Show your work and clearly explain each step (and your answer). You may only use

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Show your work and clearly explain each step (and your answer).

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2. QUESTION 2 20 pts The following regression model was fit based on measurements from an exper iment growing white pine trees conducted by the Department of Biology at Kenyon College ## Call: ## lm(formula-Hgt97 ~ Hgt90) ## Residuals: ##-261.886-44.343 7.308 55.114 196.114 ## Coefficients Min 1Q Median 30 Max ##(Intercept) 307.439 ## Hgt90 Estimate Std. Error t value Pr >ltI) 9.841 31.239

Explanation / Answer

A)

Ho: there is no significant linear relationship

H1: there is a significant linear relationship

With F=22.28, p<0.05, I reject ho and conclude that there is a significant linear relationship.

B)

R^2 = 2.687%

There is 2.687% variation in Hgt97 which is explained by Hgt90. This percentage is very less and hence fitted model is NOT a good fit to data.

C)

r= sqrt(R^2) = sqrt(2.687%) = 0.163921

D)

I know that,

SE = sqrt(SSE/df_error)

78.79 = sqrt(SSE/807)

SSE= =78.79^2*807

SSE= 5009746.329

I also know that,

R^2 = SSR/SST = 1-SSE/SST

.02687 = 1-5009746.329/SST

5009746.329/SST = 0.97313

SST= =5009746.329/0.97313

SST= 5148075.107

Thus,

SSR = SST-SSE= =5148075.107-5009746.329

SSR = 138328.778

table:

SOURCE df SS MSS F p-value model 1 138328.8 =138328.8 22.28 0.000002772 residual 807 5009746 =5009746.329/807 total =1+807 5148075

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