# Prediction with linear and quadratic regression line

Problem 3

Do the problem and answer all the questions.

Hint for question: Compare the errors on the basis of the Mean Absolute Deviation (MAD)?

Copy and paste the following data set in Excel to save the typing effort and possible mistakes in data entry.

Year Shipments

1985 14,705

1986 15,064

1987 16,676

1988 18,061

1989 21,327

1990 23,738

1991 26,966

1992 32,411

1993 38,851

1994 47,894

1995 60,171

1996 71,065

1997 82,400

1998 97,321

Solution

a.) Construct a scatter diagram between year (year 1985 is equivalent to x =1) and shipments. Add a linear trend line and a fitted equation to the chart.

b.) Use the linear equation obtained from the chart to forecast the shipments from 1985 - 1998.

1985 Y = (6115.6*1) -5391.90 = 723.70

1986 Y = (6115.6*2) -5391.90 = 6839.30

1987 Y = (6115.6*3) -5391.90 = 12954.90

1988 Y = (6115.6*4) -5391.90 = 19070.50

1989 Y = (6115.6*5) -5391.90 = 25186.10

1990 Y = (6115.6*6) -5391.90 = 31301.70

1991 Y = (6115.6*6) -5391.90 = 37417.30

1992 Y = (6115.6*6) -5391.90 = 43532.90

1993 Y = (6115.6*6) -5391.90 = 49648.50

1994 Y = (6115.6*6) -5391.90 = 55764.10

1995 Y = (6115.6*6) -5391.90 = 61879.70

1996 Y = (6115.6*6) -5391.90 = 67995.30

1997 Y = (6115.6*6) -5391.90 = 7410.90

1998 Y = (6115.6*6) -5391.90 = 80226.50

c.) Construct a scatter diagram between year (year 1985 is equivalent to x =1) and shipments. Add a quadratic trend line and a fitted equation to the chart.

d.) Use the quadratic equation obtained from the chart to forecast the shipments from 1985 - 1998.

1985 =(0.61701*(1^2))-(3139.5*13)+19288

1986 =(0.61701*(2^2))-(3139.5*2)+19288

1987 =(0.61701*(3^2))-(3139.5*3)+19288

e.) Compute the errors for each forecast and compare the errors produced by using the two different fitted equations.

Comparison of the methods based on MAD.

Year Shipments Forecast Linear Forecast Quadratic Abs Deviation Linear Abs Deviation Quadratic

1 14,705 723.70 13011.47 13981 1694

2 15,064 6839.30 9875.05 8225 5189

3 16,676 12954.90 6739.87 3721 9936

4 18,061 19070.50 3605.93 -1010 14455

5 21,327 25186.10 473.21 -3859 20854

6 23,738 31301.70 -2658.27 -7564 26396

7 26,966 37417.30 -5788.51 -10451 32755

8 32,411 43532.90 -8917.52 -11122 41329

9 38,851 49648.50 -12045.30 -10798 50896

10 47,894 55764.10 -15171.84 -7870 63066

11 60,171 61879.70 -18297.15 -1709 78468

12 71,065 67995.30 -21421.43 3070 92486

13 82,400 74110.90 -24544.07 8239 106944

14 97,321 80226.50 19288.00 17095 78033

MAD -0.10

44464.33

https://brainmass.com/statistics/regression-analysis/prediction-linear-quadratic-regression-line-458223

#### Solution Summary

In this case, predictions with linear and quadratic regression were plotted and compared.