STAT 40001/STAT 50001 Homework 3 solved

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Q.N. 1) The R data frame ”HairEyeColor” contains classifications of 592 students by gender, hair color and eye
a) Is hair color independent of eye color for men?
b) Is hair color independent of eye color for women?

Q.N. 2)A clinical dietician wants to compare two different diets, A and B, for diabetic patients. She hypothesizes
that diet A (Group 1) will be better than diet B (Group 2), in terms of lower blood glucose. She plans to get a
random sample of diabetic patients and randomly assign them to one of the two diets. At the end of the experiment,
which lasts 6 weeks, a fasting blood glucose test will be conducted on each patient.

She also expects that the average
difference in blood glucose measure between the two group will be about 10 mg/dl. Furthermore, she also assumes
the standard deviation of blood glucose distribution for diet A to be 15 and the standard deviation for diet B to be
17. How many subjects are needed in each group assuming equal sized groups? (Please use α = 0.05 and Power=0.8).

Q.N. 3)Suppose that a fire insurance company wants to relate the amount of fire damage in major residential fires
to the distance between the burning house and the nearest fire station. The study is conducted in a suburb of a
major metropolitan area. The data collected were the distance in miles between the nearest fire station and the fire
and the amount of damage to the house ( in thousands of dollars).

Distance Damage
3.4 26.2
1.8 17.8
4.6 31.3
2.3 23.1
3.1 27.5
5.5 36.0
0.7 14.1
3.0 22.3

2.6 19.6
4.3 31.3
2.1 24.0
1.1 17.3
6.1 43.2
4.8 36.2
3.8 26.5

a) Fit a simple linear regression model and analyze the residual plots.
b) What is the expected Damage if the fire station is 4 miles away?
c) Use the Box-Cox transformation to choose an appropriate value of λ to improve the model.
d) Fit a simple linear regression model after transformation.
e) Compare and contrast models in (a) and (d).

Q.N. 4) An author maintains a website on a particular book and using Google Analytics, records the number of
visits on this particular website on each day of the year. As expected there are more hits during weekdays then on
weekends. Since the book is used as a textbook for a statistics course there are more hits during the time when the
classes are in session.

Table below provides the data for 35 weeks from April through November 2009. To explore
the week by week visit patterns of these
Week Hits
1 148
2 148
3 157
4 112
5 125
6 155

7 154
8 135
9 140
10 164
11 154
12 138
13 129
14 131

15 113
16 124
17 119
18 110
19 166
20 105
21 132

22 132
23 144
24 152
25 152
26 166
27 161

28 168
29 170
30 179
31 154
32 136
33 147
34 151
35 188

a) Display the data using a scatterplot.
b) Calculate the correlation coefficient to measure the association between the week and the number of hits on the
website. Check whether rank correlation is more appropriate than Pearson correlation
c) Test for the significance of the correlation at 0.05 level.

Q.N. 5) The data set cars is one of the data sets installed with R and is available in base package. The data set
contains 50 observations of speed(mph) and dist(stopping distance in feet).
a) Display the data using scatter plot.
b) Fit a simple regression model using speed as a predictor variable.
c) Add the fitted line to the scatter plot.

d) Calculate the residuals and fitted values and print only first five observations of the residuals and fitted values.
e) Create a scatter plot of the residuals and fitted values.
f) Assuming that no intercept model is appropriate fit a simple linear regression model.
g) Calculate and compare the coefficient of determination for both the with intercept and no-intercept models.
h) Using your fitted model predict the stopping distance for a car with an speed of 21 mph.