Question

Data on advertising expenditures and revenue (in thousands of dollars) for the Four Seasons Restaurant follow.

Advertising Expenditures		Revenue
1		19
2		33
4		45
6		41
10		53
14		54
20		55

1. Let x equal advertising expenditures and y equal revenue. Complete the estimated regression equation below (to 2 decimals).
   =  +  x
   
2. Compute the following (to 1 decimal).
   

   SSE
   SST
   SSR
   MSR
   MSE

   
   
3. Test whether revenue and advertising expenditures are related at a .05 level of significance.
   
   Compute the F test statistic (to 2 decimals).
   
   
   What is the p-value? Use Table 1 of Appendix B.
   
   What is your conclusion?
   
4. Which of the following scatter displays accurately represent the residuals plotted against the independent variable?
   
   Scatter diagram #1
   
   
   Scatter diagram #2
   
   
   Scatter diagram #3
   
   
5. What does the residual plot above suggest about the assumption of linearity between x and y?
   

Answer 1

a)

y^ =30.05+1.57x

b)

SSE =Syy-(Sxy)2/Sxx=

334.9

SST=Syy=

1,048.9

SSR =(Sxy)2/Sxx =

714.0

MSR =714

MSE =67.0

c)

F test statistic =MSR/MSE =10.66

p value =0.0223 (0.01 < p value <0.025)

d)