There are three important requirements for this question. 1. The crucial part of this question is the explanations and list out every single symbols, formulas, algebra steps whether it is about the differentiation, the summation operator or anything as to explain to a primary school student who has not done this subject and know nothing about this topics. Which means I would need all the theories, step by step, and all the symbols in details. 2. The actual answers, the actuals answers must be incorporate with the explanations as shown as something in the screenshot sample where the explanations and the actual answers are combined together. 3. I will have many questions to follow afterward and the tutor must be very welcoming and have the right attitude to answer any concerns I have. The answers must be typed In a word document, with all the formulas or any algebra manipulation typed in the word document using the formula option.
For example, the question starts with 1. List out all the necessary symbols, formulas, theories. 2. Explain what the 1 list out . 3. The answer with all the manipulation steps with the explanations of each manipulation and each algebra. 4. Enthusiastic attitude about any queries I am having. 5. Work in the long run if this one works out well.
The two pdfs attached are one for the question part and the second one for the answer part with the third one with the answers and the explanations as the sample I am looking for.
I look forward to work with the tutor in the long run for months if we work this question out well, thank you for your time.
Mid-term MCQ Exam 2020
1. Other things equal, a lower standard error for the OLS estimator:
(A) Means a lower p-value.
(B) Means it is less likely to reject the null hypothesis that the coefficient is zero.
(C) Means a wider confidence interval.
(D) Means a lower t-statistic.
(E) None of the above.
2. You regress Y on X1 and a constant using survey data. In order to avoid omitted
variable bias, you should:
(A) Use heteroscedastic robust standard errors.
(B) Replace X1 with another explanatory variable that has larger variance.
(C) Use a larger sample.
(D) Use data from an ideal randomized control experiment.
(E) Include an additional regressor, X2.
3. You have data on primary school grades, gender and number of older siblings.
You find that girls have higher grades than boys. Kids with more siblings have lower
grades than kids with fewer siblings. Also, girls have a higher number of siblings
than boys.
Under these circumstances, you regress grades on a female dummy and obtain a
coefficient of 1.19. You then regress grades on a female dummy and the number of
siblings. How does the coefficient on female change?
(A) It goes up because the omitted variable bias is negative.
(B) It goes down because the omitted variable bias is negative.
(C) It goes up because the omitted variable bias is positive.
(D) It goes down because the omitted variable bias is positive.
(E) There is not enough information to answer this question.
4. Galton was interested in the relationship of heights of parents and children and
regressed the height of children on the height of parents. His data set measured
heights in inches. You re-examine this question using the same data set but heights
are now measured in centimetres.
When you compare your regression results with that of Galton, what do you expect
to find?
(A) the two slopes to be different, but standard errors to be the same.
(B) the two intercepts to be different, but standard errors to be the same.
(C) the two slopes to be the same, but the two intercepts to be different.
(D) the R2 ’s to be different, but the slopes and intercepts to be the same.
(E) the two slopes to be different, but the R2 ’s to be the same.
5. The variance of the OLS estimator crucially depends on sample size and moments
of the variable X. In particular,
(A) The larger the sample size, the higher the variance.
(B) The higher the mean of X, the higher the variance.
(C) The higher the variance of X, the lower the variance.
(D) Both statements (A) and (B) are true.
(E) Both statements (A) and (C) are true.
6. You want to study how grades vary across the four year groups in the university.
In order to avoid the dummy variable trap you regress grades on a constant and the
year group dummies except for year 4. What would you expect to find?
(A) Each year group coefficient to be the grade for each group relative to the
university mean.
(B) This regression cannot be estimated.
(C) Each year group coefficient to be the difference in the average grade of that
group and year 4.
(D) The constant to be the average grade for year 4.
(E) Both statements (C) and (D) are true.
7. You perform a regression of wages on gender, where the variable gender takes
value 5 for males and value 10 for females. How do we interpret the ‘slope’
coefficient?
(A) A fifth of the gender wage gap.
(B) It has no possible interpretation in this specification.
