Information supplied by a mail-order business for 12 cities is shown in Table P-
ID: 3064703 • Letter: I
Question
Information supplied by a mail-order business for 12 cities is shown in Table P-7.
a. Determine the fitted regression line
b. Calculate the standard error of the estimate
c. Determine the ANOVA Table
d. What percentage of the variation in mail orders is explained by the number of catalogs distributed?
e. Test to determine whether the regression slope coefficient is significantly different from zero (Use the .01 significance level)
f. Test for the significance of the regression using the F statistic from the ANOVA table. (Use the .01 significance level.) Is the result consistent with the result in part e? Should it be?
g. Forecast the number of mail orders received when 10,000 catalogs are distributed with a 90% prediction interval
Table P-7:
City Numer of Orders Received (1,000s) (Y) Number of Catalogs Distributed (1,000s) (X) A 24 6 B 16 2 C 23 5 D 15 1 E 32 10 F 25 7 G 18 15 H 18 3 I 35 11 J 34 13 K 15 2 L 32 12Explanation / Answer
a.
y=15.846+1.113*Number of Catalogs Distributed (1,000s) (X)
b.
Standard Error = 5.7566
c.
Shown above
d.
r^2 is 0.4893 which means 48.93% of variation in y is explained for by the independent variable x
e)
p-value of slope coefficient is 0.011 and hence cannot reject the null hypothesis at a=0.01. It is not significant
f)
Significant F is 0.011 and hence cannot reject the null hypothesis at a=0.01. It is not significant
SUMMARY OUTPUT Regression Statistics Multiple R 0.699518576 R Square 0.489326238 Adjusted R Square 0.438258862 Standard Error 5.756602431 Observations 12 ANOVA df SS MS F Significance F Regression 1 317.5319512 317.5319512 9.581973351 0.011337689 Residual 10 331.3847154 33.13847154 Total 11 648.9166667 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 15.84617886 3.091757953 5.125297356 0.000447226 8.957312846 22.73504488 Number of Catalogs Distributed (1,000s) (X) 1.113170732 0.359612103 3.095476272 0.011337689 0.311905034 1.91443643