Question 1

Why is it helpful to think about the moment conditions of a simple linear regression even if OLS yields the same estimates?

Accepted Answer

A)  The moment conditions are easier to program in Excel. 
B)  The moment conditions will get the smaller standard errors. 
C)  The moment conditions establish causality whereas OLS just estimates correlation. 
D)  The moment conditions facilitate assessing assumptions about causality. 
A)  The moment conditions are easier to program in Excel. 
B)  The moment conditions will get the smaller standard errors. 
C)  The moment conditions establish causality whereas OLS just estimates correlation. 
D)  The moment conditions facilitate assessing assumptions about causality.

Question 2

Suppose the regression line to describe the relationship between Y and a dichotomous treatment (X = 1 for treated, = 0 untreated) is given by Y = 4 + 3X. Suppose that one of the observations that was treated was observed to have an outcome, Y = 8. For this observation, what is the residual?

Accepted Answer

A)  0 
B)  7 
C)  1 
D)  -1 
A)  0 
B)  7 
C)  1 
D)  -1

Question 3

If we wish to use a regression line to determine the effect of multiple treatment levels , why can't we just plot the average outcome for each treatment level and "connect the dots?"

Accepted Answer

A)  Connecting the dots generally will not form a line. 
B)  Using averages for each treatment level will generally create bias. 
C)  This will cause us to have too few equations to solve for our unknown parameters. 
D)  We cannot use a regression line to measure the effects of multiple treatments. 
A)  Connecting the dots generally will not form a line. 
B)  Using averages for each treatment level will generally create bias. 
C)  This will cause us to have too few equations to solve for our unknown parameters. 
D)  We cannot use a regression line to measure the effects of multiple treatments.

Question 4

If you're running a multiple regression of employee Hours Worked on Tenure (in number of years) and MBA (a binary variable equal to 1 for an employee with an MBA, 0 otherwise), what moment conditions would not be used?

Accepted Answer

A)  
$ \frac{\sum_{i=1}^{N}\left(\text { Hours }_{i}-b-m_{1} \text { Tenure }_{i}-m_{2} M B A_{i}\right)}{N} $ = 0 
B)  
$ \frac{\left. \sum _ { i = 1 } ^ { N } \text { Hours } _ { i } - b - m _ { 1 } \text { Tenure } _ { i } - m _ { 2 } \text { MBA } _ { i } \right) \text { Tenure } _ { i }}{N} $ = 0 
C)

$ \frac{\sum _ { i = 1 } ^ { N } \left( \text { Hours } _ { i } - b - m _ { 1 } \text { Tenure } _ { i } \right) M B A _ { i }}{N} $ = 0 
D)  $\frac { \sum _ { i = 1 } ^ { N } e _ { i } } { N }$ = 0 
A)  
$ \frac{\sum_{i=1}^{N}\left(\text { Hours }_{i}-b-m_{1} \text { Tenure }_{i}-m_{2} M B A_{i}\right)}{N} $ = 0 
B)  
$ \frac{\left. \sum _ { i = 1 } ^ { N } \text { Hours } _ { i } - b - m _ { 1 } \text { Tenure } _ { i } - m _ { 2 } \text { MBA } _ { i } \right) \text { Tenure } _ { i }}{N} $ = 0 
C)

$ \frac{\sum _ { i = 1 } ^ { N } \left( \text { Hours } _ { i } - b - m _ { 1 } \text { Tenure } _ { i } \right) M B A _ { i }}{N} $ = 0 
D)  $\frac { \sum _ { i = 1 } ^ { N } e _ { i } } { N }$ = 0

Question 5

In a dichotomous regression all of the following conditions must hold except for what?

Accepted Answer

A)  The sum of residuals for the treated group must equal zero. 
B)  The sum of residuals for the untreated group must equal zero. 
C)  An equal number of positive and negative residuals. 
D)  The regression line must go through the mean of the outcomes for the treated. 
A)  The sum of residuals for the treated group must equal zero. 
B)  The sum of residuals for the untreated group must equal zero. 
C)  An equal number of positive and negative residuals. 
D)  The regression line must go through the mean of the outcomes for the treated.

