ECO 441K Weekly Quizzes over lectures(Midterm 1)

In a regression with a very large sample (ie degrees of freedom can be considered infinite) the estimated slope is 0.1 and the standard error is 0.03. Which of the following would be the 95% confidence interval for the population slope?

(0.1-1.96(0.03),0.1+1.96(0.03))

Which of the following would (generally) not lead to a reduction of the variance of the slope coefficient?

dropping half the sample

In the MLRM if Assumption MLRM5 is not satisfied then the residuals will be heteroskedastic. This will result in the coefficients being biased. (t or f)

false

Consider the following regression of sleep (minutes per week) on totwork (total work in minutes per week) education and age. The sample size is 706 Var.Coef.Std. Err. p-valuetotwork0.1480.017 0.000educ-11.135.88 0.059age2.21.45 0.129-cons3640112.28 0.000 Which of the following statements is incorrect regarding the coefficients and significance (against a two sided alternative)?

neither educ or age are significant at 10% level

The t statistic (for testing whether a coefficient is zero) equals 2.0 while the degrees of freedom are 30. Which of the following is true regarding the p-value for testing against the two sided alternative that the coefficient is not zero?

p-value is between 0.05 and 0.1

A data set is constructed containing daily Covid cases and deaths for every country in the world for which data is available. The data contains daily case and death totals from March 1 until August 31. What type of data is this?

panel data- The same cross section is observed daily in terms of covid cases and deaths.

If a decrease the level of significance of a test which of the following is true?

the power will be lower

Instead of regressing y on x suppose we do the reverse regression of x on y. In the reverse regression the slope coefficient will have what relationship to the slope in the original regression?-

-It will have the same sign as the original -The original slope is \[ \frac{Cov(x,y)}{Var{x} \] which has a different denominator than the reverse regression Cov(x,y)Var(y) . So they will generally be different but have the same sign.

In a regression of y on x it is found that the SSE is 3700 while the SSR is 6300. What will be the R squared for this regression.

.37

In a sample it is found that x and y have sample means that are zero. This implies that the intercept is equal to what?

0

An individual was more likely to receive training if they had low earnings in 1996

0.2/0.75

For a cross section of observation units a sample of 30 observations reveals that a variable x has a sample variance of 4, y has a sample variance of 1 and the variables x and y have a sample covariance of 0.5. The correlation between x and y must be equal to what?

0.25 r=0.4/(4)^1/2 * (1)^1/2

We are given a coin and we know that either it is fair (ie probability of heads is 0.5) or unfair (probability of heads is 0.6). The null hypothesis is that the coin is fair and the alternative hypothesis is that it is unfair. The decision rule is to reject the null if we flip the coin and we get heads. What is the probability of a Type II error?

0.4

In a regression of y on x1 the slope is 0.5. In a regression of y on x1 and x2 the respective slopes are 0 and 1 respectively. Which of the following gives the slope in the regression of x2 on x1.

0.5

We are given a coin and we know that either it is fair (ie probability of heads is 0.5) or unfair (probability of heads is 0.6). The null hypothesis is that the coin is fair and the alternative hypothesis is that it is unfair. The decision rule is to reject the null if we flip the coin and we get heads. What is the probability of a Type I error?

0.5

We are given a coin and we know that either it is fair (ie probability of heads is 0.5) or unfair (probability of heads is 0.8). The null hypothesis is that the coin is fair and the alternative hypothesis is that it is unfair. The decision rule is to reject the null if we flip the coin and we get heads. What is the power of the test?

0.8

In a regression of y on x it is found that the slope is equal to 0.5. This implies that the predicted change in y due to a 4 unit increase in x is equal to what value?

2

A fitted regression line is given by log(wage)^=0.3+0.09educ+0.002exper+0.04tenure. The effect of increasing experience by 2 years with the same firm is given by which calculation.

2*(0.002+0.04)

For a regression (including an intercept) with k=5 and n=106 the R2=0.5. Which of the following is the F statistic for the overall goodness of fit test for the regression?

20

For a data set with 30 observations the sample variance of variable x is 4 while the sample variance of y equals 1. Which of the following cannot be the covariance between x and y?

3 3/2(1)

For a data set consisting of high schools I have measures of percentage of students who passed a standardized math test, math10 and percentage of students who qualify for a free lunch at the school lnchprg. The fitted regression is: math10^=32−0.3lnchprg and the R squared is 0.17. What is the effect of a 10 percentage point increase (as opposed to 10 percent increase) in lnchprg on math10.

