You are given the following pairs of scores on X (Percentage of students whose families are below poverty line) and Y (Percentage of students at or above proficiency level) for nine schools.

$\begin{array}{cc}
\hline X & Y \
\hline 92.3 & 18.9 \
0.9 & 87.3 \
25.1 & 48.0 \
67.1 & 45.4 \
24.7 & 80.2 \
90.7 & 13.7 \
44.0 & 26.9 \
65.5 & 58.6 \
40.6 & 46.3 \
\hline
\end{array}$

a. Find the linear regression model for predicting Y from X.
b. Use the prediction model obtained to predict the value of Y for a school that has 50% of students whose families are below the poverty line.

Question

You are given the following pairs of scores on X (Percentage of students whose families are below poverty line) and Y (Percentage of students at or above proficiency level) for nine schools.

$\begin{array}{cc}
\hline X & Y \
\hline 92.3 & 18.9 \
0.9 & 87.3 \
25.1 & 48.0 \
67.1 & 45.4 \
24.7 & 80.2 \
90.7 & 13.7 \
44.0 & 26.9 \
65.5 & 58.6 \
40.6 & 46.3 \
\hline
\end{array}$

a. Find the linear regression model for predicting Y from X.
b. Use the prediction model obtained to predict the value of Y for a school that has 50% of students whose families are below the poverty line.

Quizplus · Accepted Answer

The Answer is a. Intercept a = 15.919, slope b = .892.
The regression model is Y_i = .892X_i + 15.919 + e_i
The prediction equation is Y'_i = .892X_i + 15.919

b. When X = 80, Y' = .892X + 15.919 = .892(80) + 15.919 = 87.279
Procedure:
Create a data set with two variables: Pretest (X), Posttest (Y). The data set should have 6 cases.

1. Go to Analyze

ightarrow

Regression

ightarrow

Linear.

2. Select Posttest to the Dependent list. Select Pretest to the Independent(s) list.

3. Click Statistics. Select Confidence interval under Regression Coefficients. Click Continue.

"4. Click OK.
Selected SPSS Output:

\begin{array}{l} ext { Model Summary }\\begin{array}{ccccc}\hline ext { Model } & R & R ext { Square } & ext { Adjusted R Square } & ext { Std. Error of the Estimate } \\hline 1 & .964 & .930 & .912 & 3.627 \\hline\end{array}\end{array}

$a. Intercept a = 15.919, slope b = .892. The regression model is Yi = .892Xi + 15.919 + ei The prediction equation is Y'i = .892Xi + 15.919 b. When X = 80, Y' = .892X + 15.919 = .892(80) + 15.919 = 87.279 Procedure: Create a data set with two variables: Pretest (X), Posttest (Y). The data set should have 6 cases. 1. Go to Analyze ightarrow Regression ightarrow Linear. 2. Select Posttest to the Dependent list. Select Pretest to the Independent(s) list. 3. Click Statistics. Select Confidence interval under Regression Coefficients. Click Continue. 4. Click OK. Selected SPSS Output: \begin{array}{l} ext { Model Summary }\ \begin{array}{ccccc} \hline ext { Model } & R & R ext { Square } & ext { Adjusted R Square } & ext { Std. Error of the Estimate } \ \hline 1 & .964 & .930 & .912 & 3.627 \ \hline \end{array} \end{array}$

You Are Given the Following Pairs of Scores on X