Question 1

If the t-stat for the sample estimate of a coefficient, M₁ calculated as the following, t = $\frac { m _ { 1 } - 1 } { S _ { m _ { 1 } } }$ , where m₁ is the estimated coefficient and S $m _ { 1 }$ is the properly estimated standard error for the coefficient, comes out to be 2.7, what is the appropriate conclusion? A) Reject the null hypothesis that the population coefficient M₁ = 1 at a 99% confidence level. B) Fail to reject the null hypothesis that the population coefficient M₁ = 1 at a 95% confidence level. C) Reject the null hypothesis that the population coefficient M₁ = 2 at a 99% confidence level. D) None of these choices are correct.

Accepted Answer

A t-statistic of 2.7 typically exceeds the critical value for a 99% confidence level, allowing us to reject the null hypothesis that the population coefficient M1 = 1.

Question 2

Suppose the regression of Output per Hour on employee Age yields a coefficient of -4.3 with a standard error of 1.2. Which of the following equations would properly report the 95% confidence interval for the population coefficient?
A) -4.3 ± 1.96
B) 0 ± 1.96(1.2)
C) -4.3 ± 1.96(1.2)
D) -4.3 ± 1.65(1.2)

Accepted Answer

We can use the formula: 
Coefficient ± (Critical Value) x Standard Error

For a 95% confidence interval, the critical value is 1.96.

Plugging in the values given: 
-4.3 ± 1.96(1.2)

This gives the range from -7.68 to -0.92.

Therefore, the correct answer is C.

Question 3

When making passive predictions, it is not important to be able conclude that:
A) your estimate of the coefficients is a consistent estimate.
B) your estimate describes a causal relationship between treatments and the outcome.
C) your estimates can be evaluated against a range of null hypothesis.
D) you are using a random sample of the target population.

Accepted Answer

When making passive predictions, it is not important to be able to conclude that your estimate describes a causal relationship between treatments and the outcome. Passive predictions simply involve identifying patterns in data and making predictions based on those patterns, without necessarily understanding or interpreting the underlying causal relationships. The other options - consistency of estimates, evaluation against null hypotheses, and use of random samples - are all important considerations when making passive predictions.

Question 4

If the residuals of a regression model, Y_i= B + MX_i + E_i, are such that their variances vary across all values of X, then they are said to be: A) heteroscedastic. B) homoscedastic. C) exogenous. D) endogenous.

Accepted Answer

Heteroscedastic residuals have varying variances across all values of X, while homoscedastic residuals have constant variances across all values of X. Exogenous and endogenous refer to variables in a different context and are not relevant to the description of residuals.

Question 5

Which of the following is not a condition to estimate a model for causality? A) E[U_i] = E[U_iX₁_i] = ... E[U_iX_ki] = 0. B) The sample is a random sample from the target population. C) The error terms are distributed normally. D) The data generating process can be described by a determining function such as $Y _ { i }$ = ?₀ + ?₁X₁_i + ...+ ?_kX_ki + U_i.

Accepted Answer

While normal distribution may be a common assumption in estimating causal models, it is not an absolute condition. Other methods, such as robust regression, can be used to handle non-normal errors. The other conditions (A, B, and D) are important for estimating the model for causality.

Question 6

Suppose you estimate the following regression of a Movie's ticket sales and the season of year (Summer =1 if in May, June, July, August, =0 otherwise) that movie's initial release was in: Sales = 295,342 + 40.24 Summer. You are willing to believe you have a random sample of store locations, and a sufficiently large sample size. Which statements are well justified by the regression results? A) Movies released in the summer tend to have higher ticket sales. B) Moving the scheduled release of a movie from the winter to the summer will increase its sales by 40.24. C) Moving the Jurassic World release date to Christmas instead of 4^th of July weekend, would have resulted in ticket sales of 295,342. D) Promotional activities increase the number of movie tickets sold holding other factors fixed.

Accepted Answer

The regression coefficient for Summer is positive and significant, suggesting that movies released in the summer tend to have higher ticket sales.

