Question 1

(Requires Appendix)The sample average of the OLS residuals is

Accepted Answer

A) some positive number since OLS uses squares. 
B) zero. 
C) unobservable since the population regression function is unknown. 
D) dependent on whether the explanatory variable is mostly positive or negative. 
A) some positive number since OLS uses squares. 
B) zero. 
C) unobservable since the population regression function is unknown. 
D) dependent on whether the explanatory variable is mostly positive or negative.

Question 2

(Requires Appendix)The sample regression line estimated by OLS

Accepted Answer

A) will always have a slope smaller than the intercept. 
B) is exactly the same as the population regression line. 
C) cannot have a slope of zero. 
D) will always run through the point ( $\bar { X }$ , $\bar { Y }$ ). 
A) will always have a slope smaller than the intercept. 
B) is exactly the same as the population regression line. 
C) cannot have a slope of zero. 
D) will always run through the point ( $\bar { X }$ , $\bar { Y }$ ).

Question 3

To decide whether the slope coefficient indicates a "large" effect of X on Y, you look at the

Accepted Answer

A) size of the slope coefficient 
B) regression R2 
C) economic importance implied by the slope coefficient 
D) value of the intercept 
A) size of the slope coefficient 
B) regression R2 
C) economic importance implied by the slope coefficient 
D) value of the intercept

Question 4

(Requires Appendix material)At a recent county fair, you observed that at one stand people's weight was forecasted, and were surprised by the accuracy (within a range). Thinking about how the person could have predicted your weight fairly accurately (despite the fact that she did not know about your "heavy bones"), you think about how this could have been accomplished. You remember that medical charts for children contain 5%, 25%, 50%, 75% and 95% lines for a weight/height relationship and decide to conduct an experiment with 110 of your peers. You collect the data and calculate the following sums: $$\begin{array} { c } 
\sum _ { i = 1 } ^ { n } Y _ { i } = 17,375 , \sum _ { i = 1 } ^ { n } X _ { i } = 7,665.5 , \\
\sum _ { i = 1 } ^ { n } y _ { i } ^ { 2 } = 94,228.8 , \sum _ { i = 1 } ^ { n } x _ { i } ^ { 2 } = 1,248.9 , \sum _ { i = 1 } ^ { n } x _ { i } y _ { i } = 7,625.9
\end{array}$$ where the height is measured in inches and weight in pounds. (Small letters refer to deviations from means as in zi = Zi - $\bar { Z }$ )
(a)Calculate the slope and intercept of the regression and interpret these.
(b)Find the regression R2 and explain its meaning. What other factors can you think of that might have an influence on the weight of an individual?

Accepted Answer

(a) @#IMG-DLM&_TB5979_11_TB5979_11_TB5979_11_TB597

Question 5

In 2001, the Arizona Diamondbacks defeated the New York Yankees in the Baseball World Series in 7 games. Some players, such as Bautista and Finley for the Diamondbacks, had a substantially higher batting average during the World Series than during the regular season. Others, such as Brosius and Jeter for the Yankees, did substantially poorer. You set out to investigate whether or not the regular season batting average is a good indicator for the World Series batting average. The results for 11 players who had the most at bats for the two teams are: $\widehat { \text { AZWsavg } }$ = -0.347 + 2.290 AZSeasavg , R2=0.11, SER = 0.145, $\widehat { \text { AZWsavg } }$ = 0.134 + 0.136 NYSeasavg , R2=0.001, SER = 0.092,
where Wsavg and Seasavg indicate the batting average during the World Series and the regular season respectively.
(a)Focusing on the coefficients first, what is your interpretation?
(b)What can you say about the explanatory power of your equation? What do you conclude from this?

Accepted Answer

(a)The two regressions are quite differe

Question 6

Multiplying the dependent variable by 100 and the explanatory variable by 100,000 leaves the

Accepted Answer

A) OLS estimate of the slope the same. 
B) OLS estimate of the intercept the same. 
C) regression R2 the same. 
D) variance of the OLS estimators the same. 
A) OLS estimate of the slope the same. 
B) OLS estimate of the intercept the same. 
C) regression R2 the same. 
D) variance of the OLS estimators the same.

