Question

Given the following regression output,

Analysis of Variance

Source DF       SS      MS F P

Regression       2  1995489  997745  20.23  0.000

Residual Error  22  1084911   49314

Total           24  3080400

S = 222.068   R-Sq = 64.8%   R-Sq(adj) = 61.6%

Predictor    Coef  SE Coef      T      P

Constant   3080.1    343.9   8.96  0.000

X1         -54.19    12.28  -4.41  0.000

X2         16.289    3.784   4.30  0.000

a) Write the regression equation.

b) If  is 5 and  is 15, what is the value of the dependent variable?

c) How large is the sample?

d) How many independent variables are there?

e) How many dependent variables are there?

f) Are all independent variables significant at the 5% significance level?

g) Is the regression significant at the 5% significance level?

h) Which independent variable(s) would you consider dropping? If any?

Answer 1

Solution:

a) Write the regression equation.

Answer: The regression equation is:

b) If X1 is 5 and X2 is 15, what is the value of the dependent variable?

Answer: The value of the dependent variable is:

c) How large is the sample?

Answer: The sample size is 25

d) How many independent variables are there?

Answer: There are two independent variables in the model and these are:

X1 and X2

e) How many dependent variables are there?

Answer: There is only one dependent variable

f) Are all independent variables significant at the 5% significance level?

Answer: Yes, all the independent variables are significant at the 5% significance level because the p-value is less than the significance level for both the coefficients of X1 and X2

g) Is the regression significant at the 5% significance level?

Answer: Yes, the regression is significant at the 5% significance level because the p-value for the F-statistic is less than the significance level.

h) Which independent variable(s) would you consider dropping? If any?

Answer: None of these should be dropped because both of these are significant.