Problem Session #2
Q.1
You have the result of a simple linear regression based on BC provincial level. 51 observations were used
for this regression. The standard error of the estimator Se is 2.04672, and r=0.6
a.
What the unexplained sum is of squares, the explained sum of squares and the total sum of
squares?
b.
Suppose the dependent variable Yi = the province’s mean income (in ‘000$) of males who are
18 years of age or older and Xi is percent of males 18 years or older who are high school
graduates. If the estimate of Bo is 11.7 and the estimate of 1 = 0.18, interpret this regression
result.
Q.2
Investment analysts generally believe the interest rate on bonds is inversely related to the prime interest rate
for loans; that is bonds perform well when lending rates are down and perform poorly when interest rates are
up. You collected data on both variables as follows:
Bond rate (%)
Prime interest rate (%)
5
16
12
6
9
8
15
4
7
7
a. Estimate the least squares regression line to predict bond rates by interest rates
b. Interpret your estimated equation
c. What is the predicted bond rate for prime rate = 20%? Is this prediction reliable? Why or why not?
d. Determine the standard error of the estimate Se
e. Find and interpret r-squared. What are the units of measurement for r-squared?
Q.3
Dr. Rosmy decides to run an experiment to measure the effect of time pressure on final exam scores.
He gives each of the 400 students in his course the same final exam, but some students have 90
minutes to complete the exam while others have 120 minutes. Each student is randomly assigned of
the examination times based on the flip of a coin. Let Yi denote the number of points scored on the
exam by the ith student (0≤Yi≤100), let Xi denote the amount of time that a student has to complete
the exam (Xi=90 or 120), and consider the regression model Yi = B0 + B1Xi + ɛi
a. Explain what the term ɛi represents? Why would different students have different values of ɛi?
b. Explain why E(ɛi| Xi) =0 for this regression
c. The estimated regression is 𝑌̂ = 49 + 0.24𝑋. What is the estimated gain in score for a student who is
given an additional 10 minutes on the exam?
Q.4
Consider the regression model : Yi = 0 + 1 Xi + i , where Yi denotes average test scores from fifthgrade classes (TS, measured in percentages) and Xi denotes the data on fifth grade class size (CS) -You
collected data on 25 classes with class sizes ranging from 25 to 36
You obtained the following information from your data,
X = 75 Y = 50, X2 = 625 Y2 = 228, XY = 30
a.
b.
c.
Q.5
What does the term I represent?
Find the regression equation and interpret it
Find SSE, SSR and the variance of the estimated regression equation,
Page 77 of the textbook Question 2.5
Page 78 of the textbook Question 2.6