Question

A regression model between sales (y in $1000), unit price (x1 in dollars), and television advertisement (x2 in dollars) resulted in the following function: ​ = 7 - 3x1 + 5x2​ ​ For this model, SSR = 3500, SSE = 1500, and the sample size is 18. At the 5% level,

options: there is no evidence that the model is significant. the conclusion is that the slope of x1 is significant. it can be concluded that the model is significant. there is evidence that the slope of x2 is significant.

Answer 1

Solution:

Given: A regression model between sales (y in $1000), unit price (x1 in dollars), and television advertisement (x2 in dollars) resulted in the following function: ​ = 7 - 3x1 + 5x2​ ​

SSR = 3500

SSE = 1500

n = 18

Level of significance= 0.05

Step 1) State H0 and H H1:

H0: the regression model is not significant.

Vs

H1: the regression model is significant.

Step 2) Test statistic:

F = MSR / MSE

where

MSR = SSR / df_regression

where

df_regression=k = Number of independent variables.

df_regression=2

thus

MSR = SSR / df_regression

MSR = 3500 / 2

MSR = 1750

and

MSE = SSE / df_error

where

df_error= n - k - 1

df_error= 18 - 2 - 1

df_error= 15

thus

MSE = SSE / df_error

MSE = 1500 / 15

MSE = 100

thus test statistic is:

F = MSR / MSE

F = 1750 / 100

F = 17.5

Step 3) Find F critical value:

df_numerator = df_regression=2

df_denominator = df_error= 15

Level of significance= 0.05

F critical value = 3.68

Step 4) Decision Rule:

Reject null hypothesis H0, if F test statistic value  > F  critical value =3.68 , otherwise we fail to reject H0.

Since F test statistic value = F = 17.5 > F  critical value =3.68 , we reject null hypothesis H0 in favor of H1.

Step 5) Conclusion:

At 0.05 level of significance, we have sufficient evidence to conclude that:  the regression model is significant.

Thus correct answer is:
it can be concluded that the model is significant