Question 7

Interpreting the intercept in a sample regression function is

Accepted Answer

A) not reasonable because you never observe values of the explanatory variables around the origin. 
B) reasonable because under certain conditions the estimator is BLUE. 
C) reasonable if your sample contains values of Xi around the origin. 
D) not reasonable because economists are interested in the effect of a change in X on the change in Y. 
A) not reasonable because you never observe values of the explanatory variables around the origin. 
B) reasonable because under certain conditions the estimator is BLUE. 
C) reasonable if your sample contains values of Xi around the origin. 
D) not reasonable because economists are interested in the effect of a change in X on the change in Y.

Question 8

Consider the following model:
Yi = ?0 + ui.
Derive the OLS estimator for ?0.

Accepted Answer

To derive the OLS estimator, minimize th

Question 9

To decide whether or not the slope coefficient is large or small,

Accepted Answer

A) you should analyze the economic importance of a given increase in X. 
B) the slope coefficient must be larger than one. 
C) the slope coefficient must be statistically significant. 
D) you should change the scale of the X variable if the coefficient appears to be too small. 
A) you should analyze the economic importance of a given increase in X. 
B) the slope coefficient must be larger than one. 
C) the slope coefficient must be statistically significant. 
D) you should change the scale of the X variable if the coefficient appears to be too small.

Question 10

At the Stock and Watson (http://www.pearsonhighered.com/stock_watson)website go to Student Resources and select the option "Datasets for Replicating Empirical Results." Then select the "California Test Score Data Used in Chapters 4-9" (caschool.xls)and open it in a spreadsheet program such as Excel.
In this exercise you will estimate various statistics of the Linear Regression Model with One Regressor through construction of various sums and ratio within a spreadsheet program.
Throughout this exercise, let Y correspond to Test Scores (testscore)and X to the Student Teacher Ratio (str). To generate answers to all exercises here, you will have to create seven columns and the sums of five of these. They are
(i)Yi, (ii)Xi, (iii)(Yi- $\bar { Y }$ ), (iv)(Xi- $\bar { X }$ ), (v)(Yi- $\bar { Y }$ )×(Xi- $\bar { X }$ ), (vi)(Xi- $\bar { X }$ )2, (vii)(Yi- $\bar { Y }$ )2
Although neither the sum of (iii)or (iv)will be required for further calculations, you may want to generate these as a check (both have to sum to zero).
a. Use equation (4.7)and the sums of columns (v)and (vi)to generate the slope of the regression.
b. Use equation (4.8)to generate the intercept.
c. Display the regression line (4.9)and interpret the coefficients.
d. Use equation (4.16)and the sum of column (vii)to calculate the regression R2.
e. Use equation (4.19)to calculate the SER.
f. Use the "Regression" function in Excel to verify the results.

Accepted Answer

Column (i): 654.156548
Column (ii): 19.6

Question 11

In the linear regression model, Yi = β0 + β1Xi + ui, β0 + β1Xi is referred to as

Accepted Answer

A) the population regression function. 
B) the sample regression function. 
C) exogenous variation. 
D) the right-hand variable or regressor. 
A) the population regression function. 
B) the sample regression function. 
C) exogenous variation. 
D) the right-hand variable or regressor.

Question 12

The OLS residuals

Accepted Answer

A) can be calculated using the errors from the regression function. 
B) can be calculated by subtracting the fitted values from the actual values. 
C) are unknown since we do not know the population regression function. 
D) should not be used in practice since they indicate that your regression does not run through all your observations. 
A) can be calculated using the errors from the regression function. 
B) can be calculated by subtracting the fitted values from the actual values. 
C) are unknown since we do not know the population regression function. 
D) should not be used in practice since they indicate that your regression does not run through all your observations.

