ECON424: Midterm

C

We are interested in measuring the effect of eating cookies on exam grades. We collect data in a sample of 150 observations (=students) on number of cookies each student has had before exam (lets say 12 hours before exam), and we have students grades. The following equation is estimated: y=65+3.5x where y represents the grades and x represents the number of cookies. Which of the following shows the correct interpretation of the relationship between number of cookies and grades. Check all that apply. (One correct answer.) A) Eating any additional cookie increases grade by 65 points. B) Eating cookies guarantees a minimum of 65 in the exam. C) Eating an additional cookie increases grade by 3.5 points. D) Eating cookies increases grade by 3.5 points.

A

In studying the factors affecting grades at your university, which one of the following CANNOT be used as possible explanatory variable? Check all that apply. (One correct answer) A) A variable that is one if the person is a student; zero if not. B) A variable that shows number of shoes the student has. C) A variable that is one if the student is female; zero if the student is male. D) A variable for the price of house of student's parents.

C

Refer to the equation in question 1 (y=65+3.5x ) between number of cookies (x) and grade (y). Which of the following shows the correct interpretation of the intercept. Check all that apply. (One correct answer.) A) Eating cookies guarantee a minimum of 65 in the exam. B) Eating any additional cookie increases grade by 65 points. C) A student who does not eat cookies is expected to have a grade of 65. D) A student who does not eat cookies is expected to have a grade of 3.5.

A

We are interested in studying the job market conditions for teenagers in Maryland. We randomly select 100 teenagers from College Park and send them questionnaires. Which one can be our population of interest? Check all that apply. (One correct answer.) A) All teenagers in Maryland B) 100 Teenage workers in College Park C) All teenagers in College Park D) All workers in Maryland

A, B

What is correct about F-test of overall validity of the model? Check all that apply. (Two correct answers.) A) A big F-statistic (bigger than critical value) means that the model has explanatory power. B) It is one sided test of R-squared being zero versus being greater than zero. C) In rare cases the value of F-statistic can be negative. D) It is a two sided test of R-squared being zero versus not being zero.

B, D

What is the benefit of multiple regression? Check all that apply. (Two correct answers.) A) Multiple regression is bigger than simple regression, bigger models are always better. B) Multiple regression allows for including more complicated functional forms of explanatory variables. C) Multiple regressions always generate unbiased results. D) Multiple regression allows for explicit control of some features, if needed.

A, B, C

What is the implication of Gauss Markov theorem? Check all that apply. (Three correct answers.) A) There may be nonlinear and more precise estimators than OLS. B) There may be biased and more precise estimators than OLS. C) All linear and unbiased estimators are less precise than OLS. D) All nonlinear and biased estimators are more precise than OLS.

B

Which one is NOT correct about goodness of fit, total variations in variable of interest, and variations in model and in residuals? Check all that apply. (One correct answer.) A) Goodness of fit measures how much of total variations in the variable of interest is explained by variations in explanatory variables (model). B) Share of variations in residuals out of total variations in variable of interest defines the measure of goodness of fit. C) Total variation is always bigger than or, in some uninteresting cases, equal to variations in residuals and in model. D) Goodness of fit is a number between zero and one, including zero and one.

A, B

Which one is correct about OLS estimators? Check all that apply. (Two correct answers.) A) OLS is the most widely used estimation method. Correct! B) OLS is based on minimizing sum of squared residuals. C) OLS is the only estimation method in econometric. D) OLS is based on minimizing sum of residuals.

B, C, D

Which one is correct about a log-log function? Check all that apply. (Three correct answers.) A) The interpretation of the slope is as always, change in the level of variable of interest divided by change in the level of explanatory variable. B) The interpretation is based on percentage change in variable of interest and percentage change in explanatory variable. C) The slope coefficient is unitless. D) The slope coefficient is elasticity.

A, B

Which one is correct about adding a variable to the model? Check all that apply. (Two correct answers.) A) If the theory we work on says a variable should be in the model, it is better to add it. B) If a variable is not highly significant, but has a test statistic of more than 1, it deserves more investigation. C) If a variable is statistically significant, it should be there, even if its significance is because of some technical issue. D) If adding a variable increases R-squared, it deserves being in the model.

