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

(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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