Determine the least squares trend equation. Estimate the amount of scrap for the year 2005.

Year Code Scrap
1999 1 2.0
2000 2 4.0
2001 3 3.0
2002 4 5.0
2003 5 6.0

Use Excel, we can get the following

SUMMARY OUTPUT

Regression Statistics
Multiple R 0.9
R Square 0.81
Adjusted R Square 0.746667
Standard Error 0.795822
Observations 5

ANOVA
df SS MS F Significance F
Regression 1 8.1 8.1 12.78947 0.037386
Residual 3 1.9 0.633333
Total 4 10

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 1.3 0.834666 1.55751 0.217224 -1.35628 3.956278 -1.35628 3.956278
X Variable 1 0.9 0.251661 3.576237 0.037386 0.099102 1.700898 0.099102 1.700898

From it, we know that the regression equation is

Scrap=1.3+0.9*Code

For 2005, Code=7, by the above equation we can predict the scraps when Code=7 (corresponding to year 2005), we get

Scrap=1.3+0.9*7=7.6

Determine a typical seasonal index for each of the four quarters.

Year I II III IV
2001 4 10 7 3
2002 5 12 9 4
2003 6 16 12 4
Quarter

Total 15 38 28 11
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Mean 5 12.667 9.333 3.667
Grand Mean 7.667
Index 0.652 1.652 1.217 0.478

How to get Grand mean?

(15+38+28+11)/12=92/12=7.667

How to get the above index?

0.652=5/7.667; 1.652=12.667/7.667; 1.217=9.333/7.667 ;

3.667/7.667=0.478

please see the attached file.