STAT 425 Homework 1 Solutions
Spring 2015
1.
(a) Since RSS ( 0 , 1 ) =
n
( y
i
2
0
1 xi ) , take the partial derivative with respect to 0 :
i =1
n
RSS
= 2 ( yi 0 1 xi ) = 0
0
i =1
(1)
Take the partial derivative with respect to 1 :
n
RSS
= 2 ( yi 0 1 x
STAT 425 Spring 2016 Sections 1UG, 1GR
Homework 1 - Solution
Problem 1
(a). Take the derivative of RSS, and set the resulting expression equal to zero:
d RSS(1 )
=
d1
n
n
2xi (yi xi 1 ) = 2(
i=1
n
x2 ) = 0
i
x i y i 1
i=1
(1)
i=1
(b). Solve the equation (
STAT 425 Fall 2013 Sections S1U, S1G
Homework 8
Please submit your assignment on paper, following the Formatting Guidelines for Homework
Submission. (Even if correct, answers might not receive credit if they are too dicult to read.)
Remember to include re
1. Using the sat dataset, t a model with the total SAT score as the response and expend,
salary, ratio and takers as predictors. Perform regression diagnostics on this model to answer
the following questions, and display any plots that are relevant.
a. Ch
STAT 425 Spring 2016 Sections 1UG, 1GR
Homework 1
Please submit your assignment on paper, following the Formatting Guidelines for Homework
Submission. (Even if correct, answers might not receive credit if they are too dicult to read.)
Remember to include
STAT 425 ~— Section 1UG7 1GB; ~— Spring 2016
Midterm Exam l
March 2, 2016
€
Full Name: K y
s This is an 80 minute exam. There are 6 problems. worth a total of 60 points.
a You may use two pages of personal notes and a standard scientiﬁc calculator. (You i
STAT 425 Fall 2013 Sections S1U, S1G
Homework 5
Please submit your assignment on paper, following the Formatting Guidelines for Homework
Submission. (Even if correct, answers might not receive credit if they are too dicult to read.)
Remember to include re
STAT 425 - 2015 Spring
Homework 3 Solution
Problem 1
$
(a) Note that z = r + z ,
$
$
$
Y = [U z ] + = U r + z + = U + r + z p + = U + z p + r p +
p
p
(
)
(
1
1
)
= U + U (U TU ) U T z p + r p + =U + (U TU ) U T z p + r p +
+ (U TU ) 1 U T z
p
+
STAT 425 HW 1
3.
a
> fit <- lm(Wt~Sex+Ht+SSF+Bfat,data=ais)
> summary(fit)
Call:
lm(formula = Wt ~ Sex + Ht + SSF + Bfat, data = ais)
Residuals:
Min
1Q Median
3Q Max
-13.8944 -4.7384 -0.7099 3.5957 31.6139
Coefficients:
Estimate Std. Error t value Pr(>|t|
STAT 425 HW 2 1UG
Name : Bo Yang NetID: boyang3
1.
> fit<-lm(Distance~Speed,data=stopping)
> par(mfrow=c(2,2)
> plot(fit, add.smooth=FALSE)
Theseareefourdefaultdiagnosticplots
(b)
Fromthefirstplot,weseethatthereisslightcurvaturerelation,butnotsoobvious.
B
STAT 425 Spring 2015
Homework 1
(Posted on Friday Jan. 23; Due Friday Feb. 6)
Please submit your assignment on paper, following the Guidelines for Homework Write-Ups and
Submissions. (Even if correct, answers might not receive credit if they are too dicul
STAT 425 Spring 2015
Homework 2
(Posted on Friday Feb. 6; Due Friday Feb. 20)
Please submit your assignment on paper, following the Guidelines for Homework posted at course
website. (Even if correct, answers might not receive credit if they are too dicult
STAT425
Fall 2012
Homework #2
Sep 14, 2012
Homework 2
Due: Sep 21, 2012
Problem 1. (2pt) Find a formula relating R2 and the F -test (H0 : intercept-only model; Ha :
the full model) for regression.
