Homework 1 Solutions
#1.5
No. The simple linear regression model is
#1.6
For : The expected value of Y when X=0 is 200.
For : When X increases by one unit, the expected value for Y increases by 5.0.
#1.20
a)
>data=read.table("CH01PR20.txt",header=T)
>atta
Statistics 108
Homework 1 (Due Friday, Oct 7)
Problems: 1.6, 1.7, 1.22, 1.26, 1.29, 1.30, 1.33
1.6 (b) 0 is the value of Y when X=0. 1 is the slope of the regression line. It is the corresponding change i
STA108 Homework7
due: 03/04/2015, Wed, in class
1. Simple linear regression in matrix form. In this problem, you will perform linear
regression of a response Y on a predictor X using matrix algebra (Your calculations should
be solely based on matrix algeb
Homework 2 Solutions
#2.1 a
Since the 95% confidence interval for 1 does not include 0, then we would reject 0 : 1 = 0 at the 0.05
significance level. So the students conclusion is warranted.
#2.4
a)
>
>
>
>
>
>
>
data = read.table("CH02PR04.txt", header
STA108 Homework3
due: 01/29/2015, Friday, in class
For all questions you must show your work. This enables us to understand your
thought process, give partial credit and prevent crude cheating.
If you use R then you must turn in a printout of your R outpu
STA108 Homework2
due: 01/21/2015, Wed, in class
1. Problem 1.7
Solution:
(a) No, because we dont know any distribution assumptions of error terms here.
Hence we dont have any distribution of Yi as well. Therefore we couldnt estimate
the probability for Y
Statistics 108
Homework 5
Due : November 10, 2014 (Monday), In Class
* Put your name and your section number on your homework.
1. Simple linear regression in matrix form. In this problem, you will perform linear
regression of a response Y on a predictor X
Homework 3
Spring 2015
STA 108
Problem 14
15
20
25
30
35
a) The boxplot looks pretty symmetric with no obvious outliers
c) The residual vs. tted value plot can help to diagnose heteroscedasticity (nonconstant variance), as well as any patterns in the resi
R Output Problems
Spring 2015
STA 108
Copier Maintenance
The Tri-City O ce Equipment Corporation sells an imported copier on a franchise
basis and performs preventative maintenance and repair service on this copier. The
data below have been collected from
STA108 Homework2
due: 01/22/2015, Friday, in class
For all questions you must show your work. This enables us to understand your
thought process, give partial credit and prevent crude cheating.
If you use R then you must turn in a printout of your R outpu
STA108 Homework4
due: 02/04/2015, Wed, in class
1. Problem 2.10
Solution:
(a) prediction interval (b) condence interval (c) prediction interval
2. Problem 2.17
Solution:
> 0.33 and conclude H0
An analyst concluded that Ha : = 0 which means the null hypot
STA 108: Applied Statistical Methods: Regression Analysis
Practice Final Exam Solution
December 19, 2014: 8:00-10:00am
Print name:
Print section number:
Print student ID (last four digits):
Sign name:
1
Instructions: This is a closed book exam. Two pages
Statistics 108
Homework 5
Due : November 10, 2014 (Monday), In Class
* Put your name and your section number on your homework.
1. Simple linear regression in matrix form. In this problem, you will perform linear
regression of a response Y on a predictor X
STA 108
Regression Analysis
Fall 2015
Homework 2 Solution
Assignment:
Textbook problems 2.7, 2.17, 2.18, 2.19, 2.26, 3.6 (only a-c), 3.9, 3.17
(in 3.17b you may calculate R2 instead of SSE and choose the transformation that maximizes R2 )
The R code used
Statistics 108
Homework 8
Not Due
1. Diabetes data. This data consist of 16 variables on 403 subjects from 1046 subjects who
were interviewed in a study to understand the prevalence of obesity, diabetes, and other
cardiovascular risk factors in central Vi
15
5
10
Dataset$Y
20
25
Homework 7 Solution
a. Y=21.09+1.14C-
0.12C2, here C = X-
mean(X)
10
15
20
25
Dataset$X
The solid black dots represent the fitted regression function. The quadratic regression
function does a
1
Homework 3
Due in class, Feb. 8th
STA 108, Winter 2013
Problem 1 (Airfreight Breakage)
Refer to the Airfreight Breakage data in homework 1
i:
Xi :
Yi :
1
1
16
2
0
9
3
2
17
4
0
12
5
3
22
6
1
13
7
0
8
8
1
15
9
2
19
10
0
11
a. Set up the ANOVA table. (calc
Homework 5 Solutions
ACM/ESE 118, Fall 2008
Date: 11/25/2008.
