SCENARIO 14-15
The superintendent of a school district wanted to predict the percentage of students passing a sixth-
grade proficiency test. She obtained the data on percentage of students passing the proficiency test
(% Passing), mean teacher salary in thousands of dollars (Salaries), and instructional spending per
pupil in thousands of dollars (Spending) of 47 schools in the state. Following is the multiple regression output with

Y = \%

Passing as the dependent variable,

X _ { 1 } =

Salaries and

X _ { 2 } =

Spending:

\begin{array}{lr}\hline {\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.4276 \\\text { R Square } & 0.1828 \\\text { Adjusted R Square } & 0.1457 \\\text { Standard Error } & 5.7351 \\\text { Observations } & 47 \\\hline\end{array}

ANOVA
$SCENARIO 14-15 The superintendent of a school district wanted to predict the percentage of students passing a sixth- grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), mean teacher salary in thousands of dollars (Salaries), and instructional spending per pupil in thousands of dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y = \% Passing as the dependent variable, X _ { 1 } = Salaries and X _ { 2 } = Spending: \begin{array}{lr} \hline {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.4276 \\ \text { R Square } & 0.1828 \\ \text { Adjusted R Square } & 0.1457 \\ \text { Standard Error } & 5.7351 \\ \text { Observations } & 47 \\ \hline \end{array} ANOVA \begin{array}{lrrrrrr} \hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \rho \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & -72.9916 & 45.9106 & -1.5899 & 0.1190 & -165.5184 & 19.5352 \\ \text { Salary } & 2.7939 & 0.8974 & 3.1133 & 0.0032 & 0.9853 & 4.6025 \\ \text { Spending } & 0.3742 & 0.9782 & 0.3825 & 0.7039 & -1.5972 & 2.3455 \\ \hline \end{array} -Referring to Scenario 14-15, which of the following is the correct null hypothesis to test whether instructional spending per pupil has any effect on percentage of students passing the Proficiency test, taking into account the effect of mean teacher salary? a) H _ { 0 } : \beta _ { 0 } = 0 b) H _ { 0 } : \beta _ { 1 } = 0 c) H _ { 0 } : \beta _ { 2 } = 0 d) H _ { 0 } : \beta _ { 3 } = 0$

\begin{array}{lrrrrrr}\hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \rho \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -72.9916 & 45.9106 & -1.5899 & 0.1190 & -165.5184 & 19.5352 \\\text { Salary } & 2.7939 & 0.8974 & 3.1133 & 0.0032 & 0.9853 & 4.6025 \\\text { Spending } & 0.3742 & 0.9782 & 0.3825 & 0.7039 & -1.5972 & 2.3455 \\\hline\end{array}

-Referring to Scenario 14-15, which of the following is the correct null hypothesis to test whether instructional spending per pupil has any effect on percentage of students passing the
Proficiency test, taking into account the effect of mean teacher salary? a)

H _ { 0 } : \beta _ { 0 } = 0

H _ { 0 } : \beta _ { 1 } = 0

H _ { 0 } : \beta _ { 2 } = 0

H _ { 0 } : \beta _ { 3 } = 0

14-30 Introduction to Multiple Regression -Referring to Scenario 14-7 radj 2r _ { \text {adj } } ^ { 2 }radj 2​

Short Answer

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14-30 Introduction to Multiple Regression
-Referring to Scenario 14-7 $r _ { \text {adj } } ^ { 2 }$

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