multi regression

Question 1

In multiple regression analysis, __________________.
a. there can be any number of dependent variables but only one independent variable
b. there must be only one independent variable
c. the coefficient of determination must be larger than 1
d. there can be several independent variables, but only one dependent variable

Answer 1

d

Question 2

2) What is the intercept coefficient for the regression equation?
Yhat = 35 + 15 X1 – 14 X2
a. 35
b. 15
c. – 14
d. Yhat

Answer 2

A

Question 3

3) What is the expected change to Yhat if both independent variables increase by 1 unit?
Yhat = 35 + 15 X1 – 14 X2
a. The effects will cancel out and there will be no change to Yhat.
b. Yhat will increase by 1 unit.
c. Yhat will increase by 29 units.
d. Yhat will decrease by some number that we cannot determine.

Answer 3

B

Question 4

4) What is the expected change to Yhat if X1 decreases by 2 units?
Yhat = 35 + 15 X1 – 14 X2
a. Yhat increases by 15 units
b. Yhat decreases by 15 units
c. Yhat increases by 30 units
d. Yhat decreases by 30 units

Answer 4

D

Question 5

5) What is the correct interpretation for the coefficient on years of education?
Income = 20,056 + 500Years Education + 1,000Masters Degree + 8.6*Hours Asleep
a. A 1 year increase in education increases yearly income by 500 dollars.
b. A 1 year increase in education increases yearly income by 500 dollars, on average,
holding all else constant.
c. A 1 year increase in education decreases yearly income by 500 dollars, on average,
holding all else constant.
d. A 1 year increase in education decreases yearly income by 500 percent, on average,
holding all else constant

Answer 5

B

Question 6

6) A multiple regression model has the form:
Y෡ = 5 + 6 X + 7 W
6) As X increases by 1 unit (holding W constant), Y is expected to _________.
a. increase by 11 units
b. decrease by 11 units
c. increase by 12 units
d. decrease by 6 units
e. increase by 6 units

Answer 6

E

Question 7

a. Y = B0 + B1 X1 + B2 X2 + ε
b. E(Y) = B0 + B1 X1
c. Y෡ = B0 + B1 X1 + B2 X2
d. E(Y) = B0 + B1 X1 + B2 X2
7) Which equation describes the multiple regression equation?
a. equation a
b. equation b
c. equation c
d. equation d

Answer 7

A

Question 8

8) The Ordinary Least Squares (OLS) criterion is _________.
a. min ∑(Xi – Yi)2
b. min ∑(Yi – Yi)2
c. min ∑(Yi – Y෡i)2
d. min ∑(Yi – Y෡i)

Answer 8

C

Question 9

9. If we regressed daily temperature on daily ice cream sales, we would expect
   to find__________________
   a. 𝛽ଵ = 0
   b. 𝛽ଵ > 0
   c. 𝛽ଵ < 0
   32
   We would expect to see a positive relationship
   between temperature and ice cream sales, so the
   slope coefficient should be positive

Answer 9

B

Question 10

10) Which of the following best describes what 𝑅ଶ represents?
a. The amount of variation in the dependent variable explained by the independent
variables
b. The amount of variation in the independent variables explained by the dependent
variable
c. The amount of variation in the dependent variable explained by the error term
d. The amount of variation in the independent variables explained by the error term

Answer 10

A

Question 11

11) Suppose you estimate a model to predict stock prices in the technology industry
and you get an R2 of 0.84. What is the correct interpretation of the R2?
a. The model explains 0.84% of variation in the data
b. The model explains 84% of variation in the data
c. The model has an SSE of .84
d. None of these are correct interpretations of R2

Answer 11

B

Question 12

12) The addition of an additional independent variable to a regression equation could
potentially ________ the adjusted R2 value.
a. Increase
b. Decrease
c. Have no effect on
d. All of the above

Answer 12

D

Question 13

13) The adjusted multiple coefficient of determination (the Adj R-squared (Adj R2))
is adjusted for _____.
a. the number of dependent variables
b. the number of independent variables
c. the number of equations
d. detrimental situations

Answer 13

B

Question 14

14) In a multiple regression analysis involving 12 independent variables and 166
observations, SSR = 878 and SSE = 122.
The coefficient of determination is __________.
a. 0.1389
b. 0.1220
c. 0.8780
d. 0.7317

Answer 14

C

Question 15

15. In a multiple regression analysis involving 12 independent variables and 166
    observations, SSR = 878 and SSE = 122.
    The coefficient of determination is __________.
    a. 0.1389
    b. 0.1220
    c. 0.8780
    d. 0.7317

Answer 15

C

Question 16

1) In Ordinary Least Squares regressions, we:
a. Create a regression line which minimizes SSE
b. Create a regression line that maximizes the dependent variable
c. Create a regression line to touch all the observations
d. Create a regression line that maximizes the SSE