(C) The gender wage gap.
(D) Five times the gender wage gap.
(E) None of the above.
8. To decide whether or not the slope coefficient is large:
(A) you should analyze the economic importance of a given increase in X.
(B) the slope coefficient must be larger than the sample average of X.
(C) the slope coefficient must be larger than zero.
(D) the slope coefficient must be statistically significant.
(E) the slope coefficient must be larger than one.
9. What would be the consequences if heteroscedasticity is present in a regression
model, but is ignored?
(A) No consequences as long as the independent variable is normally distributed.
(B) The coefficient will be biased.
(C) The standard errors will be incorrect.
(D) The standard errors will not be affected.
(E) The coefficient will have no interpretation.
10. Smaller p-values indicate more evidence in support of:
(A) the null hypothesis.
(B) the alternative hypothesis.
(C) neither, it depends on whether it is a one-sided or two-sided test.
(D) neither, it depends on how large is the confidence interval.
(E) None of the above.
11. If a hypothesis is rejected at the 5% level of significance, it:
(A) will always be rejected at the 1% level.
(B) will never be rejected at the 1% level.
(C) may be rejected or not rejected at the 1% level.
(D) will always be accepted at the 1% level.
(E) None of the above.
12. You would like to analyse the gender gap in earnings and you collect detailed
data just for females on earnings, number of children and type of education. You
regress earnings on a female gender dummy variable, the number of children and
type of education. What would you expect to find for the estimate on the female
dummy variable?
(A) it would have a large variance.
(B) it would not be estimated.
(C) it would suffer from omitted variable bias.
(D) it would represent the causal effect of gender on earnings.
(E) None of the above.
13. When two regressors are imperfectly multicollinear, then
(A) the regression cannot include both of them.
(B) the OLS estimates will be biased.
(C) the standard errors will be large.
(D) the t-statistics will be large.
(E) the confidence intervals will be small.
14. The F-statistic of a joint hypothesis test is
(A) an increasing function of the t-statistics of each coefficient involved.
(B) an increasing function of the t-statistics of each coefficient involved and the
number of observations.
(C) a function of the correlation between the t-statistics of each coefficient.
(D) Both answers (A) and (B).
(E) Both answers (A) and (C).
15. You have data on wages, gender and university degree. You find that university
graduates have higher wages than non university graduates. Females have lower
wages than males. Also, there are more women than men that attend university.
Under these circumstances, you regress wages on a male dummy and obtain a
coefficient of 8.31.
You then regress regress wages on a male dummy and a university dummy. How
does the coefficient on male change?
(A) It goes up because the omitted variable bias is negative.
(B) It goes down because the omitted variable bias is negative.
(C) It goes up because the omitted variable bias is positive.
(D) It goes down because the omitted variable bias is positive.
(E) There is not enough information to answer this question.
16. The R2 and the adjusted R2 can tell you whether
(A) an included variable is statistically significant.
(B) the regressors are a true cause of the movements in the dependent variable.
(C) there is omitted variable bias.
(D) you have chosen the most appropriate set of regressors.
(E) none of the above.
17. What is the meaning of the term ‘heteroscedasticity’?
(A) The variance of the dependent variable is not constant
(B) The variance of the errors is not constant
(C) The errors are not linearly independent of each other
(D) The errors have none-zero mean
(E) None of the above
18. You estimate a regression of earnings on both female and male gender dummy
variables, but no constant.
As females typically earn less than males, you would expect
(A) both coefficients to be the same distance from the constant, one above and the
other below.
(B) the coefficient for Male to have a positive sign and for Female a negative sign.
(C) none of the OLS estimators to exist because there is perfect multicollinearity.
(D) the coefficient for Male to have a negative sign and for Female a positive sign.
(E) None of the above.
19. Which of the following statements is true?
(A) Multicollinearity cannot be identified by examining patterns of correlations
among explanatory variables
(B) Multicollinearity occurs when explanatory variables are correlated with each
other
(C) A high correlation between the dependent variable and a given independent
variable is a sign of multicollinearity
(D) Explanatory variables that are orthogonal to each other may also suffer from
multicollinearity
(E) Only statements (B) and (C) are true.
