Deck 4: Simple Linear Regression

Question 1

The estimated slope coefficient is

A)the ratio of the variance of y to the variance of x.
B)the ratio of the variance of x to the variance of y.
C)the ratio of the covariance between x and y to the variance of x.
D)the covariance between x and y.

Answer 1

C

Question 2

Suppose you determine the estimated sample regression function to be
You would conclude that

A)y_i is estimated to equal 473.65 when x_i = 0.
B)y_i is estimated to increase by 473.65 for every one unit increase in x_i.
C)y_i is estimated to decrease by 473.65 for every one unit increase in x_i.
D)y_i is estimated to increase by 1,016.82 for every one unit increase in x_i.

Answer 2

B

Question 3

The estimated slope coefficient

A)is the true value of the population slope coefficient.
B)is found in the population regression model.
C)is found by minimizing the sum of squared residuals.
D)is the predicted value of the dependent variable.

Answer 3

C

Question 4

The term "goodness-of-fit" refers to

A)the accuracy of the estimated sample regression function.
B)whether or not the estimated sample regression function is correct.
C)method by which we determine the best-fit line.
D)the extent to which observed data match the values expected by theory.

Question 5

In simple linear regression analysis,the independent variable is

A)the variable that changes in response to changes in an independent variable.
B)the variable whose changes affect the dependent variable.
C)the left-hand side variable.
D)can be either variable.

Question 6

The estimated slope coefficient is

A)the estimated marginal effect of x on y.
B)the estimated value of y when x equals 0.
C)equal to the population slope coefficient.
D) .

Question 7

Suppose you determine the estimated sample regression function to be
You would conclude that

A)y_i is estimated to increase by 687.51 for every one unit increase in x_i.
B)y_i is estimated to increase by 3,212.97 for every one unit increase in x_i.
C)y_i is estimated to decrease by 3,212.97 for every one unit increase in x_i.
D) is estimated to equal 3,212.97 when x_i = 0.

Question 8

The explained variation in y is

A)the distance between the best-fit line and the data points.
B)the distance between the mean and the predicted value of y.
C)the distance between the mean and the data points.
D)the distance between the observed and predicted values of y.

Question 9

The residual is

A)the difference between the observed value of the dependent variable and the observed value of the independent variable.
B)the difference between the observed value of the dependent variable and the predicted value of the dependent variable.
C)the difference between the predicted value of the dependent variable and the predicted value of the independent variable.
D)the difference between the predicted value of the independent variable and the observed value of the independent variable.

Question 10

Suppose you determine the estimated sample regression function to be
You would conclude that

A) is estimated to equal 687.51 when x_i = 0.
B)y_i is estimated to increase by 3,212.97 for every one unit increase in x_i.
C)y_i is estimated to decrease by 687.51 for every one unit increase in x_i.
D)y_i is estimated to equal 3,212.97 when x_i = 0.

Question 11

A marginal effect indicates

A)the predicted value of the dependent variable,holding all else constant.
B)the effect that a one-unit change in the independent variable is expected to have on the dependent variable,holding all else constant.
C)the effect that a one-unit change in the dependent variable is expected to have on the independent variable,holding all else constant.
D)the predicted value of the dependent variable when the independent variable equals 0,holding all else constant.

Question 12

The residual is

A)the vertical distance between the observed value of y and the mean value of y.
B)the vertical distance between the predicted value of y and the mean value of y.
C)the vertical distance between the observed value of y and the probabilistic value of y.
D)the vertical distance between the observed value of y and the predicted value of y.

Question 13

We determine the estimated sample regression function by

A)minimizing the total deviations from the mean.
B)maximizing the sum of squared residuals.
C)minimizing the sum of squared residuals.
D)minimizing the least absolute deviations from the mean.

Question 14

The estimated intercept

A)is the estimated marginal effect of x on y.
B)is the estimated value of y when x equals 0.
C)is equal to the population intercept.
D)is .

Question 15

Simple linear regression analysis determines

A)the true value of the population slope coefficient.
B)the linear relationship between two random variables.
C)the linear relationship between many different random variables.
D)the true value of the population intercept.

Question 16

In simple linear regression analysis,the dependent variable

A)is the variable that changes in response to changes in an independent variable.
B)is the variable whose changes affect the dependent variable.
C)is on the right-hand side variable.
D)can be either variable.

Question 17

The population regression model includes all of the following except

A)the random error component.
B)the population slope coefficient.
C)the population intercept.
D)the estimated slope coefficient.

Question 18

The error term includes all of the following except

A)omitted variables.
B)deterministic relationships.
C)incorrect functional form.
D)measurement error.

Question 19

The predicted value of y_i is

A)the value that y_i takes on when x_iequals 0.
B)the effect that a one-unit change in the dependent variable is expected to have on the independent variable,holding all else constant.
C)the value of y_i when the slope is multiplied a specific x_i and then that value is added to the intercept.
D)the observed value of the dependent variable that is associated with a specific value of the independent variable.

Question 20

A probabilistic relationship is one for which

A)the value of the dependent variable is perfectly determined by the value of the independent variable.
B)all data points fall on the same line.
C)there is no random error component.
D)the value of the dependent variable is related to the value of the independent variable but the data points do not fall on the same line.

Question 21

Figure:
Suppose you are given the Excel output in Figure 4.1.You would conclude that each additional Yard Per Drive is estimated to be associated with

A)a $7,773,135.558 decrease in annual earnings.
B)a $2,867,254.773 increase in annual earnings.
C)a $30,737.523 increase in annual earnings.
D)a $9,823.548 increase in annual earnings.

