Statistics 108
Homework 1 (Solution)
Due : January 15, 2014, In Class
1. Please tell true or false of the following statements and briey justify your answer.
(a) The least squares line always passes the center of the data (X, Y ).
True since y = Y + 1 (x
Statistics 108
Homework 1
Due : January 15, 2014, In Class
1. Please tell true or false of the following statements and briey justify your answer.
(a) The least squares line always passes the center of the data (X, Y ).
(b) The true regression line ts the
Statistics 108
Homework 4
Due : February 5, 2014, In Class
1. Consider the simultaneous equations:
5y1 + 2y2 = 8
23y1 + 7y2 = 28
(a) Write these equations in matrix form.
(b) Use matrix algebra to nd the solutions.
2. Consider the following linear transfo
Statistics 108
Homework 7 (Solution)
Due : March 5, 2014, In Class
1. Tell true or false of the following statements. Briey justify your answer.
(a) To quantify a qualitative variable with three classes C1 , C2 , C3 , we need the following
indicator varia
STA108 Homework6
due: 02/26/2015, 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
Statistics 108
Homework 3
Due : January 29, 2014, In Class
1. A simple linear regression case study by R. You must use R and the lm function
and its associated functions to do this problem. Please also attach your R codes.
A persons muscle is expected to
Statistics 108
Homework 8
Due : March 12, 2014, In Class
1. Tell true or false of the following statements. Briey justify your answer.
(a) A correct model must be a good model.
2
2
(b) With the Rp criterion, we aim to select models with the largest Rp .
(
Statistics 108
Homework 3
Due : January 29, 2014, In Class
1. A simple linear regression case study by R. You must use R and the lm function
and its associated functions to do this problem. Please also attach your R codes.
A persons muscle is expected to
STA 108
Regression Analysis
Fall 2015
Final Exam Practice Problems
Disclaimer: These are practice problems for topics from the last third of the class (after midterm 2). The problems
merely showone way for the more recent topics to appear on the final exa
Statistics 108
Homework 8 (Solution)
Due : March 12, 2014, In Class
1. Tell true or false of the following statements. Briey justify your answer.
(a) A correct model must be a good model.
FALSE. A correct model is one has little bias, but it may have larg
Statistics 108
Homework 7
Due : March 5, 2014, In Class
1. Tell true or false of the following statements. Briey justify your answer.
(a) To quantify a qualitative variable with three classes C1 , C2 , C3 , we need the following
indicator variables:
X1 =
STA 108
Regression Analysis
Fall 2015
Midterm 2 Practice Problems - Solutions
Part I - True/False
You may receive up to 2 points for each of the following problems. You receive one point for correctly stating whether
the statement is true or false. You ma
STA 108
Regression Analysis
Fall 2015
Midterm 1 Practice Problems - Solutions
Part I - True/False
You may receive up to 2 points for each of the following problems. You receive one point for correctly stating whether
the statement is true or false. You ma
STA 108
Regression Analysis
Fall 2015
Final Exam Practice Problems - Solutions
Disclaimer: These are practice problems for topics from the last third of the class (after midterm 2). The problems
merely showone way for the more recent topics to appear on t
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 6
Due : November 14th, 2016, In Class
1. Multiple linear regression by matrix algebra in R.
We study the river pollution data (Rivers.txt). We will consider building regression models
with Nitrogen as the response variable as the l
Statistics 108
Homework 1
Due : October 3rd, 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?
2. The Toluca Company manufactures refrigeration equipment as
Statistics 108
Homework 4
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 small R2 al
Statistics 108
Homework 2
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 the parame
Statistics 108
Homework 5
Due : November 17th, 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 entire R code
Statistics 108
Homework 3
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 Y )2 + P
STA 108
Applied Statistics:
Regression Analysis
Lecture 18
Shan-Yu(Angela) Liu
Department of Statistics
University of California, Davis
Feb 24th, 2016
Topics For Today
Recap:
Multiple linear regression in R
Today:
1. ANOVA in multiple regression
Reference
STA 108
Regression Analysis
Fall 2015
Midterm 1 Practice Problems
Part I - True/False
You may receive up to 2 points for each of the following problems. You receive one point for correctly stating whether
the statement is true or false. You may then recei
STA 108
Regression Analysis
Fall 2015
Midterm 2 Practice Problems
Part I - True/False
You may receive up to 2 points for each of the following problems. You receive one point for correctly stating whether
the statement is true or false. You may then recei
Statistics 108, Final Project
Due : December 2nd, In Class
The final project is an opportunity to put all you have learned in STA 108 in action. Your task
is to conduct a start-to-finish statistical analysis of a real data set. I will guide you through ho
STA 108
Applied Statistics:
Regression Analysis
Lecture 14
Shan-Yu(Angela) Liu
Department of Statistics
University of California, Davis
Feb 8th, 2016
Topics For Today
Recap:
simultaneous inference
inverse prediction
Today:
1. multiple regression models
2.
STA 108
Applied Statistics:
Regression Analysis
Lecture 15
Shan-Yu(Angela) Liu
Department of Statistics
University of California, Davis
Feb 10th, 2016
Topics For Today
Recap:
matrix algebra
Today:
1. multiple regression models
2. Matrix representation of
STA 108
Applied Statistics:
Regression Analysis
Lecture 16
Shan-Yu(Angela) Liu
Department of Statistics
University of California, Davis
Feb 17th, 2016
Topics For Today
Recap:
Review
Today:
1. Review
Announcement
oce hour: W 3-5pm
Midterm: Friday, Feb 19th
STA 108
Applied Statistics:
Regression Analysis
Lecture 17
Shan-Yu(Angela) Liu
Department of Statistics
University of California, Davis
Feb 22th, 2016
Topics For Today
Recap:
I Matrix representation of least squares solution
I Matrix algebra
Today:
1. Mul