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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

The regression equation is computed for a set of n = 18 pairs of X and Y values with a correlation of r = +80 and SSY = 100.

  • a. Find the standard error of estimate for the regression equation.
  • b. How big would the standard error be if the sample size were n = 38?

a.

To determine

To find: The standard error of estimate for the regression equation.

Explanation

Given info:

The regression equation is computed for a set of n=18 pairs of X and Y values with a correlation of r=+0.80 and SSy=100.

Calculation:

The general formula for standard error of estimate is,

SE=SSresidualdf

Here SE is for standard error of estimate and df is degree of freedom.

Degrees of freedom:

df=n2=182=16

For calculating the standard error of estimates for the regression equation need to calculate SSresidual.The SS residual also known as unpredicted variability is calculated as:

SSresidual=(1r2)SSy

Where r is given as 0.60, so r2 is calculated as 0.64. It is because r2 is the squared correlation and SSy is given as 100

b.

To determine
The standard error if the sample size is n=38.

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