Shown below is a portion of a computer output for a linear regression analysis relating an individual's income (y in thousands of dollars) to age (x 1 in years), level of education (x 2 ranging from 1 to 5), and the individual's gender (x 3 where 0 = female and 1 = male). Coefficient Standard Error t-statistic p-value Intercept 15.934 1.389 11.47 0.000 x 1 0.625 0.094 6.65 0.000 x 2 0.921 0.190 4.85 0.000 x 3 –0.510 0.920 –0.55 0.590 Source of Variation Sum of squares Degrees of freedom Mean square F-statistic p-value Regression 84 3 28 4 0.027 Error 112 16 7 Total 196 19 a. Is there a significant relationship between an individual's income and the set of variables, age, level of education, and gender (based on a significance level α =05 )? Explain why using one of the p-values in the output tables.b.Which of the three predictor variables are significant at a significance level α =05 ?c. What percentage of the variation in income can be accounted for by the estimated linear regression equation relating income to age, level of education, and gender?

Shown below is a portion of a computer output for a linear regression analysis relating an individual's income ( y in thousands of dollars) to age ( x 1 in years), level of education ( x 2 ranging...

Shown below is a portion of a computer output for a linear regression analysis relating an individual's income (y
in thousands of dollars) to age (x
₁in years), level of education (x
₂ranging from 1 to 5), and the individual's gender (x
₃where 0 = female and 1 = male).

	Coefficient	Standard Error	t-statistic	p-value
Intercept	15.934	1.389	11.47	0.000
x ₁	0.625	0.094	6.65	0.000
x ₂	0.921	0.190	4.85	0.000
x ₃	–0.510	0.920	–0.55	0.590

Source of Variation	Sum of squares	Degrees of freedom	Mean square	F-statistic	p-value
Regression	84	3	28	4	0.027
Error	112	16	7
Total	196	19

a. Is there a significant relationship between an individual's income and the set of variables, age, level of education, and gender (based on a significance level
^α
⁼05 )? Explain why using one of the p-values in the output tables.

b.Which of the three predictor variables are significant at a significance level α =05 ?

c. What percentage of the variation in income can be accounted for by the estimated linear regression equation relating income to age, level of education, and gender?

Jun 08, 2022

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Shown below is a portion of a computer output for a linear regression analysis relating an individual's income ( y in thousands of dollars) to age ( x 1 in years), level of education ( x 2 ranging...

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