Question

A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
SUMMARY OUTPUT
Regression Statistics
Multiple R_____0.830
R Square______0.689
Adj. R Square__0.662
Std. Error_____17501.643
Observations___26
ANOVA
__________df________SS___________MS_______F_____Signif F
Regression__2____15579777040__7789888520__25.432__0.0001
Residual___23_____7045072780___306307512
Total______25___22624849820
____________Coef_________StdError_____tStat___p-value
Intercept_____15800.0000___6038.2999___2.617___0.0154
Capital_______0.1245_________0.2045____0.609___0.5485
Wages_______7.0762_________1.4729_____4.804__0.0001
At the 0.01 level of significance, what conclusion should the microeconomist reach regarding the inclusion of Capital in the regression model?

1) Capital is significant in explaining corporate sales and should be included in the model because its p-value is less than 0.01.

2) Capital is significant in explaining corporate sales and should be included in the model because its p-value is more than 0.01.

3) Capital is not significant in explaining corporate sales and should not be included in the model because its p-value is less than 0.01.

4) Capital is not significant in explaining corporate sales and should not be included in the model because its p-value is more than 0.01

Answer 1

Solution:

A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies.

The Microsoft Excel output below shows results of this multiple regression.

At the 0.01 level of significance, what conclusion should the Microeconomist reach regarding the inclusion of Capital in the regression model?

An independent variable in regression is significant or insignificant is determined by p-value corresponding to independent variable in regression analysis.

If p-value < given level of significance ,then null hypothesis H0: regression coefficient = 0 is rejected , that means regression coefficient is significantly different from 0. Thus corresponding independent variable is significant or should be included in the regression equation.

But if p-value > given level of significance ,then we fail to reject null hypothesis H0: regression coefficient = 0 , that means regression coefficient is not significantly different from 0. Thus corresponding independent variable is not significant or should not be included in the regression equation.

From above regression analysis output , we can see: p-value for Variable Capital is 0.5485 > 0.01 level of significance, thus we fail to reject null hypothesis H0: regression coefficient = 0 , that means regression coefficient is not significantly different from 0. thus the variable Capital is not significant or should not be included in the regression equation.

Thus correct option is:

4) Capital is not significant in explaining corporate sales and should not be included in the model because its p-value is more than 0.01