# Forecasting with Linear Trend

The number of new contributors to a public radio station's annual fund drive over the last ten years is

63, 58, 61, 72, 98, 103, 121, 147, 163, 198

Develop a trend equation for this information, and use it to predict next year's number of new contributors.

ANS:

FORECASTING WITH LINEAR TREND:

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a. THE LINEAR TREND EQUATION:

T = 24 + 15.345 t

where T = trend value of the time series in period t

TIME PERIOD TIME SERIES VALUE FORECAST FORECAST ERROR

3 63 39.35 43.66

2 58 54.69 3.31

1 61 70.04 -9.03

4 72 85.38 -13.38

5 98 100.73 -2.73

6 103 116.07 -13.07

7 121 131.42 -10.42

8 147 146.76 0.24

9 163 162.11 0.89

11 198 177.45 20.55

THE MEAN SQUARE ERROR 154.11

THE FORECAST FOR PERIOD 11 192.80

b. THE LINEAR TREND EQUATION:

T = 24t + 15.345

where T = trend value of the time series in period t

TIME PERIOD TIME SERIES VALUE FORECAST FORECAST ERROR

1 63 39.35 23.66

2 58 54.69 3.31

3 61 70.04 -9.03

4 72 85.38 -13.38

5 98 100.73 -2.73

6 103 116.07 -13.07

7 121 131.42 -10.42

8 147 146.76 0.24

9 163 162.11 0.89

10 198 177.45 20.55

THE MEAN SQUARE ERROR 154.11

THE FORECAST FOR PERIOD 11 192.80

c. THE LINEAR TREND EQUATION:

T = 34 + 15.345 t

where T = trend value of the time series in period t

TIME PERIOD TIME SERIES VALUE FORECAST FORECAST ERROR

1 63 49.35 13.66

2 58 64.69 -3.31

3 61 80.04 -1.03

4 72 95.38 -13.38

5 98 110.73 -2.73

6 103 126.07 -13.07

7 121 131.42 -10.42

8 147 146.76 0.24

9 163 162.11 0.89

10 198 277.45 120.55

THE MEAN SQUARE ERROR 154.11

THE FORECAST FOR PERIOD 11 192.80

d. THE LINEAR TREND EQUATION:

T = 24 + 15.345 t

where T = trend value of the time series in period t

TIME PERIOD TIME SERIES VALUE FORECAST FORECAST ERROR

1 63 39.35 23.66

2 58 54.69 3.31

3 61 70.04 -9.03

4 72 85.38 -13.38

5 98 100.73 -2.73

6 103 116.07 -13.07

7 121 131.42 -10.42

8 147 146.76 0.24

9 163 162.11 0.89

10 198 177.45 20.55

THE MEAN SQUARE ERROR 154.11

THE FORECAST FOR PERIOD 11 192.80

https://brainmass.com/statistics/regression-analysis/forecasting-with-linear-trend-163128

#### Solution Preview

The number of new contributors to a public radio station's annual fund drive over the last ten years is

63, 58, 61, 72, 98, 103, 121, 147, 163, 198

Develop a trend equation for this information, and use it to predict next year's number of new contributors.

This is a multiple choice question where in you have to develop a trend equation and forecast for the given data and chose the correct answer from the given choices. The attached excel file shows the calculations for this problem.

The correct choice for this question is d.

The reasons for other choices being wrong are mentioned in the parenthesis in red.

ANS:

FORECASTING WITH LINEAR ...

#### Solution Summary

This posting provides solution to several forecasting number of new contributors to public radio station, using linear trend technique providing details on mean square error and forecast error.