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SCENARIO 17-8
the Superintendent of a School District Wanted to Predict

question 107

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SCENARIO 17-8
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), daily mean of the percentage of students attending class (% Attendance), mean teacher
salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in
the state. Following is the multiple regression output with Y=%Y = \% Passing as the dependent variable, X1=%X _ { 1 } = \% Attendance, X2=X _ { 2 } = Salaries and X3=X _ { 3 } = Spending:

 Regression Statistics  Multiple R 0.7930 R Square 0.6288 Adjusted R 0.6029 Square  Standard 10.4570 Error  Observations 47\begin{array}{lr}\hline{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7930 \\\text { R Square } & 0.6288 \\\text { Adjusted R } & 0.6029 \\\text { Square } & \\\text { Standard } & 10.4570 \\\text { Error } & \\\text { Observations } & 47 \\\hline\end{array}

ANOVA
 SCENARIO 17-8 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), daily mean of the percentage of students attending class (% Attendance), mean teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state. Following is the multiple regression output with  Y = \%  Passing as the dependent variable,  X _ { 1 } = \%  Attendance,  X _ { 2 } =  Salaries and  X _ { 3 } =  Spending:   \begin{array}{lr} \hline{\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.7930 \\ \text { R Square } & 0.6288 \\ \text { Adjusted R } & 0.6029 \\ \text { Square } & \\ \text { Standard } & 10.4570 \\ \text { Error } & \\ \text { Observations } & 47 \\ \hline \end{array}    ANOVA     \begin{array}{lrrrrrr} \hline & \text { Coefficients } & \begin{array}{c} \text { Standard } \\ \text { Error } \end{array} & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & -753.4225 & 101.1149 & -7.4511 & 0.0000 & -957.3401 & -549.5050 \\ \text { \% Attendance } & 8.5014 & 1.0771 & 7.8929 & 0.0000 & 6.3292 & 10.6735 \\ \text { Salary } & 0.000000685 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\ \text { Spending } & 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \\ \hline \end{array}  -Referring to Scenario 17-8, the null hypothesis  H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 0  implies that percentage of students passing the proficiency test is not related to one of the explanatory variables.

 Coefficients  Standard  Error  t Stat  P-value  Lower 95%  Upper 95%  Intercept 753.4225101.11497.45110.0000957.3401549.5050 % Attendance 8.50141.07717.89290.00006.329210.6735 Salary 0.0000006850.00060.00110.99910.00130.0013 Spending 0.00600.00461.28790.20470.00340.0153\begin{array}{lrrrrrr}\hline & \text { Coefficients } & \begin{array}{c}\text { Standard } \\\text { Error }\end{array} & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -753.4225 & 101.1149 & -7.4511 & 0.0000 & -957.3401 & -549.5050 \\\text { \% Attendance } & 8.5014 & 1.0771 & 7.8929 & 0.0000 & 6.3292 & 10.6735 \\\text { Salary } & 0.000000685 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\\text { Spending } & 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \\\hline\end{array}
-Referring to Scenario 17-8, the null hypothesis H0:β1=β2=β3=0H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 0 implies that percentage
of students passing the proficiency test is not related to one of the explanatory variables.


Definitions:

Collective Agreements

Contractual agreements between employers and a group of employees, typically negotiated by unions.

Strike Action

The collective refusal of employees to work, aimed at protesting against employment conditions or bargaining for better terms.

Grievances

Formal complaints or disputes brought forward by employees regarding workplace conditions, treatment by management, or contract violations.

Conflict Resolution

The process of resolving disputes and disagreements between parties through dialogue, negotiation, or other methods.

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