Module 8 Question 2: Data on advertising expenditures and revenue (in thousands

Question

Module 8 Question 2: Data on advertising expenditures and revenue (in thousands of dollars) for the Four Seasons Restaurant follow. Please include work.

a. Let x equal advertising expenditures and y equal revenue. Complete the estimated regression equation below (to 2 decimals).

= ____ + ____ x

b. Compute the following (to 1 decimal).

c. 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?

is it less than .01 or between .01 and .025 or between .025 and .05 or between .05 and .10 or greater than .10?

What is your conclusion?

Advertising Expenditures Revenue 1 20 2 32 4 44 6 40 10 52 14 53 20 54

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Revenue
Independent Variable: Advertising Expenditures
Revenue = 29.743323 + 1.5227498 Advertising Expenditures
Sample size: 7
R (correlation coefficient) = 0.83665525
R-sq = 0.69999201
Estimate of error standard deviation: 7.5771339

Parameter estimates:

Analysis of variance table for regression model:

So,

a) = 29.74 + 1.52 x

b) SSE = 287.1

SST = 956.9

SSR = 669.8

MSR = 669.8

MSE = 57.4

c) F = 11.67

p - value = 0.0189 i..e between .01 and .025

Option B is correct.

Conclusion: p - value is less than 0.05, reject the null hypothesis.

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 29.743323 4.6239366 0 5 6.4324678 0.0013 Slope 1.5227498 0.44582396 0 5 3.4155853 0.0189

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