A, B, D

Which one is correct about adjusted R-squared? Check all that apply. (Three correct answers.) A) It increases if we add an explanatory variable that has strong explanatory power. B) It increases if we add any explanatory variable. C) It is always less than R-squared. D) It punishes adding any explanatory variable, and rewards explanatory power of variables.

A, D

Which one is correct about homoscedasticity and heteroscedasticity? Check all that apply. (Two correct answers.) A) Homoscedasticity means that variation of y's around their expected values are independent of values of explanatory variables. B) The fitted line in heteroscedastic error case is flatter than the fitted line in homoscedastic error. C) Homoscedasticity means that average of error term is not related to values of explanatory variables. D) Homoscedasticity is one of the assumptions of classical regression model.

D

Which one is correct about including an irrelevant variable (a variable whose coefficient in population is zero) in the model? Check all that apply. (One correct answer.) A) It does not matter because what we get when we estimate the model using sample will be exactly zero. B) It does matter because it tremendously increases R-squared, and give a wrong signal about the value of the model. C) It does matter, because it creates bias in estimates of the other coefficients. D) It does not matter, because based on feature 1, its expected value is zero, and even if we include it, the estimates coefficient is most likely insignificant.

D

Which one is correct about interaction between two variables in regression? Check all that apply. (One correct answer.) A) The coefficient of interaction term captors the relationship between two explanatory variables. B) The sign of interaction term is always multiplication of signs of the coefficient of two explanatory variables. C) Using interaction terms is only acceptable in log-level regressions. D) Presence of an interaction terms indicates that the effect of one variable on variable of interest depends on the value of the other explanatory variable.

D

Which one is correct about nonlinear functions? Check all that apply. (One correct answer.) A) Linearity in variables is violation of regression assumptions, but because they happen frequently, we accept them in OLS regressions. B) Nonlinearity in variables and in parameters are both violations of regression assumptions and are not acceptable in OLS regressions. C) Nonlinearity in variables and in parameters do not violate any assumption and are acceptable in OLS regressions. D) Nonlinearity in variables is not violation of regression assumptions, but nonlinearity in parameters is violation of regression assumption, and is not acceptable in OLS regressions.

C

Which one is correct about omitted variable bias? Check all that apply. (One correct answer.) A) If the omitted variable is relevant, there is a bias. B) If the omitted variable and included variable are correlated, there is a bias. C) If the omitted variable and included variable are correlated AND the omitted variable is relevant, there is a bias. D) Random assignment of included variables cuts the relationship between omitted variable and included variable and bring the bias to zero.

C, D

Which one is correct about p-value of a test? Check all that apply. (Two correct answers.) A) If it is more than the significance level, we can reject the null and claim that the variable is significant. B) It is always less than significance level. C) It is the likelihood that the test statistic is generated "just as a matter of chance". D) In the test of statistical significance, it is twice the area more extreme than the test statistic.

A, B

Which one is correct about population model and sample model? Check all that apply. (Two correct answers.) A) We use sample model to talk about population, even though the model is not based on population B) It is almost impossible to have population model C) Sample model is useless, because it is not based on population D) Population model and sample model are the same

A, B

Which one is correct about positive and negative biases and bias towards zero and bias away from zero? Check all that apply. (Two correct answers.) A) A positive bias when the true coefficient is negative, is bias towards zero. B) A positive bias when the true coefficient is positive, is bias away from zero. C) Positive bias is the same as bias towards zero and negative bias is the same as bias away from zero. D) It is impossible to have positive bias when the true coefficient is negative.

A, B, C

Which one is correct about quadratic function in regression? Check all that apply. (Three correct answers.) A) It always has a minimum or a maximum point, even if the value at which this maximum or minimum happen may not be realistic. B) It has curvature, showing different value of effect at different level of explanatory variable. C) It is a nonlinear function of variables. D) The value of variable of interest always goes up at decreasing rate.

A, D

Which one is correct about randomized experiments? Check all that apply. (Two correct answers.) A) Randomized experiments are so valuable that justifies spending huge amount of money, whenever it is possible. B) It is impossible to run a perfect randomized experiment, so randomized experiments are useless. C) It is impossible to run randomized experiments in social sciences. D) Although randomized experiments are impossible in some cases, it is always informative to think about an "ideal" experiment, whenever we study causal effect of one variable on a variable of interest.

