Stat 101 4th Exam

STAT 101 4 th Long Exam  –  Take  Take Home Exam  –  SJVV  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 i nterpretations of results, I will treat that as a case of cheating.

I.

True or False 1.

If the estimated linear correlation coefficient of two variabl es is zero, then they have no relationship. 2. If the ρ (rho) of two variables is zero, then the two variables have no linear re lationship. 3. If the estimated linear correlation coefficient is not significant, it means t hat 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 fr om 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 fac tor 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. 1.

Problem Solving. Show complete solutions. 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

a. b. c.

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 -0.006

0.003

Absence from school

0.071

4.8

1.7

Reaction time

0.025

11.8

6.66

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.) Test the significance of each slope u sing 0.05 level of significance. 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 s hows the data on 34 interest rate predictions with the actual and predicted interest rate movements. At α = 0.10, i s 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 w hy 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.

R e v e n u e a n d P r o f i t o f L a r g e E n t e r ta i n m e n t C o m p a n i e s ( n = 9 )

Company

 AMC Entertainment

Revenue

Profit

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. 2. 3.

What is your most unforgettable moment in Stat 101? Do you think you have given your best in the c ourse? What grade would you give yourself and why? What is the purpose of life?