Exam 2 Prep

The Gauss Markov Theorem tells us that ordinary least squares yields estimates that are unbiased, efficient, and consistent so long as the errors are ______. a normally distributed b homoskedastic c independent d zero on average e A and B f all of the above

F

Bob is studying the relationship between average standardized test scores (TS) and freshmen retention rates (RR, measured as a %) at U.S. universities, while controlling for the following 3 types of universities: (i), public (ii) non-profit, and (iii) for-profit. Bob defines D 1 as a dummy equal to 1 for public universities and 0 otherwise; and D 2 as a dummy equal to 1 for non-profit universities and 0 otherwise. He estimates the following: = 4 + 0.75×TS + 5×D1 +7×D2 UNIVERSITY In order for Bob to correctly use dummy variables for these 3 types of universities, the groups must be "mutually exclusive and exhaustive". What does this phrase mean? a Each university must be classified as belonging to only 1 of the 3 groups. b Each university may or may not belong to 1 of the 3 groups. c Each university must belong to at least 1 of the 3 groups. d B and C. e None of the above.

A

A medical researcher is analyzing the number of emergency room visits in rural Kansas counties using the following variables: (i) ER is the average number of emergency room visits per week; and (ii) AGE as the average age of county residents. The estimated model is: = 60 -2×AGE + 0.025×AGE 2. VISITS What is the lowest number of emergency room visits predicted by the model? a 12.25 visits b 20.0 visits c 22.5 visits d The answer cannot be determined with the available information. e None of the above.

B

Bob is studying the relationship between average standardized test scores (TS) and freshmen retention rates (RR, measured as a %) at U.S. universities, while controlling for the following 3 types of universities: (i), public (ii) non-profit, and (iii) for-profit. Bob defines D 1 as a dummy equal to 1 for public universities and 0 otherwise; and D 2 as a dummy equal to 1 for non-profit universities and 0 otherwise. He estimates the following: = 4 + 0.75×TS + 5×D1 +7×D2 UNIVERSITY What is the appropriate test to assess whether the 3 types of universities are important in explaining retention rates? a The t test for each dummy variable. b The partial F test. c The vif test. d None of the above.

B

Bob is studying the relationship between average standardized test scores (TS) and freshmen retention rates (RR, measured as a %) at U.S. universities, while controlling for the following 3 types of universities: (i), public (ii) non-profit, and (iii) for-profit. Bob defines D 1 as a dummy equal to 1 for public universities and 0 otherwise; and D 2 as a dummy equal to 1 for non-profit universities and 0 otherwise. He estimates the following: = 4 + 0.75×TS + 5×D1 +7×D2 UNIVERSITY What the predicted retention rate for a public university with an average standardized test score of 72? a 58% b 63% c 65% d None of the above.

B

Bob is studying the relationship between average standardized test scores (TS) and freshmen retention rates (RR, measured as a %) at U.S. universities, while controlling for the following 3 types of universities: (i), public (ii) non-profit, and (iii) for-profit. Bob defines D 1 as a dummy equal to 1 for public universities and 0 otherwise; and D 2 as a dummy equal to 1 for non-profit universities and 0 otherwise. He estimates the following: = 4 + 0.75×TS + 5×D1 +7×D2 UNIVERSITY Which of the following is a true statement regarding the marginal effect between TS and RR? a rr increases by 0.75 percentage points for each unit increase in TS only for for-profit universities. b rr increases by 0.75 percentage points for each unit increase in TS for all 3 types of universities. c rr increases by 5.75 percentage points for each unit increase in TS for public universities. d None of the above.

B

What is the purpose of Anscombe's Quartet? a It shows the connection between classical music and statistics. b It illustrates the importance of looking at your data and identifying influential observations. c It demonstrates the importance of looking at the p values in a regression. d It underscores the importance of checking the data for missing values. e None of the above.