Question 6

All of the following are conditions that will hold at the estimated coefficients for the simple linear regression line (of Y on X) except for what?

Accepted Answer

A)  Sum of the residuals equals zero. 
B)  Covariance between the residuals and X is zero. 
C)  Average of the residuals equals zero. 
D)  Covariance between Y and the residuals is zero. 
A)  Sum of the residuals equals zero. 
B)  Covariance between the residuals and X is zero. 
C)  Average of the residuals equals zero. 
D)  Covariance between Y and the residuals is zero.

Question 7

Which of the following settings would require the use of multiple regression (as opposed to simple regression)?

Accepted Answer

A)  Predicting grocery sales as a function of price and local population. 
B)  Predicting grocery sales as a function of being a weekend day, or a weekday day. 
C)  Predicting grocery sales as a function of being an AM hour or a PM hour. 
D)  Predicting grocery sales as a function of local number of competitors. 
A)  Predicting grocery sales as a function of price and local population. 
B)  Predicting grocery sales as a function of being a weekend day, or a weekday day. 
C)  Predicting grocery sales as a function of being an AM hour or a PM hour. 
D)  Predicting grocery sales as a function of local number of competitors.

Question 8

Suppose your lead analyst runs a simple regression of Profits (Y) on price (X). You know that the average profit in the sample was $1,000 and the average price was $25. If your analyst reports that the intercept from the simple regression is 900, what can you infer about the estimated slope?

Accepted Answer

A)  The estimated slope is 4. 
B)  The estimated slope is -4. 
C)  The estimated slope is 2. 
D)  None of these choices are correct. 
A)  The estimated slope is 4. 
B)  The estimated slope is -4. 
C)  The estimated slope is 2. 
D)  None of these choices are correct.

Question 9

In the dichotomous regression if one was to replace the regression line prediction of the outcome means (for treated/untreated) with medians, which of the following conditions would hold?

Accepted Answer

A)  The sum of all the residuals would equal zero. 
B)  The sum of the residuals for the treated observations would equal zero. 
C)  The slope of the regression line would be positive. 
D)  The number of strictly positive residuals would equal the number of strictly negative residuals. 
A)  The sum of all the residuals would equal zero. 
B)  The sum of the residuals for the treated observations would equal zero. 
C)  The slope of the regression line would be positive. 
D)  The number of strictly positive residuals would equal the number of strictly negative residuals.

Question 10

For the simple linear regression, Y = b + mX, which variable is considered the intercept?

Accepted Answer

A)  Y 
B)  b 
C)  m 
D)  X 
A)  Y 
B)  b 
C)  m 
D)  X

Question 11

The process of using a function to describe the relationship among variables is known as:

Accepted Answer

A)  regression analysis. 
B)  big data. 
C)  business analytics. 
D)  cross validation. 
A)  regression analysis. 
B)  big data. 
C)  business analytics. 
D)  cross validation.

Question 12

Why is it helpful to think about the moment conditions of a simple linear regression even if OLS yields the same estimates?

Accepted Answer

A)  The moment conditions are easier to program in Excel. 
B)  The moment conditions will get the smaller standard errors. 
C)  The moment conditions establish causality whereas OLS just estimates correlation. 
D)  The moment conditions are used directly to produce the slope and intercept. 
A)  The moment conditions are easier to program in Excel. 
B)  The moment conditions will get the smaller standard errors. 
C)  The moment conditions establish causality whereas OLS just estimates correlation. 
D)  The moment conditions are used directly to produce the slope and intercept.

Question 13

How many regression parameters will be estimated in a simple linear regression model?

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  1 + number of observations 
A)  1 
B)  2 
C)  3 
D)  1 + number of observations

Question 14

A treatment that only undergoes two statuses - treated and untreated-is known as this kind of treatment?