20. The t-statistic has the following distribution:
(A) Standard normal distribution for n < 15.
(B) Student t distribution with (n – 1) degrees of freedom regardless of the
distribution of the Y.
(C) Student t distribution with (n – 1) degrees of freedom if the Y is normally
distributed.
(D) A standard normal distribution if the sample standard deviation goes to zero.
(E) It depends on the hypothesis being tested.
Mid-term MCQ Exam 2020
1. Other things equal, a lower standard error for the OLS estimator:
*(A) Means a lower p-value.
(B) Means it is less likely to reject the null hypothesis that the coefficient is zero.
(C) Means a wider confidence interval.
(D) Means a lower t-statistic.
(E) None of the above.
2. You regress Y on X1 and a constant using survey data. In order to avoid omitted
variable bias, you should:
(A) Use heteroscedastic robust standard errors.
(B) Replace X1 with another explanatory variable that has larger variance.
(C) Use a larger sample.
*(D) Use data from an ideal randomized control experiment.
(E) Include an additional regressor, X2.
3. You have data on primary school grades, gender and number of older siblings.
You find that girls have higher grades than boys. Kids with more siblings have lower
grades than kids with fewer siblings. Also, girls have a higher number of siblings
than boys.
Under these circumstances, you regress grades on a female dummy and obtain a
coefficient of 1.19. You then regress grades on a female dummy and the number of
siblings. How does the coefficient on female change?
*(A) It goes up because the omitted variable bias is negative.
(B) It goes down because the omitted variable bias is negative.
(C) It goes up because the omitted variable bias is positive.
(D) It goes down because the omitted variable bias is positive.
(E) There is not enough information to answer this question.
4. Galton was interested in the relationship of heights of parents and children and
regressed the height of children on the height of parents. His data set measured
heights in inches. You re-examine this question using the same data set but heights
are now measured in centimetres.
When you compare your regression results with that of Galton, what do you expect
to find?
(A) the two slopes to be different, but standard errors to be the same.
(B) the two intercepts to be different, but standard errors to be the same.
*(C) the two slopes to be the same, but the two intercepts to be different.
(D) the R2 ’s to be different, but the slopes and intercepts to be the same.
(E) the two slopes to be different, but the R2 ’s to be the same.
5. The variance of the OLS estimator crucially depends on sample size and moments
of the variable X. In particular,
(A) The larger the sample size, the higher the variance.
(B) The higher the mean of X, the higher the variance.
*(C) The higher the variance of X, the lower the variance.
(D) Both statements (A) and (B) are true.
(E) Both statements (A) and (C) are true.
6. You want to study how grades vary across the four year groups in the university.
In order to avoid the dummy variable trap you regress grades on a constant and the
year group dummies except for year 4. What would you expect to find?
(A) Each year group coefficient to be the grade for each group relative to the
university mean.
(B) This regression cannot be estimated.
(C) Each year group coefficient to be the difference in the average grade of that
group and year 4.
(D) The constant to be the average grade for year 4.
*(E) Both statements (C) and (D) are true.
7. You perform a regression of wages on gender, where the variable gender takes
value 5 for males and value 10 for females. How do we interpret the ‘slope’
coefficient?
*(A) A fifth of the gender wage gap.
(B) It has no possible interpretation in this specification.
(C) The gender wage gap.
(D) Five times the gender wage gap.
(E) None of the above.
8. To decide whether or not the slope coefficient is large:
*(A) you should analyze the economic importance of a given increase in X.
(B) the slope coefficient must be larger than the sample average of X.
(C) the slope coefficient must be larger than zero.
(D) the slope coefficient must be statistically significant.
(E) the slope coefficient must be larger than one.
9. What would be the consequences if heteroscedasticity is present in a regression
model, but is ignored?
(A) No consequences as long as the independent variable is normally distributed.
(B) The coefficient will be biased.
