Chapter 14, Problem 19P

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8th Edition

Frederick J Gravetter + 1 other

ISBN: 9781133956570

Textbook Problem

A set of *n* = 20 pairs of scores (*X* and *Y* values) has *SS*_{X} = 16, *SS*_{Y} = 100, and *SP* = 32. If the mean for the *X* values is *M _{X}* = 6 and the mean for the

**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
*X* values is
*Y* values is

**Calculation:**

The general formula for Pearson correlation (r) is,

The Pearson correlation coefficient for the score is,

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

Explanation

**Calculation:**

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

Where *b* is calculated as:

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

The regression coefficient is,

Thus, the regression coefficient is

The intercept for the regression equation is,

Thus, the intercept for the regression equation is

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

Thus, the regression equation for predicting *Y* from the *X* values is

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