You are given the following pairs of scores on X (height in inches) and Y (weight in lbs).

$\begin{array}{cc}
X & Y \
\hline 66 & 140 \
69 & 155 \
72 & 195 \
74 & 160 \
72 & 155 \
67 & 145 \
66 & 135 \
71 & 170 \
70 & 130 \
68 & 170 \
72 & 190 \
69 & 145 \
73 & 155 \
68 & 150 \
68 & 130 \
69 & 145 \
69 & 150 \
66 & 120 \
62 & 131 \
62 & 120 \
64 & 102 \
68 & 110 \
63 & 116 \
64 & 125 \
62 & 110 \
\hline
\end{array}$
Perform the following computations using $\alpha$= .05.
a. The regression equation of Y predicted by X.
b. Test of the significance of X as a predictor.
c. Plot Y versus X.
d. Compute the residuals.
e. Plot residuals versus X.

Question

You are given the following pairs of scores on X (height in inches) and Y (weight in lbs).

$\begin{array}{cc}
X & Y \
\hline 66 & 140 \
69 & 155 \
72 & 195 \
74 & 160 \
72 & 155 \
67 & 145 \
66 & 135 \
71 & 170 \
70 & 130 \
68 & 170 \
72 & 190 \
69 & 145 \
73 & 155 \
68 & 150 \
68 & 130 \
69 & 145 \
69 & 150 \
66 & 120 \
62 & 131 \
62 & 120 \
64 & 102 \
68 & 110 \
63 & 116 \
64 & 125 \
62 & 110 \
\hline
\end{array}$ 
Perform the following computations using $\alpha$= .05. 
a. The regression equation of Y predicted by X.
b. Test of the significance of X as a predictor.
c. Plot Y versus X.
d. Compute the residuals.
e. Plot residuals versus X.

Quizplus · Accepted Answer

The Answer is a. Intercept a = -199.139, slope b = 5.037.
The prediction equation is Y'_i = 5.037X_i -199.139

b. Height is a good predictor of weight, F(1,23) = 29.262, p < .001. Additionally, the unstandardized slope (5.037) and standardized slope (.748) are statistically significantly different from 0 (t = 5.409, df = 23, p < .001); with every one inch increase in height, weight is expected to increase by 5.037 lbs.

