1. a) The output given below is obtained for regression of Time on INC (X) Compl

Question

1. a) The output given below is obtained for regression of Time on INC (X) Complete the following ANOVA for the straight -line regression of Time (Y) on INC (X) Source d.f MS Regression Residual Total Lack of fit Pure error 18 5 24 b) Complete the following ANOVA table for the quadratic regression of Time (Y) on INC (X) Source d.f MS Degree (X) Regression Degree 2 (x ix) Residual Pure error Lack of fit 17 Total e 300 Toman 24 Higher Eaucation c) Calculate and compare the R2-values obtained for the straight-line, quadratic, and cubic fits d) Carry out F tests for the significance of the straight-line regression and for the fit of the straight-line model Carry out F tests for the significance of the quadratic regression and for the fit of the straight-line model Which model is most appropriate: straight-line, quadratic, or cubic? e) f)

Explanation / Answer

a)

442.9145/135.1628

=3.2769

b)

442.9145/19.5793

=22.62157

2100.0807/19.5793

=107.2603

(c)

R^2 for Linear relation = SSR/ SST = 442.9145 / 2891.046 = 0.1532

R^2 for Quadratic relation = SSR/ SST = (442.9145+2100.0807) / 2891.046 = 0.8796

R^2 for Cubic relation = SSR/ SST = (442.9145+2100.0807+61.1002) / 2891.046 = 0.9007

So, R^2 for Quadratic and Cubic relation are very high and almost same.

(d)

From (a), F = 3.2769 with df for SSR and SSE as 1,18

p-value of F = 3.2769 and df = 1,18 is 0.08699.

As, p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that straight line regression is not significant model.

(e)

The F test statistic of quadratic term in quadratic regression is 107.2603 with df = 1, 17

p-value of F = 107.2603 and df = 1,17 is 0.

As, p-value is less than 0.05, we reject the null hypothesis and conclude that quadratic regression term is significant and qudratic regression is a significant model.

(f)

As, the Type I sum of squares for Quadratic is very large compared to Linear and Cubic, Quadratic term in the regression cpatures the largest percentage of variation of the resonse variable and hence the qudratic model is most appropriate.

Source df SS MS F Regression 1 442.9145 442.9145/1 = 442.9145

442.9145/135.1628

=3.2769

Residual (Lack of fit) 18 271.7487 + 2100.0807 + 61.1002 = 2432.93 2432.93/18 = 135.1628 Residual (Pure error) 5 15.2012 15.2012/5 = 3.04024 Total 24 442.9145 + 2432.93 + 15.2012 = 2891.046 2891.046/24 = 120.4602

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