How do I solve this please show step by step

The business problem facing a consumer products company is to measure the effectiveness of different types of advertising media in the promotion of its products. Specifically, the company is interested in the effectiveness of radio advertising in thousands of dollars (X) and newspaper advertising in thousands of dollars (X2) on the sales in thousands of dollars (Y). Data were collected from a sample of 22 cities. The following is the ANOVA table for the regression model:
Significance
F
Regression
Residual
Total
df
2
19
21
SS
MS
F
2028032.69 1014016.345 40.15823
Also, SSR(x) =1216940 and SSR(x) = 632259.4483
From the data above answer the following 3 questions:
11. At the 0.05 level of significance, we want to test whether there is evidence that the newspaper advertising makes a significant contribution to the regression model. The test statistic is:
a. 32.12
b. 55.28
c. 45.33
d. 31.07
е. 39.09

Question

17-05-2024
Mathematics

Answered

How do I solve this please show step by step

The business problem facing a consumer products company is to measure the effectiveness of different types of advertising media in the promotion of its products. Specifically, the company is interested in the effectiveness of radio advertising in thousands of dollars (X) and newspaper advertising in thousands of dollars (X2) on the sales in thousands of dollars (Y). Data were collected from a sample of 22 cities. The following is the ANOVA table for the regression model:
Significance
F
Regression
Residual
Total
df
2
19
21
SS
MS
F
2028032.69 1014016.345 40.15823
Also, SSR(x) =1216940 and SSR(x) = 632259.4483
From the data above answer the following 3 questions:
11. At the 0.05 level of significance, we want to test whether there is evidence that the newspaper advertising makes a significant contribution to the regression model. The test statistic is:
a. 32.12
b. 55.28
c. 45.33
d. 31.07
е. 39.09

Answer :

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hababababker2012 hababababker2012 · Answer 1 · 2024-05-17T19:07:06-04:00

1. Calculate the residual sum of squares (SSE) by subtracting the sums of squares for radio and newspaper advertising from the total sum of squares: (2028032.69 - 1216940 - 632259.4483 = 179833.2417).

2. Calculate the mean square error (MSE) by dividing SSE by the degrees of freedom for the residuals: (179833.2417 / 19 ≈ 9464.907).

3. Calculate the F-statistic for newspaper advertising by dividing its sum of squares by the MSE: (632259.4483 / 9464.907 ≈ 66.82). The closest answer is 45.33, so the correct answer is c. 45.33.