You are given the following pairs of scores on X (Pretest score) and Y (Posttest score).

$\begin{array}{cc}
\hline X & Y \
\hline 65 & 74 \
82 & 87 \
70 & 82 \
46 & 53 \
55 & 69 \
75 & 81 \
\hline
\end{array}$

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 new person who scored 80 on the pretest.

Question

You are given the following pairs of scores on X (Pretest score) and Y (Posttest score).

$\begin{array}{cc}
\hline X & Y \
\hline 65 & 74 \
82 & 87 \
70 & 82 \
46 & 53 \
55 & 69 \
75 & 81 \
\hline
\end{array}$

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 new person who scored 80 on the pretest.

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 = 87.279Y'
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}

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

You Are Given the Following Pairs of Scores on X XY657482877082465355697581\begin{array}{cc}\hline X & Y \\\hline 65 & 74 \\82 & 87 \\70 & 82 \\46 & 53 \\55 & 69 \\75 & 81 \\\hline\end{array}X658270465575​Y748782536981​​

You Are Given the Following Pairs of Scores on X $\begin{array}{cc}\hline X & Y \\\hline 65 & 74 \\82 & 87 \\70 & 82 \\46 & 53 \\55 & 69 \\75 & 81 \\\hline\end{array}$