Carleton University – School of Mathematics and Statistics
STAT 2509 – Assignment 1 – Fall 2022
Due Date and Time: Tuesday, September 27th,7:35pm
1. Find the following values from the t-table

t0.025,15, t0.995,7, t0.05,65

2. A forester wants to investigate if it is possible to estimate the volume of merchantable timber in a tree
from its height. She selected a sample of 31 tress, felled them and measured both the height and volume
for each of the 31 trees. The data set is in the excel file “Assignment 1.xlsx” posted on Brightspace.

A. Use SAS to perform residual analysis for testing the assumptions.


For the following parts, you may assume that all assumptions are valid, regardless of your findings in A.

B. Using SAS, draw a scatter plot of volume versus height and comment on the relationship.
C. Sate the simple linear regression model along with the assumptions.
D. Find the least square estimates for β0 and β1 and give the least square fitted regression line.
E. Find the estimate of σ2.
F. Use the t-test to test if there is a significant linear relationship between volume and height. Use α = 0.05.
G. Find a 95% confidence interval for β1.
H. Construct the ANOVA table and use it to test if there is a significant linear relationship between volume
and height. Use α = 0.05.
I. Find the coefficient of correlation, r, and the coefficient of determination, r2, and give their interpretation
in terms of this problem.
J. Find the 95% confidence interval and the 95% prediction when height is 68.
K. Repeat D to J using SAS.

3. What is the difference between a parameter and a statistic?
4. What is Type I error?