H0: ? 1 = 0 Ha: ? 1 0 t = 0. 154; p-value (actual p-value using Excel = 0. 8871) > ? = . 05; do not reject H0; (critical t = 3. 182) 0. 185 to 12. 185 -9. 151 to 21. 151 26. Below you are given information on annual income and years of college education. Income (In Thousands) 28 40 36 28 48 a. b. c. d. e. Years of College 0 3 2 1 4 Develop the least squares regression equation.

Estimate the yearly income of an individual with 6 years of college education. Compute the coefficient of determination. Use a t test to determine whether the slope is significantly different from zero. Let ? = 0. 05. At 95% confidence, perform an F test and determine whether or not the model is significant. = 25. 6 + 5. 2X $56,800 0. 939 t = 6. 789; p-value (actual p-value using Excel = 0. 0008) < ? = . 05; reject Ho; significant (critical t = 3. 182 c. d. ANS: a. b. c. d. a. b. c. d. e. = 25. 6 + 5. 2X $56,800 0. 939 t = 6. 789; p-value (actual p-value using Excel = 0. 0008) < ? = . 05; reject Ho; significant (critical t = 3. 182 F = 46. 091; p-value (actual p-value using Excel = 0. 0008) < ? = .

05; reject Ho; significant (critical F = 10. 13) 27. Below you are given information on a woman’s age and her annual expenditure on purchase of books. Age 18 22 21 28 a. b. c. d. Annual Expenditure ($) 210 180 220 280 Develop the least squares regression equation. Compute the coefficient of determination. Use a t test to determine whether the slope is significantly different from zero. Let ? = 0. 05. At 95% confidence, perform an F test and determine whether or not the model is significant. = 54. 834 + 7. 536X R2 = 0. 568 t = 1. 621; p-value (actual p-value using Excel = 0. 2464) > ? = . 05; do not reject Ho; not significant (critical t = 4. 303) F = 2.

628; p-value (actual p-value using Excel = 0. 2464) > ? = . 05; do not reject Ho; not significant (critical F = 18. 51) ANS: a. b. c. d. 28. The following sample data contains the number of years of college and the current annual salary for a random sample of heavy equipment salespeople. Years of College 2 2 3 4 3 1 4 3 4 4 a. b. c. Annual Income (In Thousands) 20 23 25 26 28 29 27 30 33 35 Which variable is the dependent variable? Which is the independent variable? Determine the least squares estimated regression line. Predict the annual income of a salesperson with one year of college. a. b. c. d. e. f. Which variable is the dependent variable? Which is the independent variable?

Determine the least squares estimated regression line. Predict the annual income of a salesperson with one year of college. Test if the relationship between years of college and income is statistically significant at the . 05 level of significance. Calculate the coefficient of determination. Calculate the sample correlation coefficient between income and years of college. Interpret the value you obtain. Y (dependent variable) is annual income and X (independent variable) is years of college = 21. 6 + 2X $23,600 The relationship is not statistically significant since t = 1. 51; p-value (actual p-value using Excel = 0. 1696) > ? = . 05 (critical t = 2. 306) 0. 222 0.

471; there is a positive correlation between years of college and annual income The following data shows the yearly income (in $1,000) and age of a sample of seven Income (in $1,000) 20 24 24 25 26 27 34 Age 18 20 23 34 24 27 27 Develop the least squares regression equation. Estimate the yearly income of a 30-year-old individual. Compute the coefficient of determination. Use a t test to determine whether the slope is significantly different from zero. Let ? = 0. 05. At 95% confidence, perform an F test and determine whether or not the model is significant. = 16. 204 + 0. 3848X $27,748 0. 2266 t = 1. 21; p-value (actual p-value using Excel = 0. 2803) > ? = . 05; not significant (critical t = 2.

571) F = 1. 46; p-value (actual p-value using Excel = 0. 2803) > ? = . 05; not significant (critical F = 6. 61) ANS: a. b. c. d. e. f. 29. individuals. a. b. c. d. e. ANS: a. b. c. d. e. a. b. c. d. e. = 16. 204 + 0. 3848X $27,748 0. 2266 t = 1. 21; p-value (actual p-value using Excel = 0. 2803) > ? = . 05; not significant (critical t = 2. 571) F = 1. 46; p-value (actual p-value using Excel = 0. 2803) > ? = . 05; not significant (critical F = 6. 61) 30. The following data show the results of an aptitude test (Y) and the grade point average of 10 students. Aptitude Test Score (Y) 26 31 28 30 34 38 41 44 40 43 a. b. c. d. ANS: a. b. c. d.

GPA (X) 1. 8 2. 3 2. 6 2. 4 2. 8 3. 0 3. 4 3. 2 3. 6 3. 8 Develop a least squares estimated regression line. Compute the coefficient of determination and comment on the strength of the regression relationship. Is the slope significant? Use a t test and let ? = 0. 05. At 95% confidence, test to determine if the model is significant (i. e. , perform an F test). = 8. 171 + 9. 4564X 0. 83; there is a fairly strong relationship t = 6. 25; p-value (actual p-value using Excel = 0. 0002) < ? =. 05; it is significant (critical t = 2. 306) F = 39. 07; p-value (actual p-value using Excel = 0. 0002) < ? =. 05; it is significant (critical F = 5. 32)

31. Shown below is a portion of the computer output for a regression analysis relating sales (Y in millions of dollars) and advertising expenditure (X in thousands of dollars). Predictor Constant X Analysis of Variance SOURCE Regression Error a. b. c. DF 1 18 SS 1,400 3,600 Coefficient 4. 00 0. 12 Standard Error 0. 800 0. 045 What has been the sample size for the above? Perform a t test and determine whether or not advertising and sales are related. Let ? = 0. 05. Compute the coefficient of determination. a. b. c. d. e. What has been the sample size for the above? Perform a t test and determine whether or not advertising and sales are related.

Let ? = 0. 05. Compute the coefficient of determination. Interpret the meaning of the value of the coefficient of determination that you found in Part c. Be very specific. Use the estimated regression equation and predict sales for an advertising expenditure of $4,000. Give your answer in dollars. 20 t = 2. 66; p-value is between 0. 01 and 0. 02; they are related (critical t = 2. 101) R2 = 0. 28 28% of variation in sales is explained by variation in advertising expenditure. $4,480,000 ANS: a. b. c. d. e. 32. A company has recorded data on the daily demand for its product (Y in thousands of units) and the unit price (X in hundreds of dollars).

A sample of 15 days demand and associated prices resulted in the following data. ?X = 75 ? Y = 135 ? (Y- )2 = 100 SSE = 62. 9681 a. b. c. d. ANS: a. b. c. Using the above information, develop the leastsquares estimated regression line and write the equation. Compute the coefficient of determination. Perform an F test and determine whether or not there is a significant relationship between demand and unit price. Let ? = 0. 05. Would the demand ever reach zero? If yes, at what price would the demand be zero? = 12. 138 – 0. 6277X R2 = 0. 3703 F = 7. 65; p-value is between . 01 and . 025; reject Ho and conclude that demand and unit price are related (critical F = 4. 67) Yes, at $1,934 ? (Y- )(X- ) = -59 ? (X- )2 = 94 d.

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