Answer 16

A

Question 17

2) The least squares method chooses the line that minimizes _________.
a. The absolute value of the sum of errors
b. The number of independent variables
c. The sum of squared errors, or SSE
d. The Adjusted R-squared value

Answer 17

C

Question 18

3) The least squares method minimizes the sum of which of the following?
a. The difference between the fitted value and the true value
b. The squared difference between the fitted value and the true value
c. The correlation coefficient
d. The covariance

Answer 18

B

Question 19

4) The estimated value for the intercept in a simple linear regression model is the:
a) Predicted value of the dependent variable when the independent variable is 0
b) Predicted amount of change in the dependent variable given a unit change in
the independent variable
c) Sample mean divided by the square root of its standard error
d) Sample mean divided by the variance of the independent variable

Answer 19

A

Question 20

5) You are interested in studying the relationship between the age of automobiles and
their price on the used car market. Which variable should be the independent variable?
a) Age of automobile
b) Price
c) There is probably no relationship between these variables
d) Could be either one

Answer 20

A

Question 21

6) If we ran a regression between the number of miles a car has been driven and its
selling price, what would we expect to be the sign on mileage?
a. Positive
b. Negative
c. Zero
d. Not enough information to say

Answer 21

B

Question 22

7) Which of the following relationships might you expect to be negative?
a. Number of years of experience and a person’s wages
b. A person’s height and a person’s weight
c. Number of classes skipped and a person’s (percentage) grade in a class
d. Number of hours spent studying and a person’s score on a test

Answer 22

C

Question 23

8) True or False. In a regression equation, the slope term indicates the change in the
dependent variable given a change in the independent variable.
a. True
b. False

Answer 23

A

Question 24

9) What is a residual?
a. The value of the dependent variable for a given set of independent variables.
b. The difference between out observed Y-value and the estimated Y-value
c. The difference between the various observed Y-values
d. The ratio of explained variation in Y to unexplained variation in Y

Answer 24

B

Question 25

10) True or False: the sample error term for an observation is equal to the observed
y-value minus the predicted y-value.
a) True
b) False

Answer 25

A

Question 26

11) Which of the following pairs of variables would likely have a negative relationship?
a. Hours spent jogging and ability to run a marathon.
b. Time spent in sun and number of sunburns received
c. Alcohol consumed before exam and scores on exam
d. None of these options are examples of a negative relationship

Answer 26

C

Question 27

12) Consider a professor trying to determine what contributes to students studying more for
an exam. They estimate the following equation:
𝑆𝑡𝑢𝑑𝑦ℎ𝑜𝑢𝑟𝑠 = 1.2 + 3 𝑝𝑟𝑎𝑐𝑡𝑖𝑐𝑒𝑒𝑥𝑎𝑚௜ − 1.1 𝑜𝑡ℎ𝑒𝑟𝑐𝑙𝑎𝑠𝑠௜
Where practice exam refers to a practice exam being made available and otherclass refers
to the number of other classes a student is taking. According to our model, what would we
predict to be the number of hours studied if there is no practice exam and a student is not
taking any other classes.
a. 1.2 hours
b. 4.2 hours
c. 0.1 hours
d. 2.3 hours

Answer 27

A

Question 28

13) A researcher has a dataset that contains information on the weight of a variety of
types of fish and possible determinants of weight. She runs a simple regression using
weight in grams as the dependent variable and length in cm as the independent variable,
and obtains the results below.
Coefficients Standard Error t Stat P-value
Intercept -488.581565 31.14187781 -15.68889 5.734E-34
Length cm 28.45831278 0.935112133 30.433048 9.801E-68
An increase in length of 1cm is associated with how many grams of increase in weight?
a. 31.14
b. 0.94
c. 30.43
d. 28.46

Answer 28

D

Question 29

14) A researcher has a dataset that contains information on the weight of a variety of
types of fish and possible determinants of weight. She runs a simple regression using
weight in grams as the dependent variable and length in cm as the independent variable,
and obtains the results below.
Coefficients Standard Error t Stat P-value
Intercept -488.581565 31.14187781 -15.68889 5.734E-34
Length cm 28.45831278 0.935112133 30.433048 9.801E-68
Which of the following is the sample regression equation?
a. Weight = -488 + 31length
b. Length = -488 + 31weight
c. Weight = -488 + 28length
d. Length = -488 + 28weight

Answer 29

C

Question 30

15) An economist wants to estimate the relationship between earnings (in thousands of
dollars) and years of education. Model: Earnings = β0 + β1*Education + ε.
Coefficient Standard Error p-value
Intercept 15.77 3.8 0.003
Education 4.21 1.4 0.032
Which of the following is true?
a) If education is increased by one year, we predict that earnings will increase by $4,210.
b) If earnings are increased by $1000, we predict that education will increase by .21 years.
c) If education is increased by one year, we predict that earnings will increase by $3200.
d) If earnings are increased by $1000, we predict that education will increase by .032 years

Answer 30

A