Accepted Answer

A)  Biased 
B)  Random assignment 
C)  Dichotomous 
D)  Attenuated 
A)  Biased 
B)  Random assignment 
C)  Dichotomous 
D)  Attenuated

Question 15

The process of solving for the slope and intercept that minimize the sum of squared residuals is a process known as:

Accepted Answer

A)  least absolute deviations. 
B)  mode estimation. 
C)  mean squared error. 
D)  ordinary least squares. 
A)  least absolute deviations. 
B)  mode estimation. 
C)  mean squared error. 
D)  ordinary least squares.

Question 16

In the simple linear regression, the intercept will equal the sample average of the outcome (Y) variable if which of the following is true?

Accepted Answer

A) sVar(X) > 0 B) $\bar { X }$ = 0 C) sCov(X, Y) > 0 D) sCov(X, Y) < 0 A) sVar(X) > 0 B) $\bar { X }$ = 0 C) sCov(X, Y) > 0 D) sCov(X, Y) < 0

Question 17

Why is Line A a better fit for the data in this graph?

Accepted Answer

A)  For Line B, the average error (difference between the actual Profits and point on the line) is zero. 
B)  For Line A, the errors (difference between the actual Profits and point on the line) are uncorrelated with Price. 
C)  For Line A, the average error (difference between the actual Profits and point on the line) is zero. 
D)  Line B's intercept is smaller than Line A's intercept. 
A)  For Line B, the average error (difference between the actual Profits and point on the line) is zero. 
B)  For Line A, the errors (difference between the actual Profits and point on the line) are uncorrelated with Price. 
C)  For Line A, the average error (difference between the actual Profits and point on the line) is zero. 
D)  Line B's intercept is smaller than Line A's intercept.

Question 18

A critical aspect of linear regression is that:

Accepted Answer

A)  the regression line is linear in parameters. 
B)  the regression line only involves parameters that are positive. 
C)  None of the observed variables in the regression have been transformed using the logarithm function. 
D)  None of the answers is correct. 
A)  the regression line is linear in parameters. 
B)  the regression line only involves parameters that are positive. 
C)  None of the observed variables in the regression have been transformed using the logarithm function. 
D)  None of the answers is correct.

Question 19

If one is planning to use multiple regression to summarize how the variables X1, X2, X3 explain the variation in Y, how many parameters are involved in estimating the linear regression?

Accepted Answer

A)  2 
B)  3 
C)  4 
D)  5 
A)  2 
B)  3 
C)  4 
D)  5

Question 20

The difference between the observed outcome and the corresponding point on the regression line for a given observation is a:

Accepted Answer

A)  regression line prediction. 
B)  heteroskedasticity. 
C)  residual. 
D)  mean squared error. 
A)  regression line prediction. 
B)  heteroskedasticity. 
C)  residual. 
D)  mean squared error.

Why is it helpful to think about the moment conditions of a simple linear regression even if OLS yields the same estimates?

Suppose the regression line to describe the relationship between Y and a dichotomous treatment (X = 1 for treated, = 0 untreated) is given by Y = 4 + 3X. Suppose that one of the observations that was treated was observed to have an outcome, Y = 8. For this observation, what is the residual?

If we wish to use a regression line to determine the effect of multiple treatment levels , why can't we just plot the average outcome for each treatment level and "connect the dots?"

If you're running a multiple regression of employee Hours Worked on Tenure (in number of years) and MBA (a binary variable equal to 1 for an employee with an MBA, 0 otherwise), what moment conditions would not be used?

In a dichotomous regression all of the following conditions must hold except for what?

All of the following are conditions that will hold at the estimated coefficients for the simple linear regression line (of Y on X) except for what?

Which of the following settings would require the use of multiple regression (as opposed to simple regression)?

Suppose your lead analyst runs a simple regression of Profits (Y) on price (X). You know that the average profit in the sample was $1,000 and the average price was $25. If your analyst reports that the intercept from the simple regression is 900, what can you infer about the estimated slope?

In the dichotomous regression if one was to replace the regression line prediction of the outcome means (for treated/untreated) with medians, which of the following conditions would hold?