B

What is the rule of thumb for the Central Limit Theorem to apply in a regression? a A minimum of 30 observations is needed b 30 observations are needed for a simple linear regression, then add 10-20 observations for each additional explanatory variable. c 30 observations are needed for a simple linear regression, then add 30 observations for each additional explanatory variable. d None of the above.

B

Bob is studying the relationship between average standardized test scores (TS) and freshmen retention rates (RR, measured as a %) at U.S. universities, while controlling for the following 3 types of universities: (i), public (ii) non-profit, and (iii) for-profit. Bob defines D 1 as a dummy equal to 1 for public universities and 0 otherwise; and D 2 as a dummy equal to 1 for non-profit universities and 0 otherwise. He estimates the following: = 4 + 0.75×TS + 5×D1 +7×D2 UNIVERSITY If Bob adds an interaction term for TS and D 1and another interaction term for TS and D 2 to his model, Bob should be on the lookout for what problem? a Autocorrelation b Heteroskedasticity c Multicollinearity d None of the above.

C

Consider the following variables involving autos in the year 1978: (i) lprice is the auto's price, measured in logged dollars; (ii) lweight is the auto's weight, measured in logged pounds; and (iii) foreign is an indicator variable equal to 0 if the auto was produced in the United States and 1 otherwise. The following regression was estimated (assume all coefficients are statistically signficiant): = -1.79 + 1.29×lweight + 0.53×foreign AUTOS What is the prediced price of a foreign-produced automobile that weights 2500 pounds? a $3,223.74 b $4,036.04 c $6,856.96 d None of the above.

C

Suppose you have estimated = b 0 + b 1X + b 2D + b 3Z where Z =X×D and D is a dummy variable. How does variable Z affect the estimated regression? a The regression line will shift up/down. b The relationship between and X depends on whether D is 0 or 1. c A and B. d None of the above.

C

The regression below examines monthly retail sales (in millions of dollars) at jewelry stores in the U.S. from January 1992 to January 2020. Sales are regressed on a set of indicator variables to capture seasonality. SALES. Using a 1% level of significance, how can the coefficient on month 12 (December) be interpreted? a Mean sales in December are about $4,064 million b Mean sales in December are not statistically different from November. c Mean sales in December are about $4,064 million more than in January. d Mean sales in December are about $4,064 million more in November. e None of the above

C

What can you conclude based on the Breusch-Pagan Test below? 0.03 .8537 a The population disturbances are normally distributed. b The population disturbances are not normally distributed. c The population disturbances have homoskedasticity. d The population disturbances are heteroskedasticity. e None of the above.

C

When a researcher uses the wrong functional form to estimate a regression, the consequence is _____. a inefficient standard errors b inefficient p values c biased coefficients d biased sum of squares e None of the above.

C

Autocorrelation is typically positive, which means that a time series plot would show: a the residuals randomly distributed over time. b the residuals increasing steadily over time. c a curvilinear pattern in the residuals. d a positive residual usually followed by another positive residual.

D

Consider the following variables involving autos in the year 1978: (i) lprice is the auto's price, measured in logged dollars; (ii) lweight is the auto's weight, measured in logged pounds; and (iii) foreign is an indicator variable equal to 0 if the auto was produced in the United States and 1 otherwise. The following regression was estimated (assume all coefficients are statistically signficiant): = -1.79 + 1.29×lweight + 0.53×foreign AUTOS The coefficient on lweight can be interpreted as ____________, while controlling for the variable foreign. a a 1% increase in an automobile's weight is associated with an increase in its price by $1.29 b a 1% increase in an automobile's weight is associated with an increase in its price by $129.00 c an increase in an automobile's weight by 1 pound is associated with an increase in its price by $1.29 d None of the above.

D

Demeaning an explanatory variable can help reduce the problem of _____. a a low R-squared. b heteroskedasticity c statistical insignificance d multicollinearity e serial correlation

D

The natural log of India's per capita GDP (ly) is regressed on a time trend (t) using data from 1960 to 2019. TRENDS What does the model predict for India's per capita GDP in 2019? Round your answer to the nearest dollar. a $1,651 b $7,409 c $22,011 d There is not enough information to answer this question. e None of the above.

