(Round intermediate calculations to at least 4 decimal places.) A government res

Question

(Round intermediate calculations to at least 4 decimal places.) A government researcher is analyzing the relationship between retail sales and the gross national product (GNP). He also wonders whether there are significant differences in retail sales related to the quarters of the year. He collects 10 years of quarterly data. The data are shown in the accompanying table. Retail sales GNP (in Quarter (in mi Year billions OnS 2000 696048 9740.5 753211 9983.5 746875 10048.0 0 792622 10184.9 0 2001 704757 10206.2 1 779011 10350.9 0 756128 10332.2 0 827829 10463.1 0 2002 717302 10549.7 1 790486 10634.7 0 792657 10749.1 0 833877 10832.2 0 2003 741233 10940.2 1 819940 11073.6 0 831222 11321.2 0 875437 11508.3 0 795916 11707.8 1 2004 871970 11864.2 0 873695 12047.3 0 938213 12216.6 0 2005 836952 12486.3 1 932713 12613.0 0 940880 12848.7 0 987085 12994.1 2006 897180 13264.0 1 987406 13423.3 0 978211 13514.8 0 1018775 13683.2 2007 923997 13859.8 1 1016136 14087.6 1002312 14302.9 0 1062803 14489.9 0 2008 953358 14520.7 1 1032919 14647.3 1006551 14689.2 0 966329 14317.2 0 2009 839625 14172.2 1 919646 14164.2 0 926265 14281.9 0 985649 14442.8 0

Explanation / Answer

a.

Retail Sales=263995.074+53.13GNP-98646.08d1-26350.618d2-38084.929d3

b.

Q2 and GNP=13000

263995.074+53.13(13000)-98646.08(0)-26350.618(1)-38084.929(0)=928375

Q4 and GNP=13000

263995.074+53.13(13000)-98646.08(0)-26350.618(0)-38084.929(0)=954726

c.

Quarter 2 (p-value=0.06)

d-1.

Retail Sales=225910.146+53.13GNP-60561.15d1+11734.31d2+38084.929d4.

d-2.

Yes, since the relevant p-value is greater than 0.05

q1-q2-q3:-

q1-q2-q4:-

SUMMARY OUTPUT Regression Statistics Multiple R 0.960018557 R Square 0.92163563 Adjusted R Square 0.912679702 Standard Error 30386.09169 Observations 40 ANOVA df SS MS F Significance F Regression 4 3.80065E+11 95016351326 102.9078871 7.59974E-19 Residual 35 32316009897 923314568.5 Total 39 4.12381E+11 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 263995.0744 37720.51278 6.998713829 0.00 187418.3624 340571.7865 GNP (in $ billions) 53.13310996 2.915002494 18.22746638 0.00 47.21534029 59.05087964 d1 -98646.08031 13631.46032 -7.23664802 0.00 -126319.416 -70972.74465 d2 -26350.61782 13605.4591 -1.936768 0.06 -53971.16821 1269.932576 d3 -38084.92894 13592.18073 -2.801973406 0.01 -65678.5228 -10491.33507

q1-q2-q4:-

SUMMARY OUTPUT Regression Statistics Multiple R 0.960018557 R Square 0.92163563 Adjusted R Square 0.912679702 Standard Error 30386.09169 Observations 40 ANOVA df SS MS F Significance F Regression 4 3.80065E+11 95016351326 102.9078871 7.59974E-19 Residual 35 32316009897 923314568.5 Total 39 4.12381E+11 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 225910.1455 37439.5481 6.033997657 0.00 149903.8221 301916.4689 GNP (in $ billions) 53.13310996 2.915002494 18.22746638 0.00 47.21534029 59.05087964 d1 -60561.15137 13611.64291 -4.449216877 0.00 -88194.25557 -32928.04718 d2 11734.31112 13594.29935 0.863178809 0.39 -15863.58376 39332.206 d4 38084.92894 13592.18073 2.801973406 0.01 10491.33507 65678.5228

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.