Question

A consumer products company wants to measure the effectiveness of different types of advertising media in the promotion of its products. Specially, two types of advertising media are to be considered: radio and television advertising and newspaper advertising (including the cost of discount coupons). A sample of 22 cities with approximately equal population is selected for study during a test period of one month. Each city is allocated a specific expenditure level both for radio and television advertising and for newspaper advertising. The sales of the product (in thousands of dollars) and also the levels of media expenditure (in thousands of dollars) during the test month are recorded, with the data set ADVERTISE.XLS. Using EXCEL or PHStat2, answer the following:

Sales Radio Newspaper
973 0 40
1119 0 40
875 25 25
625 25 25
910 30 30
971 30 30
931 35 35
1177 35 35
882 40 25
982 40 25
1628 45 45
1577 45 45
1044 50 0
914 50 0
1329 55 25
1330 55 25
1405 60 30
1436 60 30
1521 65 35
1741 65 35
1866 70 40
1717 70 40
a) State the multiple regression equation.
b) Interpret the meaning of the slopes b1 and b2 in this problem.
c) Interpret the meaning of the regression coefficient b0 in this problem.
d) Predict the average sales for a city in which radio and television advertising is $20,000 and newspaper advertising is $20,000.
e) Set up a 95% confidence interval estimate for the average sales for cities in which radio and television advertising is $20,000 and newspaper advertising is $20,000.
f) Set up a 95% confidence interval estimate for the sales for an individual city in which radio and television advertising is $20,000 and newspaper advertising is $20,000.
g) Determine whether there is a significant relationship between sales and the two independent variables (radio advertising and newspaper advertising) at the 0.05 level of significance.
h) Interpret the meaning of the p-value.
i) Determine the coefficient of multiple determination, r2.
j) Determine the adjusted r2.
k) Perform a residual analysis on your results and determine the adequacy of the fit of the model.
l) Set up a 95% confidence interval estimate of the population slope between sales and radio and television advertising.
m) At the 0.05 level of significance, determine whether each explanatory variable makes a significant contribution to the regression model. On the basis of these results, indicate the independent variables that should be included in this model.
n) Compute the coefficients of partial determination, r2Y1.2.and r2Y2.1.and interpret their meaning.

Answer 1

Kindly check explanation

Explanation:

Given the data:

Sales(y) __Radio (x1) __ Newspaper (x2)

973 0 40

1119 0 40

875 25 25

625 25 25

910 30 30

971 30 30

931 35 35

1177 35 35

882 40 25

982 40 25

1628 45 45

1577 45 45

1044 50 0

914 50 0

1329 55 25

1330 55 25

1405 60 30

1436 60 30

1521 65 35

1741 65 35

1866 70 40

1717 70 40

The multiple regression equation obtained for the data:

With sales, y = predicted variable

Radio, x1 = predictor variable 1

Newspaper, x2 = predictor variable 2

ŷ = 13.10812X1 + 17.07885X2 + 149.19284

Slope b1, = for every unit change in Number of radio advert, there is a 13.10812 change in sales

Slope B2, = for every unit change in Number of newspaper advert, there is a 17.07885 change in sales

b0 = intercept = 149.19284, represents the estimated amount of sales if there was no sales reported from both radio and newspaper advert.

Sales where, X1 = $20,000; X2 = $20,000

ŷ = 13.10812(20000) + 17.07885(20000) + 149.19284

y = 603888.59284

Sales (y) = $603889