Problem 2. The following are outputs from R. Some outputs
STAT 425 HW4
Suggested Solution
1. (a) By using R commands, we can get the following diagnostic plots for the specic
model M ILIM P log(SP EN D).
20
40
FORD
60
0
1
2
PEPSI
1
20
0
BUDLITE
2
Standardized residuals
Normal QQ
PEPSI
40
Residuals
40
Residuals v
STAT425
Fall 2013
Homework 4
Due: Nov 1, 2013
Problem 1. (6+6+6=18pt)The aatemp data come from the U.S. Historical Climatology network. They are the annual mean temperatures (in degrees F) in Ann
Arbor, Michigan going back about 150 years.
(a) Fit a polyn
STAT 425 Spring 2015
Homework 2 Due Feb 20
Solutions
1.
(a). Equating the two equations:
0 + 1 xi + i = 0 + 1 (xi x ) + i
0 + 1 xi + i = 0 1 x + 1 xi + i
0 = 0 1x
1 = 1 (or 0 = 0 + 1 x 1 = 1 )
1 x x
1
0
=
, X = 1 x2 x
1
(b). y = X +
1 xn x
Unit 1 : Basic Concepts and Introductory Regresssion Analysis
Sources : Chapter 1. Historical perspectives and basic denitions (Section 1.1). Planning and implementation of experiments (Section 1.2). Fishers fundamental principles (Section 1.3). Simple li
STAT 425 Spring 2016 Sections 1UG, 1GR
Homework 3 - Solution
Note: all R-code is attached in the appendix.
Problem 1
(a). The pairs plot of all variables is shown in Figure 1.
220
280
20
60
100
15 20 25
2600000 3200000
1990 2005
160
240
year
130
160
allUs
HW 7, STAT 425, Yue Wang, graduate 4 credit
Problem 1
a)
ghlogit<-glm(tumor/total~dose,family=binomial)
b)
c) Predicted values and deviance residuals are shown below:
> predict(ghlogit,type="response")
1
2
3
4
5
6
0.04439547
0.99759230
0.04841829
0.068216
STAT 425 Fall 2013 Sections S1U, S1G
Homework 4
Please submit your assignment on paper, following the Formatting Guidelines for Homework
Submission. (Even if correct, answers might not receive credit if they are too dicult to read.)
Remember to include re
STAT 425 Homework 5
March 30, 2014
1. Solution
a. Here is the summary:
> d e s t r o y e r s = r e a d . t a b l e ( C: \ \ U s e r s \ Long Tao\ Downloads \ d e s t r o y e r s . dat ) ;
> f i t 1=lm ( l o g ( D i s p l a c e m e n t ) Length+Beam , data
STAT425
Fall 2014
Homework #4
Oct 23, 2014
Homework 4
Due: Friday, Oct 31, 2014
Problem 1. (Sheather, pp. 122, Ex 1) A full professor of statistics at a major US university
is interested in estimating the third quartile of salaries for full professors wit
STAT 425 m Section DlU, DIG Spring 2014
Midterm Exam I
March 5, 2014
Full Name: K Q7
9 This is a 50 minute exam. There are 5 problems for everyone, and one additional problem
for graduate students only.
a The exam is worth a total of 42 points for under
STAT 425 Fall 2014 Section S1U
Homework 1
Please submit your assignment on paper, following the Formatting Guidelines for Homework
Submission. (Even if correct, answers might not receive credit if they are too dicult to read.)
Remember to include relevant
STAT 425 Spring 2016 Sections 1UG, 1GR
Homework 3
Please submit your assignment on paper, following the Formatting Guidelines for Homework
Submission. (Even if correct, answers might not receive credit if they are too dicult to read.)
Remember to include
STAT 425 Spring 2016 Sections 1UG, 1GR
Homework 2
Please submit your assignment on paper, following the Formatting Guidelines for Homework
Submission. (Even if correct, answers might not receive credit if they are too dicult to read.)
Remember to include
STAT 425 ~— Sections TlU, TlG ~— Fall 2015
Midterm Exam II
December 97 2015
Full Name: H
o This is an 80 minute exam. There are 6 problems, worth a total of 57 points.
0 You may use three pages of personal notes and a standard scientiﬁc calculator. (You m