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Use the Following Description and Table to Answer the Next

question 7

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Use the following description and table to answer the next few questions.
A state education department conducted a study of 1000 primary schools to find out how much parental engagement matters for improving academic performance .They measured parental engagement at each school (on a 1-5 scale) , and used regression analysis to examine the effect of engagement on the percent of students meeting state standards in English language arts .To get a better estimate of the true causal effect of engagement, they controlled for poverty and school size (enrollment) because of a concern that these variables may be influencing both parental involvement and academic performance .The results of various specifications using regression analysis are shown below.
Regression analysis of percent of students meeting ELA standards (various specifications)
 Spec 1  Spec 2  Spec 3  Spec 4 Parental engagernent (1-5  scale)  13.188.2314.189.14 Poverty (%/ of students)  0.49.47 Enrollment (# of students)  .013.009\begin{array} { | l | c | c | c | c | } \hline & \text { Spec 1 } & \text { Spec 2 } & \text { Spec 3 } & \text { Spec } 4 \\\hline \begin{array} { l } \text { Parental engagernent (1-5 } \\\text { scale) }\end{array} & 13.1 8 ^ { * } & 8 . 2 3^ * & 14.18 ^ { * } & 9.14 ^ { * } \\\hline \text { Poverty (\%/ of students) } & & - 0 . 4 9 ^{*} & & - .47 * \\\hline \text { Enrollment (\# of students) } & & & .013^*& .009^* \\\hline\end{array}
NOTE: N=1000 primary schools; dependent variable is percentage of students meeting standards in English language arts (ELA) ; * p < .05
-How did controlling for school size alone change the estimated causal effect of parental engagement?


Definitions:

Rectangular Coordinate

A system of specifying points on a plane using two distances, typically known as the x and y coordinates, which define the position relative to two perpendicular axes.

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To multiply a number by itself, or a geometric figure with four equal sides and four right angles.

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The vertical line in a coordinate plane that measures the second coordinate of a point (its ordinate).

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The x-axis is the horizontal axis in a coordinate plane, used to represent one dimension of data or to plot the values of a function.

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