B is not justified because the regression coefficient represents the increase in ticket sales for a movie released in the summer compared to a movie released in the winter, holding all other factors constant. It does not necessarily mean that moving a specific movie's release date will result in a 40.24 increase in sales.

C is not justified because the regression equation only pertains to the sample of movies in the dataset, and it cannot be generalized to a specific movie like Jurassic World without additional information.

D is not justified because the regression equation only includes season of release as a predictor variable, and does not include any measures of promotional activities. Therefore, it cannot be concluded whether promotional activities have any effect on ticket sales based on this regression alone.

Question 7

Which of the following settings best describes a setting in which one would be making a passive prediction?
A) Predicting the rise in sales following an increase in the promotional activities of your firm.
B) Predicting the increase in labor productivity following the rollout of mandatory HR workshop.
C) Predicting vehicle sales as a function of the daily max temperature and total rainfall.
D) Predicting the change in click-through rates following the change in banner size.

Accepted Answer

A passive prediction involves observing a natural phenomenon or pattern and making a prediction based on it. Predicting vehicle sales as a function of weather conditions is an example of a passive prediction, as it involves observing a pattern and making a prediction based on it. Options A, B, and D all involve intentional actions taken to influence an outcome, which do not fit the definition of a passive prediction.

Question 8

If the t-stat for the sample estimate of a coefficient, M₁ calculated as the following, t = $\frac { m _ { 1 } } { S _ { m _ { 1 } } }$ , where m₁ is the estimated coefficient and S $m _ { 1 }$ is the properly estimated standard error for the coefficient, comes out to be 2.7, what is the appropriate conclusion? A) Reject the null hypothesis that the population coefficient M₁ = 0 at a 99% confidence level. B) Fail to reject the null hypothesis that the population coefficient M₁ = 1 at a 95% confidence level. C) Reject the null hypothesis that the population coefficient M₁ = 2 at a 99% confidence level. D) None of these choices are correct.

Accepted Answer

The t-statistic of 2.7 indicates that the estimated coefficient is 2.7 standard errors away from the null hypothesis value of 0. At a 99% confidence level, the critical t-value is 2.58 for a two-tailed test. Since the calculated t-statistic of 2.7 is higher than the critical t-value of 2.58, we reject the null hypothesis that the population coefficient M₁ = 0.

Question 9

In making passive predictions, it is usually sufficient to (consistently) estimate what sort of relationships?
A) Causal relationships
B) Determining functions
C) Co-movement or partial correlations
D) None of the answers is correct.

Accepted Answer

Co-movement or partial correlations are sufficient in estimating passive predictions as they can show the degree of association between variables without implying causation or identifying the determining function. This type of relationship is particularly useful in analyzing trends and patterns in data.

Question 10

After estimating a regression of your firm's store sales and the number of local competitors as follows: Sales = 321,752 + 70.35 Number of Competitors. You are willing to believe you have a random sample of store locations, and a sufficiently large sample size. What is wrong with the following logic, "We need more competitors to enter the markets we're in, so that our sales will rise?"
A) The positive coefficient on number of competitors is not a causal estimate.
B) The positive coefficient on number of competitors isn't a consistent estimate.
C) The number of competitors might be measured with error.
D) You're making an active prediction.

Accepted Answer

The positive coefficient on the number of competitors is not a causal estimate. Although there is a positive relationship between the number of competitors and sales, it does not necessarily mean that adding more competitors will lead to an increase in sales. There could be other factors affecting sales, such as the level of advertising or the quality of service, that are not captured in the regression model. Therefore, it is not safe to assume that increasing the number of competitors will always lead to an increase in sales.

