Question

1. Which of the following conditions will lead to a smaller variance for the intercept estimator for your multiple regression model?

(A) X values cluster far from the origin of the X axis

(B) X values closely pack around the mean of X in your sample

(C) Small sample sizes

(D) High correlation among the explanatory variables

(E) Small error variance in the population regression function

2. R-squared

(A) measures the proportion of variability of the dependent variable that is explained by the explanatory variables

(B) measures the degree of linear association between the dependent and the explanatory variables

(C) measures the goodness-of fit-of a linear model

(D) all of the above

3. If X has a negative effect on Y and Z has a positive on Y, and X and Z are negatively correlated, what is the expected consequence of omitting Z from a regression of Y on X?

(A) The estimated coefficient on X will be biased downwards (too negative)

(B) The estimated coefficient on X will be biased upwards (insufficiently negative)

(C) The estimated coefficient on X will be biased upwards to the point of becoming positive

(D) The estimated coefficient on X (which should be positive) will be biased downwards to the point of becoming negative

4. We might consider introducing a quadratic term for some X variables in regression models

(A) if theory or intuition tells us that the effect on Y of a given change in X will not always be the same for all values of X

(B) because the quadratic term might be a good replacement for the linear term in X

(C) because R-squared only works if all the variables in the model are squared

(D) when we are certain that there are no non-negative values of X

5. If you wish to use a set of dummy variables to capture six different categories of and explanatory factor,

(A) you should use 5 dummy variables representing any 5 categories

(B) you should use 6 dummy variables representing 6 categories

(C) you should use 7 dummy variables representing the 6 categories plus a constant term

(D) you should use 4 dummy variables representing any 4 categories

6. The error term in linear regression models is assumed:

(A) having the mean of zero

(B) having the variance of zero

(C) being normally distributed with a positive mean

(D) being normally distributed with a negative mean

7.How should β k in the general multiple regression model be interpreted?

(A) The number of units of change in the expected value of Y for a 1 unit increase in X k when all remaining variables are unchanged.

(B) The magnitude by which X k varies in the model

(C) The amount of variation in Y explained by X k in the model.

(D) The number of variables used in the model.

8. What are the consequences of using least squares when heteroskedasticity is present?

(A) None of the above

(B) Confidence intervals and hypothesis testing are inaccurate due to inflated standard errors.

(C) All coefficient estimates are biased for variables correlated with the error term.

(D) No consequences, coefficient estimates are still unbiased.

9. The following equation has been used to estimate wages:

ln ⁡ ( Y ) = β 1 + β 2 E D U + β 3 E X P E R + β 4 E X P E R 2 + e

where Y is income, EDU is years of education and EXPER is experience in the field. If you suspect that males earn higher wages than females and that the wage difference increases with education, how would you adjust the econometric model to estimate wages?

(A) Include a binary variable for MALE and an interaction term equal to MALE*EDU

(B) Include a binary variable for gender, MALE.

(C) Include an interaction term equal to MALE*EDU.

(D) Include an indicator variable for MALE and one for FEMALE.

10. You have estimated the following equation using OLS:

y ^ = 33.75 + 1.45 M A L E

where y is annual income in thousands and MALE is an indicator variable such that it is 1 for males and 0 for females. According to this model, wha tis the average income for females?

(A) $33,750

(B) $35,200

(C) $32,300

(D) Cannot be determined.

Answer 1

Question 1.

The variance of intercept coefficient is given by,

Var(b1) = $\sigma$ ^2/($\sum$(Xi - mean of X)^2

Here $\sigma$ ^2 = error variance of population regression function

As you can see the variance of intercept coefficient is directly related to error variance. Hence for the variance of intercept coefficient to be small error variance must be small.

So the correct option is option e.

Question 2.

R squared is the measure of proportion of variability of dependent variable that is explained by the explanatory variable. And also R squared is a measure of goodness of fit of regression model and also it also measure the degree of linear association between dependent and explanatory variables.

So the correct option is option D, all of the above.

Question 3.

So X and Z are negative related which means if one increases other decreases. And X is negatively related with Y which means if X increases Y decreases and Y and Z are positively related which means that of Z increases Y also increases.

So if we omit Z from the regression Y on X then there is nor force acting on Y upwards so X will pull Y downwards more. So the correct option must be option A. That is the estimated coefficient of X will be biased downwards( too negative).

So the correct option is option A.

Question 4.

We should only introoa quadratic term if we expect that the effect on Y on is not same for all values of X and the effect might be increasing with increasing value of X.

So the correct option is option A.

Question 5.

Whenever there n categories in our model and we want to incorporate dummy variables we should always include only (n-1) dummy variables to avoid the problem of dummy trap.

Here we have 6 categories so we should be using only 5 dummy variables representing any 5 categories.

So the correct option is option A.

Under the HomeworkLib guidelines we are only suppose to at most 1 question at a time but I did 5 I hope you appreciate. For rest of the question I would request you to please repost them and we will be more than happy to answer them.

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