TABLE 14-16
the Superintendent of a School District Wanted

question 173

True/False

TABLE 14-16
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 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:
$\begin{array}{lr}\hline\text {Regression Statistics } \\\hline \text {Multiple R }& 0.7930 \\\text {R Square} & 0.6288 \\\text {Adjusted R Square} & 0.6029 \\\text {Standard Error }& 10.4570 \\\text {Observations }& 47 \\\hline\end{array}$


ANOVA
$\begin{array}{lccccc}\hline &\text { d f } &\text { SS }& \text { MS }& \text { F } & \text { Significance F} \\\hline \text { Regression }& 3 & 7965.08 & 2655.03 & 24.2802 & 2.3853 \mathrm{E}-09 \\\text { Residual} & 43 & 4702.02 & 109.35 & & \\\text { Total }& 46 & 12667.11 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline &\text { Coeffs} & \text { Stnd Err} &\text { t Stat} &\text { p -value }&\text { Lower 95\%} \text { Upper 95\%} \\\hline\text { Intercept }& -753.4225 & 101.1149 & -7.4511 & 2.88 \mathrm{E}-09 & -957.3401 & -549.5050 \\\%\text { Attend }& 8.5014 & 1.0771 & 7.8929 & 6.73 \mathrm{E}-10 & 6.3292 & 10.6735 \\\text { Salary} & 6.85 \mathrm{E}-07 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\\text { Spending }& 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \\\hline\end{array}$

-Referring to Table 14-16, the null hypothesis H0 : þ1 = þ2 = þ3 = 0 implies that percentage of students passing the proficiency test is not related to any of the explanatory variables.

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Definitions:

Soil Horizons

Layers in the soil, each with its own distinct characteristics such as composition, texture, and color, developed over time.

Facilitation Model

A concept in ecology suggesting that the presence of one species positively affects the growth, establishment, or reproduction of another species, often leading to a more complex community structure.

Soil Enriched

Soil that has been enhanced in nutrients and organic matter, improving fertility and the ability to support plant growth.

Growth Rate

The rate at which an organism grows, often measured in terms of size, height, or mass increase over time.