Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: THEend8_
STAT3008: Applied Regression Analysis
Chapter 1 Introduction
Terminologies: Response Variable (RV), Explanatory Variable (EV)
Mean Function and Variance Function
Separated Points: Outlier and Leveraged Point
Scatterplot and Scatterplot Matrix
Null Point: Constant mean and variance functions, no separated point
Chapter 2 Simple Linear Regression
OLS Estimates: Derivation
Terminologies: Fitted Value, Residuals, RSS
Properties of the OLS Estimates: Biasness and Variance
Maximum Likelihood Estimates: Derivation and Comparison against OLS Estimates
Analysis of Variance:
Decomposition of Sum of Squares (SSreg, RSS, SStotal)
Construction of ANOVA table
ANOVA Table vs Coefficient Table
Coefficient of Determination R2
Test for Betas, Confidence Interval for Fitted Value
Prediction Interval for based on new
Chapter 3 Multiple Linear Regression
Random Vector, Model Setup
OLS Estimates: Derivation, Vector/Matrix Differentiation and Trace Operation
Properties of the OLS Estimates
Biasness and Variance, Asymptotic Distribution of the OLS Estimates
Expected Value and Variance of Random Matrix
Maximum Likelihood Estimates
Analysis of Variance: Decomposition of Sum of Squares, Construction of ANOVA table
Coefficient of Determination R2
Test for Betas, Confidence Interval for Fitted Value
Prediction Interval for based on new
Questions from previous STAT3008 students
1. Is p-value computed based on one tail or two tails of the distribution?
2. How to compute SSreg if there is only one regression model specified in the problem?
*y *x
*y *x
Practice Exercises
Problem 1: Consider multiple linear regression with 3322110)|( xxxYE xX with
sample size n = 9. The coefficient table on the left shows the OLS estimates
The ANOVA table on the right tests the hypotheses:
H0: 110)|( xYE xX vs H1: 3322110)|( xxxYE xX
(a) Based on a T-statistic and a p-value from the Coefficient Table, construct the ANOVA table for
the hypotheses
H0: 22110)|( xxYE xX vs H1: 3322110)|( xxxYE xX
(b) Based on the given ANOVA table and the results from part (a), construct the ANOVA table for
the hypotheses
H0: 110)|( xYE xX vs H1: 22110)|( xxYE xX
(c) What conclusion can you draw from the ANOVA table from part (b)?
Problem2: Suppose x1, x2, …xn are known constants. Let y1, y2, …yn be independent random
variables with mean 0 and variance