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Statistics 3022 Assignment 2
1. (True False questions) Textbook Problem 2.2, 2.4, 2.5, 2.6, 2.7 (page 81). If it is false, give a reason.
2. (Multiple choice question) Textbook Problem 2.8 (page 81)
For Problem 3 through 5: Priscilla Erickson from Kenyon College collected data on a stratified random
sample of 116 Savannah sparrows at Kent Island, New Brunswick, Canada. The weight (in grams) and wing
length (in mm) were obtained for birds from nests that were reduced, controlled, or enlarged. You are only
allowed to use the provided R outputs.(Sparrows data as in the previous homework)
summary(model)
##
## Call:
## lm(formula = Weight ~ WingLength, data = data_Sparrows)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.5440 -0.9935 0.0809 1.0559 3.4168
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.36549 0.95731 1.426 0.156
## WingLength 0.46740 0.03472 13.463 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.4 on 114 degrees of freedom
## Multiple R-squared: 0.6139, Adjusted R-squared: 0.6105
## F-statistic: 181.3 on 1 and 114 DF, p-value: < 2.2e-16
3. (Sparrow) Perform t-test and conclude whether the slope of the least squares regression line for prediction
Weight from WingLength is non-zero. Use summary(model) output above.
(a) State the null and alternative hypothesis.
(b) Identify and interpret the t-test statistic and p-value from R output above.
(c) Draw the conclusion with α = 0.05 and interpret it in the context of the problem.
4. (Sparrow) Use anova(model) output to calculate Multiple R-squared ( in R output above.) and interpret
it. Show your work. (Hint: R-squared = (Variability explained by model)/(Total variability in y))
5. (Sparrow) Use the following outputs only to construct 95% confidence interval of β1 (slope) of the
model and interpret in the context of the problem. Does it agree with your conclusion from Problem 3
above? Explain.
(n<-nrow(data_Sparrows))#number of observations
## [1] 116
qt(0.975, n-2)
## [1] 1.980992
1
qt(0.95, n-2)
## [1] 1.65833
For Problem 6 through 8 In the website and online forum RateMyProfessors.com, students rate and comment
on their instructors. Launched in 1999, the site includes millions of ratings on thousands of instructors.
The data includes the summaries of the ratings of 364 instructors and a large campus in the Midwest
(Bleske-Rechek and Fritsch, 2011). Each instructor included in the data had at least 10 ratings over a several
year period. Students provided ratings of 1-5 on quality, helpfulness, clarity, easiness of instructor’s courses.
Use R command below to import the data set. In this problem we want to predict quality rating from
helpfulness rating. You may use predict() or manually calculate each answer based on R regression model
summary. rmp<-read.csv(“http://users.stat.umn.edu/~sandy/alr4ed/data/Rateprof.csv”)
6. (Rmp) Use R to construct the estimated regression model with quality as the response variable and
helpfulness as the predictor. Based on your model, What is the estimated quality rating for a randomly
selected professor if his/her helpfulness rating is 3.
7. (Rmp) Use R to construct a 95% confidence interval to estimate the mean quality rating if helpfulness
rating is 3. Interpret the result.
8. (Rmp) Use R to construct a 95% prediction interval to estimate Professor John’s quality rating if his
helpfulness rating is 3. Interpret the result.
9. Textbook Problem 3.1 (page 149)
10. Textbook Problem 3.2 (page 149)
11. Textbook Problem 3.11 (page 151 and 152).
12. Textbook Problems 3.3 and 3.15 (page 149 and 153)
2

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