$1,651

Which of the following is a polynomial of order 3? ANSWER x2/1 X3./1

...

A curvilinear relationship between variables X and Y implies_____. a) the maringal effect changes for different values of X b) a log transformation should be used c) a polynomial transformation should be used d) None of the above.

A

A disadvantage of a polynomial transformation compared to a transformation using a reciprocal or a log is that _______ . a it has fewer degrees of freedom b statistical insificance is more common c heteroskedasticity is more common d None of the above.

A

A medical researcher is analyzing the number of emergency room visits in rural Kansas counties using the following variables: (i) ER is the average number of emergency room visits per week; and (ii) AGE as the average age of county residents. The estimated model is: = 60 -2×AGE + 0.025×AGE 2. VISITS At what age does the model predict emergency room visits will be at their lowest? a Age 40 b Age 50 c Age 45 d Answer cannot be determined e non of the above

A

Biased regression coefficienets occur when the ____ assumption(s) are violated, while biased standard errors occur when the _____ assumption(s) are violated. a linearity; homoskedasticity and independence b normality; homoskedasticity and independence c homoskedasticity; linearity and independence d normality and homoskedasticity; linearity and independence e None of the above.

A

How might a researcher correct for the problem of serial correlation? a Use the Prais-Winsten transformation or add a lagged dependent variable. b Try a different functional form. c The problem can be ignored if the Central Limit Theorem applies. d Address whether or not there are any outliers. e None of the above.

A

Jackknifed residuals refers to residuals that ______. a have been studentized b can be dangerous for researchers c have high leverage d have been deflated e None of the above.

A

The regression below examines monthly retail sales (in millions of dollars) at jewelry stores in the U.S. from January 1992 to January 2020. Sales are regressed on a set of indicator variables to capture seasonality. SALES. What does the model predict average sales will be in January? a Mean sales in January are about $1,446 million b The answer cannot be calculated. c None of the above.

A

What can you conclude based on the pure-error lack-of-fit test results below using a 10% level of significance? a The expected value of the population disturbances is zero. b The expected value of the population disturbances is not zero. c The population disturbances are normally distributed. d The population disturbances are not normally distributed. e None of the above.

A

A biased statistic means that ______. a the sampling distribution has a relatively large variance. b the estimate is incorrect on average. c the probability that the estimate is correct decreases as the sample d size gets larger. e None of the above.

B

Given yhatt= 90 - 7×(lnX), how can we interpret the relationship between X and Y? a If X increases by 1 unit, then Y decreases by 7%. b If X increases by 1%, then Y decreases by 0.07 units. c If X increases by 1%, then Y decreases by 7 units. d If X increases by 1%, then Y decreases by 700 units. e None of the above.

B

Imagine you have estimated two models: (1) = 1 + 2×ln(X) which has R 2=0.55, and (2) = 1 + 2×X which has R 2=0.61. According to the coefficient of determination, which model is better? a Model 1 b Model 2 c The models are equal. d We cannot compare R2 between these models.

B

The natural log of India's per capita GDP (ly) is regressed on a time trend (t) using data from 1960 to 2019. TRENDS According the estimated model, what is India's average annual growth rate in per capita GDP? Round your answer to the nearest tenth of a percent. a 0.03% b 3.14% c 5.53% d 5.56% e None of the above.

B

The natural log of India's per capita GDP (ly) is regressed on a time trend (t) using data from 1960 to 2019. What type of trend model is this? a A quadratic trend b An exponential trend c An S-curve d None of the above.

