Consider the multiple regression model shown next between the dependent variable Y and four independent variables X₁,X₂,X₃,and X₄,which result in the following function: = 33 + 8X₁ − 6X₂ + 16X₃ + 18X₄ For this model,there were 35 observations; SSR = 1,400 and SSE = 600.
The critical F-value at the 1% level of significance is

Question

Consider the multiple regression model shown next between the dependent variable Y and four independent variables X₁,X₂,X₃,and X₄,which result in the following function:

Consider the multiple regression model shown next between the dependent variable Y and four independent variables X<sub>1</sub>,X<sub>2</sub>,X<sub>3</sub>,and X<sub>4</sub>,which result in the following function: = 33 + 8X<sub>1</sub> − 6X<sub>2</sub> + 16X<sub>3</sub> + 18X<sub>4</sub> For this model,there were 35 observations; SSR = 1,400 and SSE = 600. The critical F-value at the 1% level of significance is A) 3.83 B) 2.61 C) 4.02 D) 2.53

= 33 + 8X₁ − 6X₂ + 16X₃ + 18X₄ For this model,there were 35 observations; SSR = 1,400 and SSE = 600.
The critical F-value at the 1% level of significance is

Quizplus · Accepted Answer

To find the critical F-value, we first need to calculate the degrees of freedom:

Degrees of freedom for regression (k) = number of independent variables = 4
Degrees of freedom for error (n-k-1) = 35-4-1 = 30

Next, we can calculate the F-value using the formula:

F = SSR/k / SSE/(n-k-1)

Plugging in the given values, we get:

F = 1400/4 / 600/30
F = 11.67

To find the critical F-value, we need to use a table or calculator with F-distribution. Using a calculator, we can find that the critical F-value at the 1% level of significance with degrees of freedom (4, 30) is 4.02.

Therefore, the best choice is C, with an explanation as shown above.

Consider the Multiple Regression Model Shown Next Between the Dependent