Question 13

The regression R2 is defined as follows:

Accepted Answer

A)  $\frac { E S S } { T S S }$ 
B)  $\frac { R S S } { T S S }$ 
C)  $\frac { \sum _ { i = 1 } ^ { n } \left( Y _ {i } - \bar { Y } \right) \left( X _ {i } - \bar { X } \right) } { \sqrt { \sum _ { i = 1 } ^ { n } \left( Y _ { i } - \bar { Y } \right) ^ { 2 } \sqrt { \sum _ { i = 1 } ^ { n } \left( X _ { i} - \bar { X } \right) ^ { 2 } } } }$ 
D)  $\frac { S S R } { n - 2 }$ 
A)  $\frac { E S S } { T S S }$ 
B)  $\frac { R S S } { T S S }$ 
C)  $\frac { \sum _ { i = 1 } ^ { n } \left( Y _ {i } - \bar { Y } \right) \left( X _ {i } - \bar { X } \right) } { \sqrt { \sum _ { i = 1 } ^ { n } \left( Y _ { i } - \bar { Y } \right) ^ { 2 } \sqrt { \sum _ { i = 1 } ^ { n } \left( X _ { i} - \bar { X } \right) ^ { 2 } } } }$ 
D)  $\frac { S S R } { n - 2 }$

Question 14

The OLS estimator is derived by

Accepted Answer

A) connecting the Yi corresponding to the lowest Xi observation with the Yi corresponding to the highest Xi observation. 
B) making sure that the standard error of the regression equals the standard error of the slope estimator. 
C) minimizing the sum of absolute residuals. 
D) minimizing the sum of squared residuals. 
A) connecting the Yi corresponding to the lowest Xi observation with the Yi corresponding to the highest Xi observation. 
B) making sure that the standard error of the regression equals the standard error of the slope estimator. 
C) minimizing the sum of absolute residuals. 
D) minimizing the sum of squared residuals.

Question 15

Show first that the regression R2 is the square of the sample correlation coefficient. Next, show that the slope of a simple regression of Y on X is only identical to the inverse of the regression slope of X on Y if the regression R2 equals one.

Accepted Answer

The regression R² = @#LAT-DLM& , where ESS is given

Question 16

The reason why estimators have a sampling distribution is that

Accepted Answer

A) economics is not a precise science. 
B) individuals respond differently to incentives. 
C) in real life you typically get to sample many times. 
D) the values of the explanatory variable and the error term differ across samples. 
A) economics is not a precise science. 
B) individuals respond differently to incentives. 
C) in real life you typically get to sample many times. 
D) the values of the explanatory variable and the error term differ across samples.

Question 17

When the estimated slope coefficient in the simple regression model, $\hat { \beta }$ 1, is zero, then

Accepted Answer

A) R2 = $\bar { Y }$ 
B) 0 2 2 = 0. 
D) R2 > (SSR/TSS). 
A) R2 = $\bar { Y }$ 
B) 0 2 2 = 0. 
D) R2 > (SSR/TSS).

Question 18

Consider the following model:
Yi = ?1Xi + ui.
Derive the OLS estimator for ?1.

Accepted Answer

To derive the OLS estimator, m

Question 19

For the simple regression model of Chapter 4, you have been given the following data: $\sum _ { i = 1 } ^ { 420 } Y _ { i }$ = 274, 745.75; $\sum _ { i = 1 } ^ { 420 } X _ { i }$ = 8,248.979; $\sum _ { i = 1 } ^ { 420 } X _ { i } Y _ { i }$ = 5,392, 705; $\sum _ { i = 1 } ^ { 420 } X _ { i } ^ { 2 }$ = 163,513.03; $\sum _ { i = 1 } ^ { 420 } Y _ { i } ^ { 2 }$ = 179,878, 841.13
(a)Calculate the regression slope and the intercept.
(b)Calculate the regression R2

Accepted Answer

(a) @#IMG-DLM&_TB5979_11_TB5979_11_TB5979_11_TB597

Question 20

Changing the units of measurement, e.g. measuring testscores in 100s, will do all of the following EXCEPT for changing the

Accepted Answer

A) residuals 
B) numerical value of the slope estimate 
C) interpretation of the effect that a change in X has on the change in Y 
D) numerical value of the intercept 
A) residuals 
B) numerical value of the slope estimate 
C) interpretation of the effect that a change in X has on the change in Y 
D) numerical value of the intercept

(Requires Appendix)The sample average of the OLS residuals is

(Requires Appendix)The sample regression line estimated by OLS

To decide whether the slope coefficient indicates a "large" effect of X on Y, you look at the

Multiplying the dependent variable by 100 and the explanatory variable by 100,000 leaves the

Interpreting the intercept in a sample regression function is

Consider the following model: Y_i = ?₀ + u_i. Derive the OLS estimator for ?₀.