Question 22

The number of degrees of freedom

A)is always n - k - 1.
B)is always n - 1.
C)is the number of values in the final calculation that are free to vary.
D)is the number of values in the final calculation that are not free to vary.

Question 23

In general,a larger
Tends to suggest that

A)the estimated sample regression function explains a greater percentage of the total variation in y.
B)the estimated sample regression function is more accurate.
C)the data points fall closer to the best-fit line.
D)the data points fall further from the best-fit line.

Question 24

Suppose you wish to determine the degree to which annual earnings of PGA tour players (Earnings)are related to driving distance (Yards Per Drive).In such a case,

A)you should define Yards Per Drive as the dependent variable.
B)you should define Earnings as the dependent variable.
C)it does not matter which variable you define as the dependent variable.
D)you should define Earnings as the independent variable.

Question 25

The explained sum of squares is

A)the sum of the squared values of the predicted value of y minus the mean value of y.
B)the sum of the squared values of the predicted value of y minus the observed value of y.
C)the sum of the squared values of the observed value of y minus the mean value of y.
D)the sum of the squared values of the observed value of y minus the predicted value of y.

Question 26

How do you calculate the estimated simple linear sample regression function by Ordinary Least Squares (OLS)? Explain.

Question 27

Suppose you are given the Excel output in 4.1.You would conclude that explained sum of squares is

A)1.307E + 13.
B)2.658E + 14.
C)2.788E + 14.
D)1.308E + 14.

Question 28

The standard error of the estimated sample regression function
Is

A)the square root of the unexplained sum of squares.
B)the square root of the explained sum of squares.
C)the square root of the unexplained sum of squares divided by the degree of freedom of the regression.
D)the square root of the explained sum of squares divided by the degree of freedom.

Question 29

The unexplained variation in y is

A)the distance between the observed and predicted values of y.
B)the distance between the mean and the best-fit line.
C)the distance between the mean and the data points.
D)the distance between the mean and the predicted value of y.

Question 30

Suppose you are given the Excel output in 4.1.You would conclude that number of degrees of freedom of the regression is

A)1.
B)199.
C)200.
D)201.

Question 31

The fact that two variables are correlated tells us that

A)a linear relationship exists between two variables.
B)a quadratic relationship exists between two variables.
C)a positive relationship exists between two variables.
D)changes in one variable cause changes in the other variable.

Question 32

What is the goal of linear regression analysis? Explain.

Question 33

The fact that two variables are correlated implies that

A)a linear relationship exists between two variables.
B)a quadratic relationship exists between two variables.
C)a positive relationship exists between two variables.
D)changes in one variable cause changes in the other variable.

Question 34

Why does Ordinary Least Squares (OLS)produce the "best-fit" line? Explain.

Question 35

Figure:
Suppose you are given the Excel output in 4.1.You would conclude that the estimated sample regression function explains

A)21.65 percent of the total variation in annual earnings.
B)4.69 percent of the total variation in annual earnings.
C)4.21 percent of the total variation in annual earnings.
D)0.02 percent of the total variation in annual earnings.

Question 36

Suppose you are given the Excel output in 4.1.You would conclude that the number of golfers in the sample is

A)1.
B)199.
C)200.
D)201.

Question 37

Figure:
Suppose you are given the Excel output in 4.1.You would conclude that the standard error of the estimated sample regression function
Is

A)0.2165.
B)0.0469.
C)1,155,621.367.
D)201.

Question 38

The coefficient of determination (R²)is

A)the ratio of the unexplained variation in y to the total variation in y.
B)the ratio of the explained variation in y to the total variation in y.
C)the ratio of the explained variation in y to the unexplained variation in y.
D)the ratio of the unexplained variation in y to the explained variation in y.

Question 39

In general,a larger R² tends to suggest that

A)the estimated sample regression function explains a greater percentage of the total variation in y.
B)the estimated sample regression function is more accurate.
C)the estimated sample regression function explains a greater percentage of the explained variation in y.
D)the estimated slope coefficient is more likely to equal the population slope coefficient.

Question 40

Why is an error term included in the estimated sample regression function? What factors does this term include? Explain.

Question 41

What are the Explained Sum of Squares (ESS),the Unexplained Sum of Squares (USS),and the Total Sum of Squares (TSS)? Explain.

Question 42

Suppose that you regress the total number of medals that a country won in the 2008 Olympics on GDP per capita and that you get the results in Figure 4.2.
How would you interpret these results? What would you say about the Goodness-of-Fit of the regression? Explain.
What would be the predicted number of medals for a country with a GDP per capita of $25,000? $40,000? Show your work.

Question 43

Suppose you regress the number of days that individuals report having hunted in the past year on years of education and that you get the results in Figure 4.3.
How would you interpret these results? What would you say about the Goodness-of-Fit of the regression? Explain.
What would be the predicted number of hunting days for an individual with 12 years of education? 16 years of education? Show your work.

Question 44

A counselor working with teenagers is interested in the relationship between anxiety and depression.The counselor administers a depression and anxiety test to each teenager.The scores obtained from the administration of the two inventories are given below.

a.If anxiety is the independent variable and depression is the dependent variable,what is the sample regression function? What do the estimated slope and intercept mean in context of this problem?
b.What is R-squared and what does it mean?
c.If an individual had an anxiety score of 40,what is their predicted level of depression?