Question

Data on advertising expenditures and revenue (in thousands of dollars) for the Four Seasons Restaurant follow. Advertising Expenditures Revenue 1 19 2 32 4 44 6 40 10 52 14 53 54 + 20 a. Let x equal advertising expenditures and y equal revenue. Complete the estimated regression equation below (to 2 decimals). y= X b. Test whether revenue and advertising expenditures are related at a .05 level of significance. Compute the following (to 2 decimals). 2 SSE x SST SSR MSR MSE Compute the F test statistic (to 2 decimals).

Answer 1

). Let the regression line be: Y = A + BX, where

• X : Advertising expenditure
• Y : Revenue
• A : intercept
• B : Slope

Now for the computation of regression equation we use excel, to do this follow the given steps:

1. Firstly you have to install Data analysis toolpak in excel, for this do the following steps:
2. Go to 'file' and click on 'Options'.
3. Then a dialog box will appear, click on add-ins
4. Then in the 'manage' option, select 'excel add-ins' and then click on go.
5. Then a dialog box will appear, tick on 'Analysis ToolPak' and press ok.

Now for regression line:

1. Firstly enter the data in the excel spreadsheet
2. Then go to 'Data' option in the tool bar.
3. Click on 'Data Analysis', then a dialog box will appear.
4. In the dialog box, select regression and click on OK.
5. Then in 'Input Y range:' drag Revenue data and in 'Input X range:' drag Advertising Expenditure data and finally click on OK.

OUTPUT:

C D E F H J SUMMARY OUTPUT B 1 Advertising Expenditure (x) Revenue (Y) 2 1 19 3 2 32 4 4 44 5 6 Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.83 0.69 0.63 7.88 40 52 53 54 6 10 7 14 8 20 7 9 10 ANOVA 11 df MS F Significance F 0.02 12 1 691.72 11.15 SS 691.72 310.28 1002.00 Regression Residual Total 13 5 62.06 6 14 15 16 t Stat Lower 95% P-value 0.00 Coefficients Standard Error 29.40 4.81 1.55 0.46 Upper 95% 41.76 17 6.12 Intercept Advertising Expenditure (X) 17.04 18 3.34 0.02 0.36 2.74

BY USING OUTPUT SUMMARY:

(a) Line of regression is: y* = 29.40 + 1.55x

(b)

• SSE = 310.28
• SST = 1002.00
• SSR = 691.72
• MSR = 691.72
• MSE = 62.06
• F-test statistic = 11.15