QM 222 Midterm-with-answers 2016Exam
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QM222 SECTION D1: Modeling Business Decisions Midterm
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:
List three ways that you know based on 3 different numbers in the regression output:
i. | T | > 2
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-
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
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
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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