To decide whether or not the slope coefficient is large or small,

In the linear regression model, Y_i = β₀ + β₁X_i + u_i, β₀ + β₁X_iis referred to as

The OLS residuals

The regression R² is defined as follows:

The OLS estimator is derived by

Show first that the regression R² is the square of the sample correlation coefficient. Next, show that the slope of a simple regression of Y on X is only identical to the inverse of the regression slope of X on Y if the regression R² equals one.

The reason why estimators have a sampling distribution is that

When the estimated slope coefficient in the simple regression model, $\hat { \beta }$ ₁, is zero, then

Consider the following model: Y_i = ?₁X_i + u_i. Derive the OLS estimator for ?₁.

Changing the units of measurement, e.g. measuring testscores in 100s, will do all of the following EXCEPT for changing the

Economic Questions and Data

Review of Probability

Review of Statistics

Regression With a Single Regressor: Hypothesis Tests and Confidence Intervals

Linear Regression With Multiple Regressors

Hypothesis Tests and Confidence Intervals in Multiple Regression

Nonlinear Regression Functions

Assessing Studies Based on Multiple Regression

Regression With Panel Data

Regression With a Binary Dependent Variable

Instrumental Variables Regression

Experiments and Quasi-Experiments

Introduction to Time Series Regression and Forecasting

Estimation of Dynamic Causal Effects

Additional Topics in Time Series Regression

The Theory of Linear Regression With One Regressor

The Theory of Multiple Regression

Filters

Exam 4: Linear Regression With One Regressor

(Requires Appendix)The sample average of the OLS residuals is

(Requires Appendix)The sample regression line estimated by OLS

To decide whether the slope coefficient indicates a "large" effect of X on Y, you look at the

Multiplying the dependent variable by 100 and the explanatory variable by 100,000 leaves the

Interpreting the intercept in a sample regression function is

Consider the following model: Yi = ?0 + ui. Derive the OLS estimator for ?0.

To decide whether or not the slope coefficient is large or small,

In the linear regression model, Yi = β0 + β1Xi + ui, β0 + β1Xi is referred to as

The OLS residuals

The regression R2 is defined as follows:

The OLS estimator is derived by

Show first that the regression R2 is the square of the sample correlation coefficient. Next, show that the slope of a simple regression of Y on X is only identical to the inverse of the regression slope of X on Y if the regression R2 equals one.

The reason why estimators have a sampling distribution is that

When the estimated slope coefficient in the simple regression model, β^\hat { \beta }β^​ 1, is zero, then

Consider the following model: Yi = ?1Xi + ui. Derive the OLS estimator for ?1.

Changing the units of measurement, e.g. measuring testscores in 100s, will do all of the following EXCEPT for changing the

Economic Questions and Data

Review of Probability

Review of Statistics

Regression With a Single Regressor: Hypothesis Tests and Confidence Intervals

Linear Regression With Multiple Regressors

Hypothesis Tests and Confidence Intervals in Multiple Regression

Nonlinear Regression Functions

Assessing Studies Based on Multiple Regression

Regression With Panel Data

Regression With a Binary Dependent Variable

Instrumental Variables Regression

Experiments and Quasi-Experiments

Introduction to Time Series Regression and Forecasting

Estimation of Dynamic Causal Effects

Additional Topics in Time Series Regression

The Theory of Linear Regression With One Regressor

The Theory of Multiple Regression

Filters

Consider the following model: Y_i = ?₀ + u_i. Derive the OLS estimator for ?₀.

In the linear regression model, Y_i = β₀ + β₁X_i + u_i, β₀ + β₁X_iis referred to as

The regression R² is defined as follows:

Show first that the regression R² is the square of the sample correlation coefficient. Next, show that the slope of a simple regression of Y on X is only identical to the inverse of the regression slope of X on Y if the regression R² equals one.

When the estimated slope coefficient in the simple regression model, $\hat { \beta }$ ₁, is zero, then

Consider the following model: Y_i = ?₁X_i + u_i. Derive the OLS estimator for ?₁.