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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

For the following data:

X Y
1 2
4 7
3 5
2 1
5 14
3 7
  • a.  Find the regression equation for predicting Y from X.
  • b. Does the regression equation account for a significant portion of the variance in the Y scores? Use α = .05 to evaluate the F-ratio.

To determine

To Find: The regression equation for predicting Y using X.

Explanation

Given info:

The data represents the numerical values for two variables X and Y.

Calculations:

The regression equation for predicting Y using X is obtained as follows:

X Y (XMX)2 (YMY)2 (XMX)(YMY)
1 2 4 16 8
4 7 1 1 1
3 5 0 1 0
2 1 1 25 5
5 14 4 64 16
3 7 0 1 0
X=18 Y=36 (XMX)2=10 (YMY)2=108 (XMX)(YMY)=30

Mean:

The general formula for mean of X is,

MX=Xn=186=3

Thus, the mean of the variable X  is 3.

The general formula for mean of Y is,

MY=Yn=366=6

Thus, the mean of the variable Y is 6

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