PART 2: Simple Regression Analysis

Question 2: Each group of students will be provided with different sets of data and regression model to answer this question. Students MUST use the dataset and regression model assigned to them by their instructor for this question. Students who used a dataset not assigned to them by their instructor will be penalized by getting a ZERO grade for this question, even if their answers are correct and the project done appropriately.

Question: The following model shows the relationship between body weight and level of cholesterol in mg/dL for a group of 20 mice.

BodyWeight=a+b Cholesterol Level+ui

where

ui

𝒖𝒊

is the error term.

Use the data provided on the EXCEL spreadsheet to answer the following questions:

a) Calculate the correlation coefficient (

r

r

) between bodyweight (Y) and cholesterol level (X).

b) What is the standard deviation of the bodyweight variable (

σY

𝜎Y

) and the cholesterol level variable (

σX

𝜎X

)

c) Perform a simple linear regression on the data and interpret the values of the parameter estimates. [Hint: Find

aˆ

𝒂^

and

bˆ

𝒃^

d) Calculate the 99% confidence interval for the slope parameter,

bˆ

𝒃^

in the linear regression model which expresses the bodyweight as a function of the cholesterol level.

e) Estimate the explanatory power of the regression (

R2

R2

) and interpret your result.

f) What is the bodyweight of a mouse with a cholesterol level of 72 mg/dL?

g) Write a short report on your findings.