Instruction 13-13
the Education Department's Regional Executive Officer Wanted to Predict

question 185

True/False

Instruction 13-13
The education department's regional executive officer wanted to predict the percentage of students passing a Grade 6 proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing),daily average of the percentage of students attending class (% Attendance),average 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,
X₁ = % Attendance,X₂ = Salaries and X₃ = Spending:
$\begin{array}{lr}\hline {\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7930 \\\text { R Square } & 0.6288 \\\text { Adjusted R } & 0.6029 \\\text { Square } & \\\text { Standard } & 10.4570 \\\text { Error } & \\\text { Observations } & 47\end{array}$
ANOVA
$\begin{array}{lrrrrr} & \text { df } &{\text { SS }} & \text { MS } & F&\text { Significance F } \\\hline \text { Regression } & 3 & 7965.08 & 2655.03 & 24.2802 & 0.0000 \\\text { Residual } & 43 & 4702.02 & 109.35 & & \\\text { Total } & 46 & 12667.11 & & &\end{array}$

$\begin{array}{lrrrrrr} & \text { Coefficients } & \begin{array}{c}\text { Standard } \\\text { Error }\end{array} & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -753.4225 & 101.1149 & -7.4511 & 0.0000 & -957.3401 & -549.5050 \\\text { \% Attendance } & 8.5014 & 1.0771 & 7.8929 & 0.0000 & 6.3292 & 10.6735 \\\text { Salary } & 0.000000685 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\\text { Spending } & 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153\end{array}$
-Referring to Instruction 13-13,the null hypothesis should be rejected at a 5% level of significance when testing whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables.

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Definitions:

Standard Deviation

A measure of the amount of variation or dispersion of a set of values, indicating how much the values differ from the mean.

T-Distribution

A probability distribution used in statistics that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population variance is unknown.

Confidence Interval

A range of values, derived from the sample data, that is believed, with a certain degree of probability, to contain the true population parameter.

Margin Of Error

An estimate of the amount by which an observed sample result may differ from the true value, providing a confidence interval for the estimation.