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**preview**shows pages 1-2. to view the full**6 pages of the document.**QM222 SECTION D1: Modeling Business Decisions Midterm

BOSTON UNIVERSITY

Question School of Business

Fall 2016 WITH ANSWERS

NOTE THAT THE OMITTED VARIABLE BIAS QUESTIONS HERE HAVE ANSWERS IN ITALICS

SECTION 1 Your Regression

• Answer the following questions regarding the regressions that you have brought with you or the

regressions that Professor Kahn gives to you.

• Be sure to put your name on the page with your regression. When you complete the test, I will

staple your regression sheet to your test.

• If you use your own regression, make sure all variables are defined (including your Y variable) on the

sheet with your regressions or in your answers below. ANSWERS ARE FOR THE REGRESSIONS AT

THE END OF THIS TEST.

Answer these questions based on your simple (1 variable) regression:

1. What does each observation in the data set represent? (in a few words at most)

A SURVEYED PERSON.

2. Use the value of the coefficient on your variable in a sentence that explains what it tells us. In other

words, interpret this coefficient. (Do not use statistics terms in your answer. Be specific but concise.)

Note: If your “simple” regression includes two (or more) X-variables that are different categories of the

same categorical variable, answer this question and the next only about the first of these variables.

EACH $000 OF FAMILY INCOME DECREASES THE CLINTON SCORE BY 5.57 PERCENTAGE POINTS. NOTE:

PERCENTAGE POINTS ARE DIFFERENT FROM PERCENTAGES. IF CLINTON’S AVERAGE SCORE WAS 50, THEN

THIS WOULD BE 5.56/50 = 11.1%

3. Does this variable have a statistically significant effect on your dependent variable? Circle one:

YES NO

List three ways that you know based on 3 different numbers in the regression output:

i. | T | > 2

ii. P<.05

iii. THE 95% CONFIDENCE INTERVAL DOES NOT INCLUDE ZERO.

Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

4. When a variable does have a statistically significant effect, what does that mean, in everyday non-

statistics terms?

WE ARE AT LEAST 95% CERTAIN THAT THE COEFFICIENT IS NOT ZERO; OR, WE ARE AT LEAST 95% CERTAIN

THAT THE VARAIBLE HAS AN IMPACT OF THAT SIGN.

Now answer these questions based on both your multiple regression and your simple regression:

5. Compare the two coefficients on the key variable that enters both regressions.

In which regression is there omitted variable bias, simple or multiple: SIMPLE

Exactly how much is this bias? (Be sure to include a negative if it is a negative bias) -.05571 +.04857= -.00714

Exactly what do you learn from these regressions about the correlation between the two explanatory

variables in the multiple regression? Is the correlation (CIRCLE ONE):

POSITIVE NEGATIVE CAN’T TELL

Explain exactly how you know the amount/sign of the bias and the sign of the correlation (or explain why one

can’t tell.)

THE VARIABLE NEWINT HAS A POSITIVE COEFFICIENT (WHICH WE CALL B2) IN THE FULL MODEL. THE BIAS

IS NEGATIVE. SINCE BIAS = - .00714 = A1 B2, THEN A1 MUST BE NEGATIVE. THE SIGN OF A1 IS THE SIGN OF

THE CORRELATION, SO THE CORRELATION IS NEGATIVE.

5. Name one other possibly confounding factor that you will or should add to this regression to remove some

of the omitted variable bias on the coefficient of the “key” explanatory variable (i.e. the one that is in both

regressions above.)

BLACK

Logically, why do you think this is possibly confounding?

BLACKS WOULD BE MORE LIKELY TO BE FAVORABLE TO CLINTON (THIS IS B2). ALSO BLACKS HAVE ON

AVERAGE LOWER FAMILY INCOME (THIS HAS THE SIGN OF A1).

6. If you added this new possibly-confounding variable to the multiple regression, how would the coefficient

on the key variable (the one in all 3 regressions) change? CIRCLE ONE

BIAS= A1 B2 = NEGATIVE * POSITIVE = NEGATIVE BIAS.

IF WE ADD IN BLACK, THE COEFFICIENT ON INCOME WOULD LOSE THIS NEGATIVE BIAS SO IT WOULD

INCREASE (BECOME LESS NEGATIVE) AND COULD EVEN TURN POSITIVE. SO:

THE COEFFICIENT WOULD INCREASE (THIS INCLUDES A NEGATIVE COEFFICIENT BECOMING LESS NEGATIVE)

6. Going back to the two original regressions, which one fits the data better? CIRCLE ONE

THE MULTIPLE REGRESSION

List two ways that you know, using different numbers from the regressions:

1. THE ADJUSTED R-SQUARED IS HIGHER.

2. THE ROOT MSE IS LOWER

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