c. Plot of Y versus X.
$a. Intercept a = -199.139, slope b = 5.037. The prediction equation is Y'i = 5.037Xi -199.139 b. Height is a good predictor of weight, F(1,23) = 29.262, p < .001. Additionally, the unstandardized slope (5.037) and standardized slope (.748) are statistically significantly different from 0 (t = 5.409, df = 23, p < .001); with every one inch increase in height, weight is expected to increase by 5.037 lbs. c. Plot of Y versus X. (d) Residuals ei = Yi-Y'i. \begin{array}{|c|c|c|} \hline X_{i} & Y_{i} & e_{i} \ \hline 66 & 140 & 6.705 \ \hline 69 & 155 & 6.594 \ \hline 72 & 195 & 31.484 \ \hline 74 & 160 & -13.590 \ \hline 72 & 155 & -8.516 \ \hline 67 & 145 & 6.668 \ \hline 66 & 135 & 1.705 \ \hline 71 & 170 & 11.520 \ \hline 70 & 130 & -23.443 \ \hline 68 & 170 & 26.631 \ \hline 72 & 190 & 26.484 \ \hline 69 & 145 & -3.406 \ \hline 73 & 155 & -13.553 \ \hline 68 & 150 & 6.631 \ \hline 68 & 130 & -13.369 \ \hline 69 & 145 & -3.406 \ \hline 69 & 150 & 1.594 \ \hline 66 & 120 & -13.295 \ \hline 62 & 131 & 17.852 \ \hline 62 & 120 & 6.852 \ \hline 64 & 102 & -21.221 \ \hline 68 & 110 & -33.369 \ \hline 63 & 116 & -2.184 \ \hline 64 & 125 & 1.779 \ \hline 62 & 110 & -3.148 \ \hline \end{array} (e) Plot of residuals versus X. Procedure: Create a data set with two variables: Height (X), Weight (Y). The data set should have 25 cases. 1) Go to Analyze ightarrow Regression ightarrow Linear. 2) Select Weight to the Dependent list. Select Height to the Independent(s) list. 3) Click Statistics. Select Confidence interval under Regression Coefficients. Click Continue. 4) To save residuals for the residual plot, click Save. Select Unstandardized under Residuals. Click Continue. Click OK. 5) To plot Y versus X, go to Graphs ightarrow Legacy Dialogs ightarrow Scatter/Dot. Select Simple Scatter. Click Define. Select Weight to Y axis, and Height to X axis. Click OK. 6) To obtain the residual plot, go to Graphs ightarrow Legacy Dialogs ightarrow Scatter/Dot. Select Simple Scatter. Click Define. Select RES_1 to Y axis, and Height to X axis. Click OK. Selected SPSS Output: \begin{array}{l} ext { Model Summary }\ \begin{array}{ccccc} \hline ext { Model } & R & R ext { Square } & ext { Adjusted RSquare } & ext { Std. Error of the Estimate } \ \hline 1 & .748 & .560 & .541 & 16.196 \ \hline \end{array} \end{array} ANOVA^{b} \begin{array}{cccccc} \hline ext { Model } & ext { Sum of Squares } & d f & ext { Mean Square } & F & ext { Sig. } \ \hline ext { Regression } & 7676.012 & 1 & 7676.012 & 29.262 & .000^{a} \ 1 ext { Residual } & 6033.348 & 23 & 262.319 & & \ ext { Total } & 13709.360 & 24 & & & \ \hline \end{array} a. Predictors: (Constant), height b. Dependent Variable: weight$ (d) Residuals e_i = Y_i-Y'_i.

\begin{array}{|c|c|c|}\hline X_{i} & Y_{i} & e_{i} \\hline 66 & 140 & 6.705 \\hline 69 & 155 & 6.594 \\hline 72 & 195 & 31.484 \\hline 74 & 160 & -13.590 \\hline 72 & 155 & -8.516 \\hline 67 & 145 & 6.668 \\hline 66 & 135 & 1.705 \\hline 71 & 170 & 11.520 \\hline 70 & 130 & -23.443 \\hline 68 & 170 & 26.631 \\hline 72 & 190 & 26.484 \\hline 69 & 145 & -3.406 \\hline 73 & 155 & -13.553 \\hline 68 & 150 & 6.631 \\hline 68 & 130 & -13.369 \\hline 69 & 145 & -3.406 \\hline 69 & 150 & 1.594 \\hline 66 & 120 & -13.295 \\hline 62 & 131 & 17.852 \\hline 62 & 120 & 6.852 \\hline 64 & 102 & -21.221 \\hline 68 & 110 & -33.369 \\hline 63 & 116 & -2.184 \\hline 64 & 125 & 1.779 \\hline 62 & 110 & -3.148 \\hline\end{array}

(e) Plot of residuals versus X.