*(C) The standard errors will be incorrect.
(D) The standard errors will not be affected.
(E) The coefficient will have no interpretation.
10. Smaller p-values indicate more evidence in support of:
(A) the null hypothesis.
*(B) the alternative hypothesis.
(C) neither, it depends on whether it is a one-sided or two-sided test.
(D) neither, it depends on how large is the confidence interval.
(E) None of the above.
11. If a hypothesis is rejected at the 5% level of significance, it:
(A) will always be rejected at the 1% level.
(B) will never be rejected at the 1% level.
*(C) may be rejected or not rejected at the 1% level.
(D) will always be accepted at the 1% level.
(E) None of the above.
12. You would like to analyse the gender gap in earnings and you collect detailed
data just for females on earnings, number of children and type of education. You
regress earnings on a female gender dummy variable, the number of children and
type of edcuation. What would you expect to find for the estimate on the female
dummy variable?
(A) it would have a large variance.
*(B) it would not be estimated.
(C) it would suffer from omitted variable bias.
(D) it would represent the causal effect of gender on earnings.
(E) None of the above.
13. When two regressors are imperfectly multicollinear, then
(A) the regression cannot include both of them.
(B) the OLS estimates will be biased.
*(C) the standard errors will be large.
(D) the t-statistics will be large.
(E) the confidence intervals will be small.
14. The F-statistic of a joint hypothesis test is
(A) an increasing function of the t-statistics of each coefficient involved.
(B) an increasing function of the t-statistics of each coefficient involved and the
number of observations.
(C) a function of the correlation between the t-statistics of each coefficient.
(D) Both answers (A) and (B).
*(E) Both answers (A) and (C).
15. You have data on wages, gender and university degree. You find that university
graduates have higher wages than non university graduates. Females have lower
wages than males. Also, there are more women than men that attend university.
Under these circumstances, you regress wages on a male dummy and obtain a
coefficient of 8.31.
You then regress regress wages on a male dummy and a university dummy. How
does the coefficient on male change?
*(A) It goes up because the omitted variable bias is negative.
(B) It goes down because the omitted variable bias is negative.
(C) It goes up because the omitted variable bias is positive.
(D) It goes down because the omitted variable bias is positive.
(E) There is not enough information to answer this question.
16. The R2 and the adjusted R2 can tell you whether
(A) an included variable is statistically significant.
(B) the regressors are a true cause of the movements in the dependent variable.
(C) there is omitted variable bias.
(D) you have chosen the most appropriate set of regressors.
*(E) none of the above.
17. What is the meaning of the term ‘heteroscedasticity’?
(A) The variance of the dependent variable is not constant
*(B) The variance of the errors is not constant
(C) The errors are not linearly independent of each other
(D) The errors have none-zero mean
(E) None of the above
18. You estimate a regression of earnings on both female and male gender dummy
variables, but no constant.
As females typically earn less than males, you would expect
(A) both coefficients to be the same distance from the constant, one above and the
other below.
(B) the coefficient for Male to have a positive sign and for Female a negative sign.
(C) none of the OLS estimators to exist because there is perfect multicollinearity.
(D) the coefficient for Male to have a negative sign and for Female a positive sign.
*(E) None of the above.
19. Which of the following statements is true?
(A) Multicollinearity cannot be identified by examining patterns of correlations
among explanatory variables
*(B) Multicollinearity occurs when explanatory variables are correlated with each
other
(C) A high correlation between the dependent variable and a given independent
variable is a sign of multicollinearity
(D) Explanatory variables that are orthogonal to each other may also suffer from
multicollinearity
(E) Only statements (B) and (C) are true.
20. The t-statistic has the following distribution:
(A) Standard normal distribution for n < 15.
(B) Student t distribution with (n – 1) degrees of freedom regardless of the
distribution of the Y.
*(C) Student t distribution with (n – 1) degrees of freedom if the Y is normally
distributed.
(D) A standard normal distribution if the sample standard deviation goes to zero.
(E) It depends on the hypothesis being tested.
