As a sales manager of your company you decided to examine if the sales (in quant

Question

As a sales manager of your company you decided to examine if the sales (in quantity), Q, is determined by your own product price ( in dollars), P, advertisement expenditure ( in million dollars), A, and consumers average income (in 1,000 dollars), Y, you estimated a multiple regression equation of:
Q= a + bP + cA + dY where a, b, c, and d are coefficients.
The following is a partial printout of the multiple regression estimation obtained with missing values due to ink shortage:
Summary Output
Regression Statistics
Multiple R R Square Adjusted R Square Standard Error 150 Observations. 10 ANOVA

Coefficients:
Intercept: 20 Price: -10 Advertise: 15 Income: 30
Standard error:
Intercept: Price: 2.3173 Advertise: 9.1597 Income: 11.7587
T-stat:
Intercept: 2.0172 Price: Advertise: Income:
P-value:
Intercept: 0.090245 Price: 0.005008 Advertise: 0.15262 Income: 0.043415

Suppose that you wish to statistically test if the income coefficient is equal to 50 at a 5% significance level. Your conclusion is ____.
A. Reject the null hypothesis B. Accept the null hypothesis C. Inconclusive D. The income coefficient explains the dependent variable E. The income coefficient is important with a 5% uncertainty

As a sales manager of your company you decided to examine if the sales (in quantity), Q, is determined by your own product price ( in dollars), P, advertisement expenditure ( in million dollars), A, and consumers average income (in 1,000 dollars), Y, you estimated a multiple regression equation of:
Q= a + bP + cA + dY where a, b, c, and d are coefficients.
The following is a partial printout of the multiple regression estimation obtained with missing values due to ink shortage:
Summary Output
Regression Statistics
Multiple R R Square Adjusted R Square Standard Error 150 Observations. 10 ANOVA

Coefficients:
Intercept: 20 Price: -10 Advertise: 15 Income: 30
Standard error:
Intercept: Price: 2.3173 Advertise: 9.1597 Income: 11.7587
T-stat:
Intercept: 2.0172 Price: Advertise: Income:
P-value:
Intercept: 0.090245 Price: 0.005008 Advertise: 0.15262 Income: 0.043415

Suppose that you wish to statistically test if the income coefficient is equal to 50 at a 5% significance level. Your conclusion is ____.
A. Reject the null hypothesis B. Accept the null hypothesis C. Inconclusive D. The income coefficient explains the dependent variable E. The income coefficient is important with a 5% uncertainty

As a sales manager of your company you decided to examine if the sales (in quantity), Q, is determined by your own product price ( in dollars), P, advertisement expenditure ( in million dollars), A, and consumers average income (in 1,000 dollars), Y, you estimated a multiple regression equation of:
Q= a + bP + cA + dY where a, b, c, and d are coefficients.
The following is a partial printout of the multiple regression estimation obtained with missing values due to ink shortage:
Summary Output
Regression Statistics
Multiple R R Square Adjusted R Square Standard Error 150 Observations. 10 ANOVA

Coefficients:
Intercept: 20 Price: -10 Advertise: 15 Income: 30
Standard error:
Intercept: Price: 2.3173 Advertise: 9.1597 Income: 11.7587
T-stat:
Intercept: 2.0172 Price: Advertise: Income:
P-value:
Intercept: 0.090245 Price: 0.005008 Advertise: 0.15262 Income: 0.043415

Suppose that you wish to statistically test if the income coefficient is equal to 50 at a 5% significance level. Your conclusion is ____.
A. Reject the null hypothesis B. Accept the null hypothesis C. Inconclusive D. The income coefficient explains the dependent variable E. The income coefficient is important with a 5% uncertainty

Explanation / Answer

We wish to statistically test if the income coefficient is equal to 50 at a 5% significance level.

So we are 95% confident that we are going to accept (or fail to reject) null hypothesis when it is true and there is 5% possiblity that it is going to be wrongly classified.

Here the p-value for testing income co-efficient to equal to 50 at 5% significance level is 0.043415. Since p-value < 0.05 i.e. the level of significance, we reject the null hypothesis.

So Option (A) is correct choice.

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