Question 11

Suppose that the following regression equation best describes the co-movement between Sales, Price and Number of Competitors: Sales_i = B + M₁Price_i + M₂NumComp_i. What moment condition would not be used to yield a consistent estimate of B, M₁, M₂? A) $\frac { \sum _ { i = 1 } ^ { N } e _ { i } } { N }$ = 0 B) $ \frac{\sum _ { i = 1 } ^ { N } \left( \text { Sales } _ { i } - b - m _ { 1 } \text { Price } _ { i } - m _ { 2 } \text { Num Comp } _ { i } \right) \text { Price } _ { i }}{N} $ = 0 C) $ \frac{\sum _ { i = 1 } ^ { N } \left( \text { Sales } _ { i } - b - m _ { 1 } \text { Price } _ { i } - m _ { 2 } \text { NumComp } _ { i } \right)}{N} $ = 0 D) $ \frac{\sum _ { i = 1 } ^ { N } \left( \text { Sales } _ { i } - b - m _ { 1 } \text { Price } _ { i } \right) \text { Price } _ { i }}{N} $ = 0

Accepted Answer

The moment condition in choice D is incorrect because it omits the term involving the number of competitors, NumComp, which is part of the regression equation. This omission would lead to an inconsistent estimate of the parameters.

Question 12

In the following determining function, Earnings_i = α₀ + α₁Education_i + U_i, what might be a factor contained in U_i? A) Predictions of earnings B) Innate ability, which might be correlated with education and earnings C) Proximity to a 4-year college, which is known to not impact earnings D) Heteroscedasticity

Accepted Answer

U_i represents the error term in the earnings determining function, which could include factors not explicitly accounted for in the model, such as innate ability. This term might capture the variation in earnings not explained by the model's included variables (like education), and innate ability is a plausible factor that could influence earnings but is not directly measured by the variables in the model.

Question 13

Why can't the regression coefficients in correlation analysis be interpreted as the causal effect of a treatment on the outcome?
A) Co-movement/correlation amongst two variables could be generated by their relationship to other variables.
B) Regression coefficients in correlation analysis cannot be consistent.
C) Regression coefficients in correlation analysis cannot be unbiased.
D) You cannot conduct hypothesis tests on coefficients in correlation analysis.

Accepted Answer

Correlation analysis only shows the relationship between two variables and cannot establish causation. This is because there could be other variables influencing the relationship between the two variables being analyzed. Therefore, regression coefficients in correlation analysis cannot be interpreted as the causal effect of a treatment on the outcome.

Question 14

When making passive predictions, which type of relationship must you believe continues to hold when you move your estimation sample to your forecasting sample?
A) The (semi) partial correlations of your dependent and independent variables
B) The determining function
C) Random treatment assignment
D) Selection bias

Accepted Answer

When making passive predictions, you must believe that the (semi) partial correlations of your dependent and independent variables continue to hold when you move your estimation sample to your forecasting sample. This assumption is essential for the accuracy and reliability of passive predictions.

Question 15

After estimating a regression of each employee's number of contracts sold and their tenure (in number of years) at the company as follows: Contracts = 30.5 + 4.5 Tenure. You are willing to believe you have a random sample of employees, and a sufficiently large sample size. Given these results, is it appropriate to make the following claim, "Our more tenured employees at the company on average get awarded more contracts"?
A) No, this is an active prediction.
B) Yes, you're making a passive prediction.
C) Yes, you're making an active prediction.
D) No, you're making a passive prediction.

Accepted Answer

The regression equation suggests that for each additional year of tenure, an employee sells an average of 4.5 more contracts. This supports the claim that more tenured employees, on average, get awarded more contracts, making it a passive prediction based on observed data.

Question 16

Which of the following conditions ensures that the estimates of the coefficients for the population regression equation are distributed normally?
A) The residuals are distributed normally.
B) The residuals are homoscedastic.
C) The residuals are heteroscedastic.
D) The sample is "large" enough.

Accepted Answer

The answer of Which of the following conditions ensures that...

Question 17

Which of the following conditions is necessary for the sample estimates of the population coefficients that best describe the co-movement amongst the variables to be consistent?
A) The sample is a random sample.
B) The errors are distributed normally.
C) The errors are homoscedastic.
D) The errors are heteroscedastic.