3 percentage point decrease

I run a regression (including an intercept) in which n=35 and k=4. I perform an F test for whether two of the regressors are jointly significant and find that the p-value for this test is 0.05. What must be the value of the F statistic for this test?

3.32

An estimated coefficient is 0.5. What is the confidence level associated with the one sided confidence interval (0.5,∞)?

50%

In a regression with 1000 observations I use 6 regressors and include an intercept. What is the degrees of freedom for the t distribution for testing the significance of the regression coefficients?

993

In the regression of math10 on the log of expenditure per student lexpend I get a slope of 11. Which of the following is a correct interpretation?

A 1% increase in expenditure is predicted to increase math10 by 0.11 units (percentage points)

Consider the following regressions of individual labor market earnings in 1998 on whether or not that individual received job market training in 1997 (train = 1 if they received training train =0 if they did not): earn98^=10−2.0train Suppose I also include earnings from 1996 as an additional control: earn98^=4+2.5train+0.4earn96 Based on these regressions which of the following statements is correct?

An individual was more likely to receive training if they had low earnings in 1996

Suppose that x and u are statistically independent and E(u)=0. Does this imply that the ZCM assumption is satisfied?

True- Since x and u are independent then E(u|x)=E(u)=0 so ZCM is true

Prof Donald creates a data set consisting of the demographic and grades of an ECO441K class from Fall 2019. What type of data is this?

Cross-section-This is a set of measurements of a group of individuals at a point in time. The time period is the semester. It could be panel if repeated measurements of the same thing were taken - eg: weight or performance on a test.

Suppose instead of using log of wage in dollars I instead used the log of wage in cents (ie wagecents = 100 * wage). Which of the following describes what will happen to the slope and intercept? (Hint log(c*x)=log(c)+log(x) )

Intercept changes slope is unaffected

Suppose I start with the simple regression of y on x1 where the slope is given by b1. I add an additional variable x2 to the regression and find that in the multiple regression the slope cofficient on x2 is exactly zero. What can we say about the coefficient on x1 in the multiple regression?

It will be exactly the same as b1

If I add a measure of individual's IQ to a regression of lwage on educ what is the most plausible effect on the coefficient on educ? ie How does the slope on educ in the MLRM with educ and IQ compare to the slope in the SLRM with just educ?

It will decrease

Under the classical linear model assumptions MLR1-MLR6 what is the sampling distribution of the slope coefficient estimator if the sample size is 100 and the regression contains an intercept and two regressors?

a normal distribution

In a regression of lwage (log wage) on tenure (job tenure) the slope is 0.02. Which of the following is a correct interpretation?

One additional year of job tenure is predicted to increase the wage by 2%

Suppose I start with the simple regression of y on x1 where the slope is given by b1. I add an additional variable x2 to the regression and find that in the multiple regression the slope cofficient on x2 is exactly zero. What is the relationship between the R squared in SLRM and R squared in MLRM?

R squared for MLRM will be same as for SLRM

In the MLRM (with at least 2 regressors) which of the following is not necessarily true?

R squared will be the square of the correlation between y and the regressors

In wage data the correlations between lwage and the three variables education, experience and job tenure (all measured in years) are respectively 0.4, 0.1 and 0.3. Which regression will have the highest R squared?

Regression of lwage on education

Note that the 5% critical value for the t distribution with df larger than 120 is between 1.658 and 1.645. The t statistic on experience is 2.4 in the regression (with n=526) of lwage on education, experience and tenure. Therefore if I was doing a 5% level test of theH0:βexperience=0 vs HA:βexperience>0 what would be my decision?

Reject the null hypothesis

Compare the SLRM with y on x1 only with the MLRM that regresses y on x1 and x2. If x1 and x2 have zero correlation then what can we say about the relationship between the standard error on the coefficient of x1 in the SLRM as compared to the standard error on the coefficient on x1 in the MLRM?

Standard errors will be smaller for the model that has the lower estimated residual variance

If I add a variable to a regression which of the following statements is NOT correct concerning the R squared in the new regression compared to the original regression without that variable?

The R squared will be smaller after I add the regressor

If I run a regression of voteA (percentage of votes received by candidate A) on lexpendA (log expenditure of candidate A) ;expendB (log of expenditure on candidate B) and prtystr (percentage of the most recent presidential election that went to A's party) I get the following results in table form: Variable. Coef. Std. Err. p-value lexpendA6.10.380.000 lexpendB-6.60.380.000 prtystrA0.150.0620.012_ cons45.083.920.000

The slopes are all statistically significant at the 1% level

The p-value for a t test of a null hypothesis against a two sided alternative is 0.02. The degrees of freedom are 23. Which of the following is correct concerning the possible values for the t statistic?