B

The regression below examines monthly retail sales (in millions of dollars) at jewelry stores in the U.S. from January 1992 to January 2020. Sales are regressed on a set of indicator variables to capture seasonality. SALES. Using a 1% level of significance, how can the coefficient on month 9 (September) be interpreted? a Mean sales in September are $0 b Mean sales in September are not statistically different from January. c Mean sales in September are not statistically different from August. d Mean sales in September are about $281 million more than in January. e Mean sales in September are about $281 million more in August.

B

Which of the following should a researcher consider if she wishes to evaluate whether or not the errors have a constant variance? a Shapiro-Wilk W Test. b Szroeter's Test. c The Durbin Watosn Test. d Cook's D Statistic. e None of the above.

B

A reseaercher is planning on studying factors that influence a college student's GPA. The researcher wishes to control for a student's gender by using a dummy variable. How should the gender dummy be coded? a The gender dummy equals 1 if the student is female and 0 otherwise. b The gender dummy equals 1 if the student is male and 0 otherwise. c Either A or B. The results will be the same. d None of the above.

C

A researcher should not use the ______ when the regression model has _______. a Durbin-Watson Test; seasonality b Breusch-Godfrey; trend c Durbin-Watson Test; a lagged dependent variable d Breusch-Godfrey; a lagged explanatory variable e None of the above.

C

If a researcher observes a cone-shaped appearance in the residuals, she may wish to stabilize the variance by _____. a centering the data b specifying the model as a polynomial in X c taking the square root or natural log of Y d scaling the data e None of the above.

C

Suppose a researcher finds a negative relationship between X and Y exists only when a particular observation is included in the regression, otherwise the relationship between X and Y is always positive. What should the researcher ethically do when presenting his findings? a Report a negative relationship. b Report no statistical significant relationship was found. c Report a positive relationship. d Report an inconclusive relationship.

C

The dummy variable trap refers to a researcher _____ a interpreting the coefficient of a dummy variable when it is not statistically significant. b interpreting the coefficient of a dummy variable when it is biased. incorrectly coding dummy variables. c including the same number of dummies in the regression as there are groups. d None of the above.

C

Ideally, the _____ should have ____ when graphed. a population errors; a linear appearance b population errors; no pattern c residuals; a linear appearance d residuals; no pattern e None of the above.

D

If the standardized residuals follow a normal distribution, we should expect to see approximately _____ of these values within a range of _____. a 90%; +/- 1 b 90%; +/- 2 c 95%; +/- 1 d 95%; +/- 2 e None of the above.

D

Suppose you run a Durbin-Watson Test and the statistic is 1.5. If the lower critical value is 1.4 and the upper critical value is 1.6, what can you conclude? a The model has heteroskedasticity and autocorrelation. b The model does have autocorelation. c The model does not have autocorelation. d It is indeterminate whether or not the model has autocorelation. e None of the above.

D

Which of the following should a researcher consider if she wishes to evaluate whether the data contain influential observations? a Shapiro-Wilk W Test. b Szroeter's Test. c The Durbin Watson Test. d Cook's D Statistic. e None of the above.

D

The scatterplot below shows: (i) Y = annual revenue generated by a movie, and (ii) X = revenue generated in the movie's opening weekend. Based on the scatterplot, what is the most appropriate transformation? a Polynomial of X b Inverse of X c Log-linear model d Linear-log model e Log-log model f The question cannot be answered with the available information.

E

What transformation(s) can be used if the observations for the explanatory variable have strictly positive values? a Polynomial of X. b Reciprocal of X. c Logarithm of X. d A and B. e A and B and C.

E

What type of relationship do X and Y have in the following regression? yhat= 13 + 500× 1/x a X and Y are negatively related. b X and Y are positively related. c X and Y are negatively related when X > 513. d X and Y are positively related when X < 513. e C and D. f None of the above.

E

Which of the following models is "linear in the parameters" and can therefore be estimated using ordinary least squares methodology? a Y = β0 + β1X1 + X2 + e b yhat= β0 + β1X + e c Y = β0 + β1D + e d A and B. e All of the above. f None of the above.

E