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Essentials of Statistics for the B...

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

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BuyFindarrow_forward

Essentials of Statistics for the B...

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

Problem 9 examined the relationship between weight and income for a sample of n = 10 women. Weights were classified in five categories and had a mean of M = 3 with SS = 20. Income, measured in thousands, had a mean score of M = 66 with SS = 7430, and SP = −359.

  • a. Find the regression equation for predicting income from weight. (Identify the income scores as X values and the weight scores as Y values.)
  • b. What percentage of the variance in the income is accounted for by the regression equation? (Compute the correlation, r. then find r2.)
  • c. Does the regression equation account for a significant portion of the variance in income? Use α= .05 to evaluate the F-ratio.
Weight (X) Income (Y)
1 125
2 78
4 49
3 63
5 35
2 84
5 38
3 51
1 93
4 44

a.

To determine
The regression equation for predicting income from weight.

Explanation

Given info: For 10 women weights are classified in five categories with mean of  M=3 and SS=20. The income measured in thousands with mean M=66 and and SS=7430. The given data are shown below,

Weight(X) Income(Y)
1 125
2 78
4 49
3 63
5 35
2 84
5 38
3 51
1 93
4 44

Calculation:

Generally the linear regression equation is defined as

Y=bX+a

Formula to calculate b is,

b=SPSSx

Formula to calculate the a is,

a=MYbMX

Mean of the variable X is,

MX=1+2+4+3+5+2+5+3+1+410=3010=3

Thus, the mean of the variable X is 3.

Mean of the variable Y is,

MY=125+78+49+63+35+84+38+51+93+4410=66010=66

Thus the mean of the variable y is 66.

For calculating SSx and SP the table is shown below,

Sr

b.

To determine
The Percentage of variance in the income accounted for the regression equation.

c.

To determine
The significance of the regression equation.

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