B, C, D

Which one is correct about testing the joint significance of more than one variable? Check all that apply. (Three correct answers.) A) It is equivalent to a set of t-tests, each for one variable. B) The restricted model can be calculated by imposing restrictions to unrestricted model. C) It compares equivalency of two models, one with restrictions and the other one without restrictions. D) Test of overall validity of model is a special case of this test in which restricted model does not have any explanatory variable.

A, B

Which one is correct about tests of hypothesis? Check all that apply. (Two correct answers.) A) Tests are only about parameters in population. B) The idea of hypothesis testing is to find an evidence in sample for or against a hypothesis. C) Using hypothesis testing, we can find the values of a parameter in population with certainty. D) We may test a hypothesis about a parameter in population or a statistic in sample.

C, D

Which one is correct about the experiments on mice in lab mentioned in the text? Check all that apply. (Two correct answers.) A) To save time and cost of experiments, we can give two types of medicines (two treatments) to mice and run two experiments at once. B) If the color of the two mice vary, it violates ceteris paribus, even if it is unrelated to mouse's health. C) For causal interpretation of the results, everything should be the same for control and treatment observations. D) The mouse that does not receives medicine is used as comparison observation.

A, B

Which one is correct about the relationship between errors and residuals? Check all that apply. (Two correct answers.) A) For those observations from the population that are in sample, there is no relationship between residual and error. B) Errors are defined for population and residuals are defined for sample. C) For those observations from the population that are in sample, residuals and errors are the same. D) For those observations from the population that are in sample, positive (or negative) residuals are necessarily accompanied by positive (or negative) error.

B, D

Which one is correct about the tradeoff between bias and variance? Check all that apply. (Two correct answers.) A) If two variables are highly correlated, the inflation in variance will be negligible. B) If the variance is very inflated, we prefer to accept a small bias to avoid inflated variance. C) We should always avoid bias, even if there is a big variance. D) If the two variables are absolutely uncorrelated, we have neither bias problem nor inflated variance problem.

A, B, D

Which one is correct about type one and type two errors. Check all that apply. (Three correct answers.) A) There is a tradeoff between two types of error, reducing one is associated to increasing the other one. B) Type I error is similar to sending an innocent person to prison. C) Type one and type two errors can be reduced to zero at the same time. D) Type I error is the error we make if we reject the null hypothesis while the hypothesis is indeed correct.

A

Which one is correct about unbiasedness and consistency? Check all that apply. (One correct answer.) A) An estimator can be unbiased, consistent, both, or none. B) An unbiased estimator is consistent, and vice versa. C) A consistent estimator is necessarily unbiased, but not the other way around. D) An unbiased estimator is necessarily consistent, but not the other way around.

D

Which one is the meaning of perfect collinearity? Check all that apply. (One correct answer.) A) Two or more explanatory variables have any types of relations, linear or non-linear. B) ‌Two or more explanatory variables have correlations. C) Two or more explanatory variables have positive correlations. D) Two or more explanatory variables are perfectly related in a linear way.

A, B

Which one is the most important feature of having nonlinear variables in regression? Check all that apply. (Two correct answer.) A) Change in the level of variable of interest associated with the change in the level of an explanatory variable cannot be expressed in a constant number. B) The effect of explanatory variable changes by that explanatory variable or other explanatory variables. C) The effect of an explanatory variable decreases as the value of explanatory variable increases. D) There is always higher order polynomials that explain the variations in the variable of interest.

D

Which one of the following is NOT correct about algebraic characteristics of OLS estimators? Check all that apply. (One correct answer.) A) Sum of all residuals is zero. B) The regression line always passes through the average of the sample C) The sample covariance between x and residuals is zero. D) The regression line always passes through the origin (x=0, y=0)

D

Which one violates the assumption of linearity of parameters? Check all that apply. (One correct answer.) A) Using squared value of an explanatory variable. B) Using a parameters as constant value in the regression. C) Using inverse of an explanatory variables. D) Using multiplication of two parameters.

D

Why RAND experiment is considered as a very important study? Check all that apply. (One correct answer.) A) It is an example of a randomized experiment in social science in which perfect random assignment is very easy, and there is no contamination in experiment. B) It is an example of randomized experiment, and any randomized experience is important. C) It is about health and everything about health is important. D) It is an example of randomized experiment in an area where randomized experiment is almost impossible, both because of the nature of the issue and its cost.