STAT 101 4th Long Exam – Take Home Exam – SJVV

This exam is a take-home exam. Write your answers on a yellow pad paper. Deadline of this exam is on

October 9, 2013 during your final examination. Cheating will incur a grade of 5.0. If I see two papers with

very similar solutions and the same wording of the interpretations of results, I will treat that as a case of

cheating.

I. True or False

1. If the estimated linear correlation coefficient of two variables is zero, then they have no

relationship.

2. If the ρ (rho) of two variables is zero, then the two variables have no linear relationship.

3. If the estimated linear correlation coefficient is not significant, it means that the variables

may have a quadratic relationship.

4. If the slope of a simple regression line is not significantly different from zero, then the

independent variable cannot significantly explain the response variable.

5. In deterministic mathematical models, the coefficient of determination is always equal to

1.

6. A linear regression model which gives large deviations of the observed values of Y from its

predicted values is preferred over a model which gives smaller deviations.

7. If the confidence interval estimate of the slope of a simple regression model contains 0,

then the independent variables is not a significant predictor or factor of the response

variable.

8. If the correlation between anxiety and performance on complex tasks is -.73, then high

level of anxiety causes poor performance on complex tasks.

9. Two variables which are not categorical in nature cannot be tested for independence

using chi square test of independence.

10. The coefficient of determination tells us the percentage of variability of the independent

variable (X) that can be explained by the dependent variable (Y).

II. Problem Solving. Show complete solutions.

1. Simple linear regression was employed to establish the effects of childhood exposure to lead. The

effective sample size was about 122 subjects. The independent variable was the level of dentin

lead (parts per million). Below are the simple linear regressions using various dependent variables.

Dependent Variable R2 Estimated Slope Std Error (Sb1)

Highest grade achieved 0.061 -0.027 0.009

Reading grade equivalent 0.121 -0.07 0.018

Class Standing 0.039 -0.006 0.003

Absence from school 0.071 4.8 1.7

Reaction time 0.025 11.8 6.66

a. Interpret the slope of the models. Are the interpretations sensible and realistic? (Do a short

web search for information about effects of childhood lead exposure.)

b. Test the significance of each slope using 0.05 level of significance.

c. Which among the dependent variables gives the best fit?

2. Forecasters’ interest rate predictions over the period 1982-1990 were studied to see whether the

predictions corresponded to what actually happened. The table below shows the data on 34

interest rate predictions with the actual and predicted interest rate movements. At α = 0.10, is the

actual change independent of the predicted change?

Predicted Interest

Rate Actual Interest Rate

1 Rates Would Fall Rates Fell

2 Rates Would Fall Rates Fell

3 Rates Would Fall Rates Fell

4 Rates Would Fall Rates Fell

5 Rates Would Fall Rates Fell

6 Rates Would Fall Rates Fell

7 Rates Would Fall Rates Fell

8 Rates Would Fall Rates Rose

9 Rates Would Fall Rates Rose

10 Rates Would Fall Rates Rose

11 Rates Would Fall Rates Rose

12 Rates Would Fall Rates Rose

13 Rates Would Fall Rates Rose

14 Rates Would Fall Rates Rose

15 Rates Would Fall Rates Rose

16 Rates Would Fall Rates Rose

17 Rates Would Fall Rates Rose

18 Rates Would Fall Rates Rose

19 Rates Would Fall Rates Rose

20 Rates Would Rise Rates Fell

21 Rates Would Rise Rates Fell

22 Rates Would Rise Rates Fell

23 Rates Would Rise Rates Fell

24 Rates Would Rise Rates Fell

25 Rates Would Rise Rates Fell

26 Rates Would Rise Rates Fell

27 Rates Would Rise Rates Fell

28 Rates Would Rise Rates Fell

29 Rates Would Rise Rates Rose

30 Rates Would Rise Rates Rose

31 Rates Would Rise Rates Rose

32 Rates Would Rise Rates Rose

33 Rates Would Rise Rates Rose

34 Rates Would Rise Rates Rose

3. Below are financial ratios for a random sample of 20 integrated health care systems. Operating

Margin is total revenue minus total expenses divided by total revenue plus net operating profits.

Equity Financing is fund balance divided by total assets.

a. Make a scatter plot of Y = operating margin and X = equity financing (both variables are

percent). Interpret. Is the estimate sensible? Why or why not?

b. Fit the regression and interpret the estimates.

c. Test for the significance of the slope at 0.01 level of significance. Interpret.

d. Construct the 99% confidence interval of the slope. Interpret.

e. Will the model be useful for policymakers? How can it be useful?

4. Below are revenue and profit (both in $ billions) for nine large entertainment companies.

a. Compute and interpret the correlation coefficient. Explain why such linear relationship holds.

b. Test for the significance of ρ at 0.05 level of significance.

c. Without fitting the regression model, what would be the coefficient of determination of the

model with Profit as the response variable and Revenue the predictor variable? Interpret.

Revenue and Profit of Large Entertainment Companies (n = 9)

Company Revenue Profit

AMC Entertainment 1.792 -0.020

Clear Channel Communication 8.931 1.146

Liberty Media 2.446 -0.978

Metro-Goldwyn-Mayer 1.883 -0.162

Regal Entertainment Group 2.490 0.185

Time Warner 43.877 2.639

Univision Communications 1.311 0.155

Viacom 26.585 1.417

Walt Disney 27.061 1.267

Bonus Questions:

1. What is your most unforgettable moment in Stat 101?

2. Do you think you have given your best in the course? What grade would you give yourself and

why?

3. What is the purpose of life?