Use the \"Retail Sales\" data set in Canvas for the following problem. A governm

Question

Use the "Retail Sales" data set in Canvas for the following problem. A government researcher is analyzing the relationship between retail sales (in $ millions) and gross national product (GNP) (in $ billions). He also wonders whether there are significant differences in retail sales related to the quarters of the year.

a. Estimate y = 0+1x+2d1+3d2+4d3+ where y is retail sales, x is GNP, and d corresponds with the quarter of the year (e.g. d1 equals 1 if quarter 1 and 0 otherwise). Based on the results, provide the sample regression model.

b. Predict retail sales in quarters 2 and 4 if GNP equals $13,000 billion.

c. Which of the quarterly sales are significantly different from those of the 4th quarter at the 5%

Retail sales (in millions) GNP (in billions) d1 d2 d3 1 696048 9740.5 1 0 0 1 2 753211 9983.5 0 1 0 2 3 746875 10048.0 0 0 1 3 4 792622 10184.9 0 0 0 4 1 704757 10206.2 1 0 0 1 2 779011 10350.9 0 1 0 2 3 756128 10332.2 0 0 1 3 4 827829 10463.1 0 0 0 4 1 717302 10549.7 1 0 0 1 2 790486 10634.7 0 1 0 2 3 792657 10749.1 0 0 1 3 4 833877 10832.2 0 0 0 4 1 741233 10940.2 1 0 0 1 2 819940 11073.6 0 1 0 2 3 831222 11321.2 0 0 1 3 4 875437 11508.3 0 0 0 4 1 795916 11707.8 1 0 0 1 2 871970 11864.2 0 1 0 2 3 873695 12047.3 0 0 1 3 4 938213 12216.6 0 0 0 4 1 836952 12486.3 1 0 0 1 2 932713 12613.0 0 1 0 2 3 940880 12848.7 0 0 1 3 4 987085 12994.1 0 0 0 4 1 897180 13264.0 1 0 0 1 2 987406 13423.3 0 1 0 2 3 978211 13514.8 0 0 1 3 4 1018775 13683.2 0 0 0 4 1 923997 13859.8 1 0 0 1 2 1016136 14087.6 0 1 0 2 3 1002312 14302.9 0 0 1 3 4 1062803 14489.9 0 0 0 4 1 953358 14520.7 1 0 0 1 2 1032919 14647.3 0 1 0 2 3 1006551 14689.2 0 0 1 3 4 966329 14317.2 0 0 0 4 1 839625 14172.2 1 0 0 1 2 919646 14164.2 0 1 0 2 3 926265 14281.9 0 0 1 3 4 985649 14442.8 0 0 0 4

Explanation / Answer

b)

The model looks like the one below:-

Retail Sales=165349+53.13311(GNP)+0d1+72295.46d2+60561.15d3+98646.08d4

Retail Sales=165349+53.13311(13000)+0+72295.46(1)+0+98646.18(1)

Retail Sales=1027021.07

c)

Quarter 1 and 2

SUMMARY OUTPUT Regression Statistics Multiple R 0.960019 R Square 0.921636 Adjusted R Square 0.884108 Standard Error 30386.09 Observations 40 ANOVA df SS MS F Significance F Regression 5 3.8E+11 7.6E+10 102.9079 1.58E-19 Residual 35 3.23E+10 9.23E+08 Total 40 4.12E+11 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 165349 36682.82 4.507532 7.03E-05 90878.91 239819.1 90878.91 239819.1 GNP (in billions) 53.13311 2.915002 18.22747 1.91E-19 47.21534 59.05088 47.21534 59.05088 d1 0 0 65535 #NUM! 0 0 0 0 d2 72295.46 13595.16 5.317737 #NUM! 44695.83 99895.1 44695.83 99895.1 d3 60561.15 13611.64 4.449217 8.36E-05 32928.05 88194.26 32928.05 88194.26 d4 98646.08 13631.46 7.236648 1.9E-08 70972.74 126319.4 70972.74 126319.4

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