# Statistical problem - coefficient of multiple correlation

Suppose a large consumer product company wants to measure the effectiveness of different types of advertising media in the promotion of its products. Specifically, two types of advertising media are to be considered: (1) radio and TV advertising, and (2) newspaper advertising including the cost of discount coupons. A sample of 22 cities with approximately equal populations is selected for study during a test period of 1 month. Each city is allocated a specific expenditure level for both types of advertising. The sales of the product (in thousands of dollars) and also the level of media expenditure during the test month are recorded as follows:

City Radio & TV Advertising ($000) Newspaper Advertising ($000) Sales ($000)

1 0 40 973

2 0 40 1,119

3 25 25 875

4 25 25 625

5 30 30 910

6 30 30 971

7 35 35 931

8 35 35 1,177

9 40 25 882

10 40 25 982

11 45 45 1,628

12 45 45 1,577

13 50 0 1,044

14 50 0 914

15 55 25 1,329

16 55 25 1,330

17 60 30 1,405

18 60 30 1,436

19 65 35 1,521

20 65 35 1,741

21 70 40 1,866

22 70 40 1,717

Using Megastat or MS EXCEL (Data Analysis, Phstat or Megastat):

A) State the coefficient of multiple correlation (R) between sales and advertising costs. Interpret the result.

B) State the coefficient of multiple determination (R2). Interpret the result.

C) State the multiple regression equation.

D) Interpret the meaning of the slopes in the equation.

E) If you were Director or Marketing, which method of advertising would you use most ¿ TV & radio advertising or newspaper advertising? Why?

F) Predict the average sales for a city in which radio and TV advertising is $20,000 and newspaper advertising is $20,000.

G) Is the data free from autocorrelation?

H) Is the data free from multicollinearity?

https://brainmass.com/statistics/regression-analysis/statistical-problem-coefficient-of-multiple-correlation-115335

#### Solution Preview

A) State the coefficient of multiple correlation (R) between sales and advertising costs. Interpret the result.

R = 0.899. This is a very good regression.

B) State the coefficient of multiple determination (R2). Interpret the result.

R2 = 0.809. 80.9% of the variation in Y is explained by the variations in X's.

C) State the multiple ...

#### Solution Summary

The solution calculates coefficient of multiple correlation, multiple regression equations, and predicts the average sales for a city in which radio and TV advertising is $20,000 and newspaper advertising is $20,000.