AMS2320 Business Regression Analysis Assignment 1 Semester 2, 2024-25 | HSUHK

AMS2320 Assignment 1

There are two questions. Please answer all questions and show your steps clearly. Correct your numerical answers to 4 decimal places. You may use SAS and/or R to do the calculations. Please include the program codes in your answer script. Combine all materials in a single PDF file with the file name: AMS2320 Assignment 1 - [StudentID].pdf (e.g. AMS2320 Assignment 1 - s123456.pdf) and submit it via Moodle. 

Question 1. Consider the following hypothetical data on rainfall and crop yield 

(a)[5 marks] Obtain a scatter plot for the variables rainfall (x-axis) and crop yield (y-axis). 

Consider the simple linear regression model 

(Yield)=β0+β1 (Rainfall) +Error .(0.1) 

Here, we assume that the error terms are independent Normal random variables N (0, σ2 ) with unknownσ2. 

(b)[5 marks] Obtain the least square estimate of (β0, β1 ). 

(c)[5 marks] Obtain 95% confidence intervals forβ0andβ1 . 

(d)[5 marks] Give an estimate ofσ2 . 

(e)[5 marks] Construct the corresponding ANOVA table. 

Consider another regression model 

(Yield)=α0+α1(Rainfall) +α2 (Rainfall)2 +Error .(0.2) 

Here, we assume that the error terms are independent Normal random variables N (0, τ2 ) with unknownτ2. 

(f)[5 marks] Obtain the least square estimate of (α0, α1, α2 ). 

(g)[5 marks] Obtain 95% confidence interval forα0, α1,andα2 . 

(h)[5 marks] Give an estimate ofτ2