a) RCB manufacturers black & white television sets for overseas markets. Annual exports in thousands of units are tabulated below for the past 6 years. Given the long term decline in exports, forecast the expected number of units to be exported next year. |Year |Exports |Year |Exports | |1 |33 |4 |26 | |2 |32 |5 |27 | |3 |29 |6 |24 |

b) A small hospital is planning for future needs in its maternity wing. The data below show the number of births in each of the past eight years. |Year |Births |Year |Births | |1 |565 |5 |615 | |2 |590 |6 |611 | |3 |583 |7 |610 | |4 |597 |8 |623 |

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Forecasting: Regression Analysis and Exponential Smoothing

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Use simple linear regression to forecast the annual number of births for each of the next three years.

Determine the coefficient of determination for the data and interpret its meaning.

Moving Averages

IPC’s Plant estimates weekly demand for its many materials held in inventory. One such part, the CTR 5922, is being studied. The most recent 12 weeks of demand for the CTR 5922 are : |Week |Demand in units |Week |Demand in units | |1 |169 |7 |213

| |2 |227 |8 |175 | |3 |176 |9 |178 | |4 |171 |10 |158 | |5 |163 |11 |188 | |6 |157 |12 |169 |

Use the moving average method of short range forecasting with an averaging period of three weeks to develop a forecast of the demand for the CTR 5922 component in Week 13.

What is the mean absolute deviation for averaging period of 3 weeks and 5 weeks?

Exponential Smoothing

A toy company buys large quantities of plastic pellets for use in the manufacture of its products. The Production Manager wants to develop a forecasting system for plastic pellet prices. The price per kilo of plastic pellets has varied as shown: |Month |Plastic Pellet price/kilo in Rs|Month |Plastic Pellet price/kilo | | | | |in Rs | |1 |39 |9 |35 | |2 |41 |10 |38 | |3 |45 |11 |39 | |4 |44 |12 |43 | |5 |40 |13 |37 | |6 |41 |14 |38 | |7 |38 |15 |36 | |8 |36 |16 |39 |

Use exponential smoothing to forecast monthly plastic prices per kilo. Compute what the forecasts would have been for all the months of historical data for exponential constant = 0.1, 0.2 and 0.5. if the assumed forecast for all the exponential constants in the first month is 39.

Which exponential smoothing constant value gives the mean absolute deviation?

Use the best exponential smoothing constant value to compute the forecast for pellet price for Month 17.

Multiple Regression

A company manufacturers and sells two products X1 and X2. The production and sales of the products and the corresponding profits for the last five months are: |Month |Units of X1 |Units of X2 |Profit, Rs | |1 |12000 |16000 |192000 | |2 |14000 |13000 |87000 | |3 |10000 |11000 |-181000 | |4 |14000 | 8000 |-216000 | |5 |16000 |10000 |-8000 |

Compute the Total Fixed Costs and Contribution per units of X1 and X2

Profit Y = A + b1X1 + b2X2 , where Fixed Cost = -A

Seasonalized Forecasts

A tractor dealer needs to estimate sales for the next year. Sales in the

past years have tended to be seasonal, as shown below. |Year |Quarter 1 |Quarter 2 |Quarter 3 |Quarter 4 | |1 |49 |72 |114 |41 | |2 |55 |88 |135 |44 | |3 |60 |93 |149 |49 |

Develop a forecast for the next 4 quarters by computing the season indices

Compute the seasonal Indices. Deseasonalise by dividing the demand data by respective seasonal index. Estimate the trend by using the deseasonalised data. Multiply the forecasted value by respective seasonal index