Instruction 13.16
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size) and education of the head of household (School). House size is measured in hundreds of square metres, income is measured in thousands of dollars and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
OUTPUT
SUMMARY
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \ \text { R Square } & 0.748 \ \text { Adj. R Square } & 0.726 \ \text { Std. Error } & 5.195 \ \text { Observations } & 50 \end{array}$

ANOVA
$\begin{array} { l l l l l l } & d f & \text { SS } & \text { MS } & F & \text { Signiff } \ \text { Regression } & & 3605.7736 & 901.4434 & & 0.0001 \ \text { Residual } & & 1214.2264 & 26.9828 & & \ \text { Total } & 49 & 4820.0000 & & & \ & & & & & \ & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text { value } & \ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 & \ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 & \ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 & \ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 & \end{array}$ Note: Adj. R Square = Adjusted R Square; Std. Error = Standard Error
-Referring to Instruction 13.16,which of the following values for the level of significance is the smallest for which at least two explanatory variables are significant individually?
A) 0.15
B) 0.025
C) 0.05
D) 0.01

Question

Instruction 13.16
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size) and education of the head of household (School). House size is measured in hundreds of square metres, income is measured in thousands of dollars and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
 OUTPUT
SUMMARY
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \ \text { R Square } & 0.748 \ \text { Adj. R Square } & 0.726 \ \text { Std. Error } & 5.195 \ \text { Observations } & 50 \end{array}$

ANOVA
$\begin{array} { l l l l l l } & d f & \text { SS } & \text { MS } & F & \text { Signiff } \ \text { Regression } & & 3605.7736 & 901.4434 & & 0.0001 \ \text { Residual } & & 1214.2264 & 26.9828 & & \ \text { Total } & 49 & 4820.0000 & & & \ & & & & & \ & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text { value } & \ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 & \ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 & \ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 & \ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 & \end{array}$ Note: Adj. R Square = Adjusted R Square; Std. Error = Standard Error
-Referring to Instruction 13.16,which of the following values for the level of significance is the smallest for which at least two explanatory variables are significant individually?
A) 0.15
B) 0.025
C) 0.05
D) 0.01

Quizplus · Accepted Answer

We need to look at the p-values for the individual explanatory variables. As per the given Excel output, the p-values for Income, Size, and School are 0.01, 0.171, and 0.002 respectively. 
For there to be at least two variables significant at a level of significance, we need to choose a level of significance that is smaller than the smallest p-value among them. Therefore, the smallest level of significance we can choose is 0.002, which corresponds to p-value of School. Hence, the answer is D.

Instruction 13 ANOVA Note: Adj R Square = Adjusted R Square; Std