In a multiple regression with three explanatory variables,the total sum of squares SST = 1008,the model mean square MSM = 76,and the test statistic F = 2.533.How many observations were used?
A)26
B)29
C)30
D)31

Question

Quizplus · Accepted Answer

We can start by using the formula F = (MSM/MSE) and rearranging it to solve for MSE. This gives:
MSE = MSM/F = 76/2.533 = 30

We also know that SST = SSE + SSR, where SSE is the sum of squared errors and SSR is the sum of squared residuals.

Since we have three explanatory variables, the degrees of freedom for SSE is n - 4 (where n is the sample size) and the degrees of freedom for SSR is 3. Therefore, the degrees of freedom for SST is n - 1.

Using the information given, we can set up the following equation:
1008 = SSE + SSR
1008 = (n-4) * 30 + 3 * MSR
1008 = 30n - 120 + 3 * 76
1008 = 30n + 108

Solving for n gives:
n = 31

Therefore, the answer is choice letter D.

In a Multiple Regression with Three Explanatory Variables,the Total Sum