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Essentials of Statistics for the B...

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

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Chapter
Section
BuyFindarrow_forward

Essentials of Statistics for the B...

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

A set of n = 20 pairs of scores (X and Y values) has SSX = 16, SSY = 100, and SP = 32. If the mean for the X values is MX = 6 and the mean for the Y value is MY = 20.

  • a. Calculate the Pearson correlation for the scores.
  • b. Find the regression equation for predicting Y from the X values.

a.

To determine

To find: The Pearson correlation coefficient for the scores.

Answer

The Pearson correlation coefficient for the scores is 0.8.

Explanation

Given info:

The set of n=20 Pairs of scores (X and Y values) , SSx=16,SSy=100, SP=32. Mean for the X values is Mx=6 and the mean for the Y values is My=20.

Calculation:

The general formula for Pearson correlation (r) is,

r=SP(SSx)×(SSy)

The Pearson correlation coefficient for the score is,

r=SP(SSx)×(SSy)=32(16)×(100)=3240=0.8

Thus, the Pearson correlation coefficient for the scores is 0.8.

b.

To determine

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

Answer

The regression equation for predicting Y from the X values is Y^=2X+8.

Explanation

Calculation:

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

Y^=bX+a

Where b is calculated as:

b=SPSSx

The regression equation for predicting Y from the X values is obtained as follows:

The regression coefficient is,

b=SPSSx=3216=2

Thus, the regression coefficient is b=2.

The intercept for the regression equation is,

a=MybMx=202×6=2012=8

Thus, the intercept for the regression equation is a=8

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

Y^=bX+a=2×X+8=2X+8

Thus, the regression equation for predicting Y from the X values is Y^=2X+8.

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