代写STATS 3860B、代写R语言编程

日期：2023-03-20 09:41

Assignment 3

STATS 3860B/9155B

Winter 2023

This assignment is due Monday, April 10th, at 11:55 pm.

You must write your R code and answers using Rmarkdown generating a

single pdf file.

Submissions must be made via Gradescope. You must carefully assign each

question part to its corresponding page (or pages) on your pdf file. Question parts

with no pages assigned to them will receive zero marks.

Each student must submit their own work. Scholastic offences are taken seriously,

and students are directed to read the appropriate policy, specifically, the definition of

what constitutes a Scholastic Offence, at the following Web site: http://www.uwo.ca/u

nivsec/pdf/academic_policies/appeals/scholastic_discipline_undergrad.pdf

Question 1

The denim dataset concerns the amount of waste in material cutting for a jeans manufacturer

due to five suppliers. Consider the code below to first remove two outliers from the dataset.

library(faraway)

data(denim)

### removing 2 outliers

denim <- denim[-which(denim$waste == max(denim$waste)),]

denim <- denim[-which(denim$waste == max(denim$waste)),]

dim(denim); head(denim)

## [1] 93 2

## waste supplier

## 1 1.2 1

## 2 16.4 2

## 3 12.1 3

## 4 11.5 4

## 5 24.0 5

## 6 10.1 1

1

a) Plot the data and comment.

b) Fit the linear fixed effects model. Is the supplier significant?

c) Analyze the data with supplier as a random effect. What is the estimated standard

deviation of the supplier random effect?

d) Regarding the model fitted in c), test the significance of the supplier term. Compare

with the results in b).

e) Compute confidence intervals for the random effects standard deviations. Compare with

the results in d).

Question 2

Refer to Exercise 2 page 251 of the textbook. Dataset hprice. Work on parts a) to g).

library(faraway)

str(hprice)

## 'data.frame': 324 obs. of 8 variables:

## $ narsp : num 4.22 4.27 4.33 4.36 4.39 ...

## $ ypc : int 13585 14296 15413 16490 17634 18210 17958 18659 19360 15354 ...

## $ perypc : num 6.47 5.23 7.81 6.99 6.94 ...

## $ regtest: int 20 20 20 20 20 20 20 20 20 18 ...

## $ rcdum : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...

## $ ajwtr : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...

## $ msa : Factor w/ 36 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 2 ...

## $ time : int 1 2 3 4 5 6 7 8 9 1 ...

Question 3

The data set prostate (library faraway) is from a study of 97 men with prostate cancer who

were due to receive a radical prostatectomy. Consider lweight as the response and only age

as a predictor.

a) Plot the data and fit a curve using kernel methods with a cross-validated choice of

bandwidth. Plot the fit on the top of the data. What is the effect of the outlier? Does

the fit look linear?

b) Compute the smoothing spline with default amount of smoothing (by cross-validation)

along with a 95% confidence band. Do you think a linear fit is plausible for these data?

2

Question 4

The mcycle dataset contains the head acceleration (y) over time (x) after impact when

simulating a motorcycle accident.

library(MASS)

data(mcycle)

str(mcycle)

## 'data.frame': 133 obs. of 2 variables:

## $ times: num 2.4 2.6 3.2 3.6 4 6.2 6.6 6.8 7.8 8.2 ...

## $ accel: num 0 -1.3 -2.7 0 -2.7 -2.7 -2.7 -1.3 -2.7 -2.7 ...

a) Fit a regression splines to these data with 40 basis functions. Plot the data along with

the fitted curve. Comment on the estimated function obtained by this fit.

b) Compute the percentage of the variance in y explained by the regression splines fit

obtained in a) adjusting for the degrees of freedom (that is, taking into account the

number of parameters).

c) Fit a smoothing splines fit choosing λ by cross-validation. Plot the data along with the

fitted curve and compare it with the fitted curve in a).

d) Compute the percentage of the variance in y explained by the smoothing splines fit

obtained in c) adjusting for the degrees of freedom. Compare with the result obtained

in part b).