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 ago
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