For the simple linear regression, Y = b + mX, which variable is considered the intercept?

The process of using a function to describe the relationship among variables is known as:

Why is it helpful to think about the moment conditions of a simple linear regression even if OLS yields the same estimates?

How many regression parameters will be estimated in a simple linear regression model?

A treatment that only undergoes two statuses - treated and untreated-is known as this kind of treatment?

The process of solving for the slope and intercept that minimize the sum of squared residuals is a process known as:

In the simple linear regression, the intercept will equal the sample average of the outcome (Y) variable if which of the following is true?

Why is Line A a better fit for the data in this graph?

A critical aspect of linear regression is that:

If one is planning to use multiple regression to summarize how the variables X₁, X₂, X₃ explain the variation in Y, how many parameters are involved in estimating the linear regression?

The difference between the observed outcome and the corresponding point on the regression line for a given observation is a:

The Roles of Data and Predictive Analytics in Business

Reasoning With Data

Reasoning From Sample to Population

The Scientific Method: The Gold Standard for Establishing Causality

Correlation Vs Causality in Regression Analysis

Basic Methods for Establishing Causal Inference

Advanced Methods for Establishing Causal Inference

Prediction for a Dichotomous Variable

Identification and Data Assessment

Filters

Exam 5: Linear Regression As a Fundamental Descriptive Tool

Why is it helpful to think about the moment conditions of a simple linear regression even if OLS yields the same estimates?

Suppose the regression line to describe the relationship between Y and a dichotomous treatment (X = 1 for treated, = 0 untreated) is given by Y = 4 + 3X. Suppose that one of the observations that was treated was observed to have an outcome, Y = 8. For this observation, what is the residual?

If we wish to use a regression line to determine the effect of multiple treatment levels , why can't we just plot the average outcome for each treatment level and "connect the dots?"

If you're running a multiple regression of employee Hours Worked on Tenure (in number of years) and MBA (a binary variable equal to 1 for an employee with an MBA, 0 otherwise), what moment conditions would not be used?

In a dichotomous regression all of the following conditions must hold except for what?

All of the following are conditions that will hold at the estimated coefficients for the simple linear regression line (of Y on X) except for what?

Which of the following settings would require the use of multiple regression (as opposed to simple regression)?

Suppose your lead analyst runs a simple regression of Profits (Y) on price (X). You know that the average profit in the sample was $1,000 and the average price was $25. If your analyst reports that the intercept from the simple regression is 900, what can you infer about the estimated slope?

In the dichotomous regression if one was to replace the regression line prediction of the outcome means (for treated/untreated) with medians, which of the following conditions would hold?

For the simple linear regression, Y = b + mX, which variable is considered the intercept?

The process of using a function to describe the relationship among variables is known as:

Why is it helpful to think about the moment conditions of a simple linear regression even if OLS yields the same estimates?

How many regression parameters will be estimated in a simple linear regression model?

A treatment that only undergoes two statuses - treated and untreated-is known as this kind of treatment?

The process of solving for the slope and intercept that minimize the sum of squared residuals is a process known as:

In the simple linear regression, the intercept will equal the sample average of the outcome (Y) variable if which of the following is true?

Why is Line A a better fit for the data in this graph?

A critical aspect of linear regression is that:

If one is planning to use multiple regression to summarize how the variables X1, X2, X3 explain the variation in Y, how many parameters are involved in estimating the linear regression?

The difference between the observed outcome and the corresponding point on the regression line for a given observation is a:

The Roles of Data and Predictive Analytics in Business

Reasoning With Data

Reasoning From Sample to Population

The Scientific Method: The Gold Standard for Establishing Causality

Correlation Vs Causality in Regression Analysis

Basic Methods for Establishing Causal Inference

Advanced Methods for Establishing Causal Inference

Prediction for a Dichotomous Variable

Identification and Data Assessment

Filters

If one is planning to use multiple regression to summarize how the variables X₁, X₂, X₃ explain the variation in Y, how many parameters are involved in estimating the linear regression?