The t statistic could be 2.5 or -2.5

Consider regression on a constant'': y=β0+u The OLS estimator is simply the sample average of the y's in the sample β0^=1n(y1+y2+y3+.....+yn) Consider an alternative estimator which is obtained as a weighted average of the y's with weights that add up to 1 but which are not necessarily the same: β0~=w1y1+w2y2+.....+wnyn Which statement is correct concerning these estimators assuming the the five assumptions MLRM1-5 are satisfied (here MLRM3 is not needed and MLRM4 is just E(u)=0)?

The variance of OLS is no larger than the variance of the weighted estimator

Suppose I start with the simple regression of y on x1 where the slope is given by b1. I add an additional variable x2 to the regression and find that in the multiple regression the slope cofficient on x2 is exactly zero. This implies that the fitted values in SLRM and MLRM will be exactly the same? (t or f)

True

In a house price regression of sale price (in thousand of dollars) of houses on the characteristics bdrms (number of bedrooms) lotsize (size of the lot on which house is located) and sqrft (size of house in square feet) the slopes are respectively 13.85, 0.002 and 0.122. Which of the following provides the appropriate estimated partial effect on house price (holding bdrms and lotsize fixed) of increasing sqrft by 100 units?

100*0.122 thousand dollars

What critical value should I use if I am doing a one sided test (ie the alternative hypothesis is that the coefficient is strictly positive) with 25 degrees of freedom and a significance level (alpha) equal to 0.1?

1.316

In a regression of y on x1 and x2 (including an intercept) with 103 observations I find that the SSR is equal to 100. The total variation in x1 is 10 and the correlation between x1 and x2 is 0.1. Which calculation will give the estimated variance of the coefficient on x1?

1/9.9

Suppose instead of regressing y on x I instead regress 100y on 10x. How would the new slope look compared to the slope in the regression of y on x.

10 times the original

From the regression in the previous question one can plausibly conclude that participating in the lunch program causes students to do worse in the math test?

False

In a fitted regression none of the slopes equals 0 exactly. It is still possible for the R squared to be exactly 0.

False

In a regression of wage on experience and the square of experience the coefficient on experience gives me the partial effect of experience holding fixed experience squared.

False

In a simple regression of y on x including an intercept (ie it is not restricted to be zero) it is possible for all the residuals to be strictly negative?

False

Since the fitted residuals are perfectly uncorrelated with the regressor then the ZCM assumptions is satisfied?

False, ZCM is about the residual - not the fitted residual. The algebraic result holds regardless of the relationship between the residual and the regressor.

The students in my ECO441K classes can be considered a random sample from the population of students at UT

False- A random sample of UT students would require that everyone at UT has the same chance of being selected in the sample. This is clearly not the case as only UT students studying ECO441K with Prof Donald are the sample. People studying other had no chance to be selected. Also, depending one what one was measuring this class is not representative of UT as you all have preferences and skills the led you to Economics.

In the population regression of y on x1 and x2 the population slope coefficient on x2 is strictly positive. If I omit x2 and just regress y on x1 then the slope coefficient on x1 will:

Have a negative bias if x1 and x2 are negatively correlated

Assume that education and ability are positively correlated and that ability has a positive effect on log wage if I also control for education. If I do not have a measure of ability and just regress log wage on education then which of the following statements is correct.

I would expect on average to get an coefficient on education that is larger than if I could control for ability

Suppose the value a is inside the 95% confidence interval for a coefficient in a regression. If I were to test the hypothesis that the population coefficient is equal to a against a two sided alternative that the coefficient is not equal to a. Which of the following is a correct statement?

I would not reject the null at the 5% level

The p-value for a test for a specific hypothesis concerning a slope coefficient is 0.08. Which of the following statements is correct?

I would reject the null at the 10% level but not the 5% level.

An estimated coefficient and standard error in a regression are 1.5 and 1 respectively. If the degrees of freedom is 150 then if I am testing the H0:βj=0vs HA:βj≠0 then which of the following is true regarding the conclusion of the hypothesis test?

I would reject the null at the 20%

An estimated slope coefficient is -0.9 and its associated standard error is 0.5 in a regression where the degrees of freedom is 20. If I am doing a test of the H0:βj=0 vs HA:βj<0 at the 5% level then which of the following is true?

I would reject the null hypothesis.

Which of the following will not result in a lower variance for the coefficient on x1 in a regression of y on x1 and x2?

Increasing the correlation between x1 and x2