$a. Intercept a = -199.139, slope b = 5.037. The prediction equation is Y'i = 5.037Xi -199.139 b. Height is a good predictor of weight, F(1,23) = 29.262, p < .001. Additionally, the unstandardized slope (5.037) and standardized slope (.748) are statistically significantly different from 0 (t = 5.409, df = 23, p < .001); with every one inch increase in height, weight is expected to increase by 5.037 lbs. c. Plot of Y versus X. (d) Residuals ei = Yi-Y'i. \begin{array}{|c|c|c|} \hline X_{i} & Y_{i} & e_{i} \ \hline 66 & 140 & 6.705 \ \hline 69 & 155 & 6.594 \ \hline 72 & 195 & 31.484 \ \hline 74 & 160 & -13.590 \ \hline 72 & 155 & -8.516 \ \hline 67 & 145 & 6.668 \ \hline 66 & 135 & 1.705 \ \hline 71 & 170 & 11.520 \ \hline 70 & 130 & -23.443 \ \hline 68 & 170 & 26.631 \ \hline 72 & 190 & 26.484 \ \hline 69 & 145 & -3.406 \ \hline 73 & 155 & -13.553 \ \hline 68 & 150 & 6.631 \ \hline 68 & 130 & -13.369 \ \hline 69 & 145 & -3.406 \ \hline 69 & 150 & 1.594 \ \hline 66 & 120 & -13.295 \ \hline 62 & 131 & 17.852 \ \hline 62 & 120 & 6.852 \ \hline 64 & 102 & -21.221 \ \hline 68 & 110 & -33.369 \ \hline 63 & 116 & -2.184 \ \hline 64 & 125 & 1.779 \ \hline 62 & 110 & -3.148 \ \hline \end{array} (e) Plot of residuals versus X. Procedure: Create a data set with two variables: Height (X), Weight (Y). The data set should have 25 cases. 1) Go to Analyze ightarrow Regression ightarrow Linear. 2) Select Weight to the Dependent list. Select Height to the Independent(s) list. 3) Click Statistics. Select Confidence interval under Regression Coefficients. Click Continue. 4) To save residuals for the residual plot, click Save. Select Unstandardized under Residuals. Click Continue. Click OK. 5) To plot Y versus X, go to Graphs ightarrow Legacy Dialogs ightarrow Scatter/Dot. Select Simple Scatter. Click Define. Select Weight to Y axis, and Height to X axis. Click OK. 6) To obtain the residual plot, go to Graphs ightarrow Legacy Dialogs ightarrow Scatter/Dot. Select Simple Scatter. Click Define. Select RES_1 to Y axis, and Height to X axis. Click OK. Selected SPSS Output: \begin{array}{l} ext { Model Summary }\ \begin{array}{ccccc} \hline ext { Model } & R & R ext { Square } & ext { Adjusted RSquare } & ext { Std. Error of the Estimate } \ \hline 1 & .748 & .560 & .541 & 16.196 \ \hline \end{array} \end{array} ANOVA^{b} \begin{array}{cccccc} \hline ext { Model } & ext { Sum of Squares } & d f & ext { Mean Square } & F & ext { Sig. } \ \hline ext { Regression } & 7676.012 & 1 & 7676.012 & 29.262 & .000^{a} \ 1 ext { Residual } & 6033.348 & 23 & 262.319 & & \ ext { Total } & 13709.360 & 24 & & & \ \hline \end{array} a. Predictors: (Constant), height b. Dependent Variable: weight$
Procedure:
Create a data set with two variables: Height (X), Weight (Y). The data set should have 25 cases.

1) Go to Analyze

ightarrow

Regression

ightarrow

Linear.
2) Select Weight to the Dependent list. Select Height to the Independent(s) list.
3) Click Statistics. Select Confidence interval under Regression Coefficients. Click Continue.
4) To save residuals for the residual plot, click Save. Select Unstandardized under Residuals. Click Continue. Click OK.
5) To plot Y versus X, go to Graphs

ightarrow

Legacy Dialogs

ightarrow

Scatter/Dot. Select Simple Scatter. Click Define. Select Weight to Y axis, and Height to X axis. Click OK.
"6) To obtain the residual plot, go to Graphs

ightarrow

Legacy Dialogs

ightarrow

Scatter/Dot. Select Simple Scatter. Click Define. Select RES_1 to Y axis, and Height to X axis. Click OK.
Selected SPSS Output:

\begin{array}{l} ext { Model Summary }\\begin{array}{ccccc}\hline ext { Model } & R & R ext { Square } & ext { Adjusted RSquare } & ext { Std. Error of the Estimate } \\hline 1 & .748 & .560 & .541 & 16.196 \\hline\end{array}\end{array}

