Question
In: Statistics and Probability
Data on advertising expenditures and revenue (in thousands of dollars) for the Four Seasons Restaurant follow....
Data on advertising expenditures and revenue (in thousands of dollars) for the Four Seasons Restaurant follow. Advertising Expenditures Revenue 1 20 2 33 4 44 6 40 10 52 14 53 20 54
a. Let X equal advertising expenditures and Y equal revenue. Complete the estimated regression equation below (to 2 decimals). y =( )+( )x b. Compute the following (to 1 decimal). SSE ( ) SST ( ) SSR ( )MSR ( ) MSE ( )
c. Test whether revenue and advertising expenditures are related at a .05 level of significance. Compute the F test statistic ( to 2 decimals).
Solutions
Expert Solution
| x | y | (x-xbar)^2 | (y-ybar)^2 | (x-xbar)*(y-ybar) | |
| 1 | 20 | 51.020408 | 496.65306 | 159.1836735 | |
| 2 | 33 | 37.734694 | 86.22449 | 57.04081633 | |
| 4 | 44 | 17.163265 | 2.9387755 | -7.102040816 | |
| 6 | 40 | 4.5918367 | 5.2244898 | 4.897959184 | |
| 10 | 52 | 3.4489796 | 94.367347 | 18.04081633 | |
| 14 | 53 | 34.306122 | 114.79592 | 62.75510204 | |
| 20 | 54 | 140.59184 | 137.22449 | 138.8979592 | |
| sum | 57 | 296 | 288.85714 | 937.42857 | 433.7142857 |
| mean | 8.142857143 | 42.28571429 | sxx | syy | sxy |
| slope=b1=sxy/sxx | 1.50148368 | ||||
| intercept=b0=ybar-(slope*xbar) | 30.05934718 | ||||
| SST | SYY | 937.42857 | |||
| SSR | sxy^2/sxx | 651.21492 | |||
| SSE | syy-sxy^2/sxx | 286.21365 |
The Fitted model is
y=30.1+1.50(Expenditure)
Ansb:
SSE=286.22
SST=937.43
SSR=651.21
#MSR=SSR/1=651.21
#MSE=SSE/(n-2)=57.24273
| ANOVA | |||||
| df | SS | MS | F | ||
| Regression | 1 | 651.2149216 | 651.2149 | 11.37638 | |
| Residual | (n-2)=5 | 286.2136499 | 57.24273 | ||
| Total | 6 | 937.4285714 |
Ansc:
F-statistics=MSR/MSE=11.38
F-critical=6.608----using FINV(0.05,1,5)
P-value=0.0074
#P-value<0.05 hence we reject the null hypothesis at 5% l.o.s
#we reject the H0. Hence claim is significant
orchestra answered 2 years agoRelated Solutions
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