In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed. = 12 - 18x₁ + 4x₂ + 15x₃

Also, the following standard errors and the sum of squares were obtained.
S_b₁= 3
S_b₂= 6
S_b₃= 7
SST = 4900
SSE = 1296

The test statistic for testing the significance of the model is

Question

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

= 12 - 18x₁ + 4x₂ + 15x₃

Also, the following standard errors and the sum of squares were obtained.
S_b₁= 3
S_b₂= 6
S_b₃= 7
SST = 4900
SSE = 1296

The test statistic for testing the significance of the model is

Quizplus · Accepted Answer

The test statistic for testing the significance of the model can be calculated using the formula:

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

where SSR is the sum of squares due to regression (also known as the explained sum of squares), k is the number of predictor variables (in this case, k=3), SSE is the sum of squares due to error (also known as the residual sum of squares), and n is the sample size (in this case, n=25).

To calculate SSR, we need to subtract SSE from SST:

SSR = SST - SSE = 4900 - 1296 = 3604

Now we can plug in the values into the formula:

F = (SSR/k) / (SSE/(n-k-1))
F = (3604/3) / (1296/21)
F = 19.47

Therefore, the test statistic is 19.47. The closest choice is C.

In a Regression Analysis of a First-Order Model Involving 3