Accepted Answer

The consistency of sample estimates of population coefficients depends on a random sample that represents the population. The other conditions mentioned (normality of errors and homoscedasticity of errors) are assumptions made during the estimation procedure but do not guarantee consistency on their own.

Question 18

Suppose you estimate the following regression of a firm's Sales and number of employees at each location across the country: Sales = 95,342 + 0.76 Number of Employees. You are willing to believe you have a random sample of store locations, and a sufficiently large sample size. Which statements are not yet justified by the regression results?
A) On average a store with 100 employees is likely to have Sales of about = 95,342 + 0.76(100) = 95,418
B) On average, stores with more sales have more employees.
C) Increasing the number of employees at a store by 2 will raise sales by 0.76 × 2 = 1.52
D) None of the answers is correct.

Accepted Answer

The answer of Suppose you estimate the following regression of...

Question 19

If the determining function for the likelihood of a mortgage application receiving a loan is given by, Loan Successful = 0.60 + 0.01 Credit Score. What would be the causal effect of increasing your credit score by 10 points?
A) Your expected probability of getting a loan would be 0.60 + 0.01(10) = 0.61.
B) Your expected probability of getting a loan would be 0.60
C) Your expected probability of getting a loan would increase by 0.01(10) = 0.10
D) Your expected probability of getting a loan would increase by 10.

Accepted Answer

The causal effect of increasing your credit score by 10 points is calculated by multiplying the coefficient of the credit score (0.01) by the increase in points (10), which equals 0.10. This means the expected probability of getting a loan increases by 0.10, not to 0.10.

Question 20

In characterizing determining functions, the "error term" represents:
A) unobserved factors that determine the outcome.
B) factors that correlate with the treatment.
C) deviations from random sampling.
D) deviations from random treatment assignment.

Accepted Answer

The error term represents unobserved factors that determine the outcome. These factors may affect the dependent variable but are not included in the model, leading to unexplained variation in the outcome variable.

Quiz 6: Correlation Vs Causality in Regression Analysis

Suppose the regression of Output per Hour on employee Age yields a coefficient of -4.3 with a standard error of 1.2. Which of the following equations would properly report the 95% confidence interval for the population coefficient?

When making passive predictions, it is not important to be able conclude that:

If the residuals of a regression model, Yi = B + MXi + Ei, are such that their variances vary across all values of X, then they are said to be:

Which of the following is not a condition to estimate a model for causality?

Which of the following settings best describes a setting in which one would be making a passive prediction?

In making passive predictions, it is usually sufficient to (consistently) estimate what sort of relationships?

Suppose that the following regression equation best describes the co-movement between Sales, Price and Number of Competitors: Salesi = B + M1Pricei + M2NumCompi. What moment condition would not be used to yield a consistent estimate of B, M1, M2?

In the following determining function, Earningsi = α0 + α1Educationi + Ui, what might be a factor contained in Ui?

Why can't the regression coefficients in correlation analysis be interpreted as the causal effect of a treatment on the outcome?

When making passive predictions, which type of relationship must you believe continues to hold when you move your estimation sample to your forecasting sample?

Which of the following conditions ensures that the estimates of the coefficients for the population regression equation are distributed normally?

Which of the following conditions is necessary for the sample estimates of the population coefficients that best describe the co-movement amongst the variables to be consistent?

If the determining function for the likelihood of a mortgage application receiving a loan is given by, Loan Successful = 0.60 + 0.01 Credit Score. What would be the causal effect of increasing your credit score by 10 points?

In characterizing determining functions, the "error term" represents:

If the residuals of a regression model, Y_i= B + MX_i + E_i, are such that their variances vary across all values of X, then they are said to be:

Suppose that the following regression equation best describes the co-movement between Sales, Price and Number of Competitors: Sales_i = B + M₁Price_i + M₂NumComp_i. What moment condition would not be used to yield a consistent estimate of B, M₁, M₂?

In the following determining function, Earnings_i = α₀ + α₁Education_i + U_i, what might be a factor contained in U_i?