   Chapter 14, Problem 23P Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

Solutions

Chapter
Section Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

For the following scores, X Y 3 6 6 1 3 4 3 3 5 1 a. Find the regression equation for predicting Y from X. b. Calculate the predicted Y value for each X.

a.

To determine

To Find: The regression equation for predicting Y from the X values.

The regression equation for predicting Y from the X values is Y^=1.25X+8_.

Explanation

Given info:

The data represents the scores of X and Y.

Calculation:

The general regression equation for predicting Y from the X values is,

Y^=bX+a

Where, parameter b is calculated as b=SPSSx and parameter a calculated as a=MybMx

Regression equation:

SP=(XMx)(YMy)

Squared deviations SSx and SSy are calculated as:

SSx=(XMx)2 and SSy=(YMy)2

The below table showing the calculations required for calculating correlation:

 S.no. X Y Deviation Deviation square Product (X−Mx) (Y−My) (X−Mx)2 (Y−My)2 (X−Mx)(Y−My) 1 3 6 -1 3 1 9 -3 2 6 1 2 -2 4 4 -4 3 3 4 -1 1 1 1 -1 4 3 3 -1 0 1 0 0 5 5 1 1 -2 1 4 -2 Sum/ average 4 3 8 18 -10

So, the sum of product of deviation (SP) is 10, SSx is 8 and SSy is 18.

The value of regression coefficient is,

b=SPSSx=108=1.25

The value of the intercept of the regression equation is,

a=MybMx=3(1.25)×4=3+5=8

The regression equation is,

Y^=bX+a=(5/4)×X+8=1.25X+8

Thus, the regression equation is Y^=1.25X+8_.

b.

To determine

To find: The predicted Y values from the given X values.

The predicted Y values for the given X scores are:

 X Y Predicted Y value 3 6 4.25 6 1 0.50 3 4 4.25 3 3 4.25 5 1 1.75
Explanation

Calculation:

The regression equation for predicting Y from the X values is Y^=1.25X+8.

Substitute the given X scores in the above calculated regression equation for getting the predicted Y values. The predicted Y values are showing in the below table:

 X Y Predicted Y value ( Y^=−1.25X+8) 3 6 4.25 6 1 0.50 3 4 4.25 3 3 4.25 5 1 1.75

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