ANOVA^{b}

\begin{array}{cccccc}\hline ext { Model } & ext { Sum of Squares } & d f & ext { Mean Square } & F & ext { Sig. } \\hline ext { Regression } & 7676.012 & 1 & 7676.012 & 29.262 & .000^{a} \1 ext { Residual } & 6033.348 & 23 & 262.319 & & \ ext { Total } & 13709.360 & 24 & & & \\hline\end{array}

a. Predictors: (Constant), height
b. Dependent Variable: weight

$a. Intercept a = -199.139, slope b = 5.037. The prediction equation is Y'i = 5.037Xi -199.139 b. Height is a good predictor of weight, F(1,23) = 29.262, p < .001. Additionally, the unstandardized slope (5.037) and standardized slope (.748) are statistically significantly different from 0 (t = 5.409, df = 23, p < .001); with every one inch increase in height, weight is expected to increase by 5.037 lbs. c. Plot of Y versus X. (d) Residuals ei = Yi-Y'i. \begin{array}{|c|c|c|} \hline X_{i} & Y_{i} & e_{i} \ \hline 66 & 140 & 6.705 \ \hline 69 & 155 & 6.594 \ \hline 72 & 195 & 31.484 \ \hline 74 & 160 & -13.590 \ \hline 72 & 155 & -8.516 \ \hline 67 & 145 & 6.668 \ \hline 66 & 135 & 1.705 \ \hline 71 & 170 & 11.520 \ \hline 70 & 130 & -23.443 \ \hline 68 & 170 & 26.631 \ \hline 72 & 190 & 26.484 \ \hline 69 & 145 & -3.406 \ \hline 73 & 155 & -13.553 \ \hline 68 & 150 & 6.631 \ \hline 68 & 130 & -13.369 \ \hline 69 & 145 & -3.406 \ \hline 69 & 150 & 1.594 \ \hline 66 & 120 & -13.295 \ \hline 62 & 131 & 17.852 \ \hline 62 & 120 & 6.852 \ \hline 64 & 102 & -21.221 \ \hline 68 & 110 & -33.369 \ \hline 63 & 116 & -2.184 \ \hline 64 & 125 & 1.779 \ \hline 62 & 110 & -3.148 \ \hline \end{array} (e) Plot of residuals versus X. Procedure: Create a data set with two variables: Height (X), Weight (Y). The data set should have 25 cases. 1) Go to Analyze ightarrow Regression ightarrow Linear. 2) Select Weight to the Dependent list. Select Height to the Independent(s) list. 3) Click Statistics. Select Confidence interval under Regression Coefficients. Click Continue. 4) To save residuals for the residual plot, click Save. Select Unstandardized under Residuals. Click Continue. Click OK. 5) To plot Y versus X, go to Graphs ightarrow Legacy Dialogs ightarrow Scatter/Dot. Select Simple Scatter. Click Define. Select Weight to Y axis, and Height to X axis. Click OK. 6) To obtain the residual plot, go to Graphs ightarrow Legacy Dialogs ightarrow Scatter/Dot. Select Simple Scatter. Click Define. Select RES_1 to Y axis, and Height to X axis. Click OK. Selected SPSS Output: \begin{array}{l} ext { Model Summary }\ \begin{array}{ccccc} \hline ext { Model } & R & R ext { Square } & ext { Adjusted RSquare } & ext { Std. Error of the Estimate } \ \hline 1 & .748 & .560 & .541 & 16.196 \ \hline \end{array} \end{array} ANOVA^{b} \begin{array}{cccccc} \hline ext { Model } & ext { Sum of Squares } & d f & ext { Mean Square } & F & ext { Sig. } \ \hline ext { Regression } & 7676.012 & 1 & 7676.012 & 29.262 & .000^{a} \ 1 ext { Residual } & 6033.348 & 23 & 262.319 & & \ ext { Total } & 13709.360 & 24 & & & \ \hline \end{array} a. Predictors: (Constant), height b. Dependent Variable: weight$

You Are Given the Following Pairs of Scores on X