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Talk to an Expert| Category | Assignment | Subject | Business |
|---|---|---|---|
| University | The Hang Seng University of Hong Kong | Module Title | AMS2320 Business Regression Analysis |
| Assessment Title | Assignment 1 |
|---|---|
| Academic Year | 2024-25 |
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
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