Question

Multiple regression

Please show all work on paper.

For a sample of n= 20 individuals, we have measurements of y = body fat, x1 = triceps skinfold thickness,

x2 = thigh circumference, and x3 = mid-arm circumference. The result of a multiple linear regression

applied to these data is:

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Model 1:

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 117.085 99.782 1.173 0.258

Triceps 4.334 3.016 1.437 0.170

Thigh -2.857 2.582 -1.106 0.285

Midarm -2.186 1.595 -1.370 0.190

Residual standard error: 2.48 on 16 degrees of freedom

Multiple R-squared: 0.8014, Adjusted R-squared: 0.7641

F-statistic: 21.52 on 3 and 16 DF, p-value: 7.343e-06

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(a) Is this a good model fit? Explain.

(b) If you were to apply backwards stepwise variable selection/elimination, the Thigh variable would be

removed first. Explain why?

(c) The result of a multiple linear regression applied to the data, removing the Thigh variable (model 2) is:

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Model 2:

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 6.7916 4.4883 1.513 0.1486

Triceps 1.0006 0.1282 7.803 5.12e-07 ***

Midarm -0.4314 0.1766 -2.443 0.0258 *

Residual standard error: 2.496 on 17 degrees of freedom

Multiple R-squared: 0.7862, Adjusted R-squared: 0.761

F-statistic: 31.25 on 2 and 17 DF, p-value: 2.022e-06

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d) Which of the two models would you use based on these outputs? Justify your reasoning.

Answer 1