Suppose a multiple regression analysis involving 25 data points has and SSE = 36.Then, the number of the independent variables must be:
A) 3
B) 4
C) 5
D) 6

Question

Suppose a multiple regression analysis involving 25 data points has  and SSE = 36.Then, the number of the independent variables must be:
A) 3 
B) 4 
C) 5 
D) 6

Quizplus · Accepted Answer

The number of independent variables can be calculated using the formula: 
number of independent variables = number of data points - number of parameters estimated - 1
where the number of parameters estimated includes the intercept and slope coefficients.
In this case, we have 25 data points and SSE = 36, which means that the sum of squared residuals (SSR) is:
SSR = SST - SSE
where SST is the total sum of squares. We do not have information on SST in this question, but we can assume that it is positive, since otherwise SSE would be greater than SST, which is not possible. Therefore, we can conclude that SSR < SST, which means that there is some variability in the data that is not explained by the regression model. This is an indication that the model may be overfitted, i.e., it has too many independent variables relative to the amount of data available.
Now, we need to estimate the number of parameters in the model. Since we have 25 data points and one dependent variable, the intercept and slope coefficients are two parameters that need to be estimated. For each additional independent variable, we need to estimate one additional slope coefficient. Therefore, the number of parameters estimated is p = 2 + k, where k is the number of independent variables.
Using the formula above, we get:
k = number of data points - number of parameters estimated - 1 = 25 - (2 + k) - 1 = 22 - k
Solving for k, we get:
k = 4
Therefore, the model has 4 independent variables.

Suppose a Multiple Regression Analysis Involving 25 Data Points Has