(a) First we will fit the first-order regression model y = ß0 + ß1x + e to the data and produce

the scatter plot of predictors xi and the residuals eˆi

.

i. Attach your R-code, regression results (the table), and the the scatter plot of xi and

eˆi

. (2 pt)

( You may refer to the last page of Lab note 2 to store figures in “png” file )

ii. Write down the equation of the fitted line from R output. (2 pt)

iii. From the scatter plot for the residuals eˆi versus xi

, do you detect any trends? If so,

what does the pattern suggest about the model fit (or lack of fit)? (2 pt)

(b) Now, we fit the quadratic model y = ß0 + ß1x + ß2x

2 + e and produce the the scatter plot

for the residuals eˆi versus x

2

i

i. Attach your R-code, regression results (the table), and the the scatter plot of x

2

i

and

eˆi

. (2 pt)

( You may refer to the last page of Lab note 2 to store figures in “png” file )

ii. Write down the fitted equation from R output (2 pt)

iii. Explain (a) the usefulness, (b) the explainability and (c) the model fit (and/or random

assumption satisfaction) of the quadratic model by referring to (a) F-statistics, (b)

R2

, and (c) the residual plot, respectively (2 pt)

iv. Has the addition of the quadratic term improved model adequacy, i.e., the quadratic

term is significant? Explain it with using a relevant hypothesis testing. (2 pt)

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