STA 108 Homework 6 Solutions
Problem 7.22:
This can be explained by multicollinearity. For example, when you do a t-test for single 1 and 2 and get
the result that an estimate is statistically signicant, but when you do an F test for simultaneous inferenc
HW2 Brief Solution
HW 2: 2.1, 2.3, 2.7, 2.15 (a,b,c only), 2.22, 2.25
It is mainly for checking numerical answers, only partial steps are provided here.
The discussion 3 notes examples also provides some partial steps.
Students answers should contain reas
HW4 Brief Solution
HW #4: 3.13, 3.15, 3.16, 3.19, 4.1, 4.3
It is mainly for checking numerical answers, only partial steps are provided here.
Students answers should contain reasonable justifications or steps to some extent.
3.13
a.
H0 : E(Y ) = 0 + 1 X
H
HW3 Brief Solution
HW 3: 2.29, 2.42, 2.51, 3.2, 3.3, 3.10
It is mainly for checking numerical answers, only partial steps are provided here.
The discussion 4 notes examples also provides some partial steps or codes.
Students answers should contain reasona
Solutions to Homework 1, STA 108
Problem 1.2: The appropiate relationship is Y = 300 + 2X Since there is no error involved, it is a functional
relationship.
Problem 1.3: This objection is not valid, since there will be measurement error and there are othe
Solutions to Homework 2, STA 108
Problem 2.1:
a) Since the value zero does not fall within the condence interval for the slope, this suggests that there is
a linear relationship between Y and X. The implied level of signicance is = 1 0.95 = 0.05
b) Since
Solutions to Homework 4, STA 108
Problem 4.10:
a) For Xh = 45 : Yh = 102.7968, scfw_Yh = 1.7146, and W = 2 F1;1,n2 = 6.3119 = 2.5123. Then, the
joint condence interval is: Yh scfw_Yh W or 102.7968 1.7146 2.5123 or [98.4891, 107.1044].
For Xh = 55 : Yh =
Solutions to Homework 5, STA 108
Problem 7.1:
The number of degrees of freedom is the number of extra X variables, or the number of Xs we are interested
given the information on the other Xs. Therefore, the degrees of freedom are as follows:
Extra SS
(1)S
STA 108 Homework 7 Solutions
Problem 9.17:
a) In step 1, we add the variable X1 since it has the highest F value of 71.481.
In step 2, we add the variable X3 since it has the highest F value of 7.580.
In step 3, we see if we need to remove either X1 or X3
Solutions to Homework 3, STA 108
Problem 2.29
a) The appropriate plots are found below:
It is clear from the above graphs that there is more variation in Yi Y then in Yi Yi . Therefore we should
2
expect that SSR is bigger than SSE, and that the R value i
STA 108
Applied Linear Models: Regression Analysis
Spring 2011
Solution for Homework #1
1.2
Let Y = the dollar cost per year, X = the number of visits per year.
Then the mathematical relation between X and Y is: Y = 300 + 2X. This is a functional
relation
HW1 Brief Solution
HW 1: 1.2, 1.3, 1.4, 1.5, 1.7, 1.8, 1.21, 1.29
Reference only
Answers should contain reasonable justifications to some extent.
1.2 Y = 300 + 2X, functional
1.3 Some thoughts about measurement errors, or linear approximation, or other
152 Part One Simple Linear Regression
3.23. A linear regression model with intercept f30 = 0 is under consideration. Data have been
obtained that contain replications. State the full and reduced models for testing the appropriateness of the regression fun
Statistics 108
Homework 1 Solution
Due : October 3, 2016, In Class
1. When asked to state the simple linear regression model, a student wrote it as follows : E(Yi ) =
0 + 1 Xi + i . Do you agree? Why?
Solution:
No. The simple linear regression model is Yi
Statistics 108
Homework 2 Solutions
Due : October 10th, 2016, In Class
1. For the simple linear regression model
Yi = 0 + 1 Xi + i ,
i = 1, . . . , n,
where i s are independent with mean 0 and variance 2 , we use the method of least squares
and estimated
Statistics 108
Homework 4 Solutions
Due : October 24th, 2016, In Class
1. Tell true or false of the following statements and briefly justify your answer.
(a) A large R2 always means that the fitted linear regression line is a good fit of the data.
(b) A s
Statistics 108
Homework 3 Solution
Due : October 17th, 2016, In Class
1. For the simple linear regression model, let 1 be the least square estimator for the slope and
Yi be the fitted value for ith observation , show the following equalities:
Pn
2 Pn (Yi
STA 108: Applied Statistical Methods: Regression Analysis
Practice Midterm Exam
October 28, 2016, 2:10-3:00 pm
So Luff/0314
Print name:
Print section number:
Print student ID (last four digits):
Sign name: Instructions: This is a closed book exam. One pag
STA 108: Applied Statistical Methods: Regression Analysis
Midterm Exam
October 28, 2016: 2:103:00 pm
Print name: <0 iutnm
Print section number:
Print student ID (last four digits):
Sign name: Instructions: This is a closed book exam. One page of notes (do
Statistics 108
Homework 5 Solutions
Due : November 7th, 2016, In Class
1. Simple linear regression by matrix algebra in R. We revisit the Toluca Company data
in homework 1. Here, we practice to use matrix operations in R to do the problem. Attach
the enti
STA 108: Applied Statistical Methods: Regression Analysis
Practice Final Exam Solution
December 2, 2016
Print name:
Print section number:
Print student ID (last four digits):
Sign name:
1
Instructions: This is a closed book exam. Two pages of double-sided
. Drop all the cases having missing value(s). (There are other better ways to deal with
1
missing data and here we take the brutal easy way. You would end up with 366 cases.) You
may use the code:
> mydata = read.table("diabetesfull.txt", header=T)
> ind
HW 1: 1.2 1.3 1.4 1.5 1.7 1.8 1.21 1.29
Reference only
Answers should contain reasonable justifications to some extent.
1.2 Y = 300 + 2X functional
1.3 Some thoughts about measurement errors or linear approximation or
other good thoughts
1.4 The error i
1
3/30/16
"Statistical thinking will one day be as necessary for efficient citizenship as the ability to read
and write."
-H.G. Wells
Simple Linear Regression Model
Suppose for random variable Y the population mean changes based on another variable X
Let’