(1) Air Pollution and Mortality
Before going on to a more detailed analysis, as a rst pass we can try simply tting all
the data using all the regressors. We get the following:
Coefficients:
Est
Stat 108 HW #5 Solution
5.22 Y12+ 3Y22+ 9Y32+8 Y1Y3
6.15 a. One way of doing the stem-
and-
leaf plots (there are other ways of choosing
the stems, which may be also ac
STA 108 B1-B2 Spring 2015
MIDTERM 1
Note: This is a closed book, closed notes exam. You can bring one page {twosided) with your own
handwritten notes and a handheld calculator. For all problems, give brief but complete solutions. You
must show your work
Statistics 108
Homework 2
Due : October 17, 2014, In Class
* Put your name and your section number on your homework.
1. For the simple linear regression model (1.1) in the textbook, show the following properties of
the residuals ei = Yi Yi .
(a)
(b)
n
i=1
Solutions to Project 1, STA 108
Part I:
Part a): Let Y = the number of active physicians, X1 = total population, X2 = number of hospital beds,
and X3 =total personal income. Since we are interested in seeing how the number of active physicians varies,
our
1
Homework 8
Due in class, March 15th
STA 108, Winter 2013
Problem 1
State the number of degrees of freedom that are associated with each of the following extra sums of
squares:
1. SSR(X1 |X2 )
df [SSR(X1 |X2 )] = 1
2. SSR(X2 |X1 , X3 )
df [SSR(X2 |X1 , X
1
Homework 4
Due in class, Feb. 15th
STA 108, Winter 2013
Problem 1 (Grade Point Average)
Refer to Grade point average data in Problem 1.19. The data can be downloaded or read into R from:
http:/www.stat.lsu.edu/exstweb/statlab/datasets/KNNLData/CH03PR03.
Statistics 108
Homework 2 Solution
Due : October 17, 2014, In Class
* Put your name and your section number on your homework.
1. For the simple linear regression model (1.1) in the textbook, show the following properties of the
residuals ei = Yi Yi .
(a)
Statistics 108
Homework 6
Due : November 26, 2014 (Wednesday), In Class
* Put your name and your section number on your homework.
1. A multiple linear regression case study by R (contd). You may quote results from
homework 5.5. Please also attach your R c
STA108 Homework1
due: 06/29/2015, Monday, in class
For all questions you must show your work. This enables us to understand your
thought process, give partial credit and prevent crude cheating.
If you use R then you must turn in a printout of your R outpu
Fornlulas ( l.30a) and (1.30b) are identical to the earlier least squares normal equations ( 1.9), and
formula ( 1 . 3 0 ~i)s the biased estimator of a given earlier in (1.27).
'
j estimates
of
Cited
References
n Figure 1.9b.
ares estimators
:gression mod
1
STA108 fall 2016 Homework 6 solutions
typo fixed 11/8/16 10:30am
fixed another typo 11/8/16 12:30
Part A
1. Show that the sum of residuals is 0. That is show that
n
X
(yi yi ) = 0
i=1
Hints:
(a) start with
n
P
(yi yi )
i=1
(b) yi = b0 + b1 xi so substit
1
STA108 fall 2016 Homework 5 solutions
Part A
Suppose we have run a regression model with n = 30 (x, y) pairs. The sample variance of
y1 , . . . , y30 is 946 and the MSE is 822.
1. Find the SSR (sum of squares regression).
To find the SSR, we first find
1
STA108 fall 2016 Homework 4 solutions
The simple linear regression model is
Yi = 0 + 1 xi + i for i = 1, . . . , n
(1)
where Yi is a random variable for the outcome of the ith experimental unit, 0 and 1 are
parameters and i is a random variable. We make