Deck 2: The Simple Regression Model

Question 1

A dependent variable is also known as a(n) _____.

A)explanatory variable
B)control variable
C) predictor variable
D) response variable

Answer 1

D
Explanation: A dependent variable is known as a response variable.

Question 2

If a change in variable x causes a change in variable y, variable x is called the _____.

A)dependent variable
B)explained variable
C) explanatory variable
D) response variable

Answer 2

C
Explanation: If a change in variable x causes a change in variable y, variable x is called the independent variable or the explanatory variable.

Question 3

What does the equation denote if the regression equation is ?

A)The explained sum of squares
B)The total sum of squares
C) The sample regression function
D) The population regression function

Answer 3

C
Explanation: The equation denotes the sample regression function of the given regression model.

Question 4

What is the estimated value of the slope parameter when the regression equation, y = ₀ + ₁x₁ + u passes through the origin?

A)
B)
C)

D)

Question 5

The sample correlation between xi and yi is denoted by _____.​

A)​
B)​
C) ​

D) ​

Question 6

Which of the following is a nonlinear regression model?

A)y = ₀ + ₁x^1/2 + u
B)log y = ₀ + ₁log x +u
C) y = 1 / (
₀ +
₁x) + u
D) y =
₀ +
₁x + u

Question 7

If x_i and y_i are positively correlated in the sample then the estimated slope is _____.​

A)​less than zero
B)​greater than zero
C) ​equal to zero
D) ​equal to one

Question 8

Consider the following regression model: y = ₀ + ₁x₁ + u. Which of the following is a property of Ordinary Least Square (OLS) estimates of this model and their associated statistics?

A)The sum, and therefore the sample average of the OLS residuals, is positive.
B)The sum of the OLS residuals is negative.
C) The sample covariance between the regressors and the OLS residuals is positive.
D) The point (
) always lies on the OLS regression line.

Question 9

A natural measure of the association between two random variables is the correlation coefficient.

Question 10

Which of the following is assumed for establishing the unbiasedness of Ordinary Least Square (OLS) estimates?

A)The error term has an expected value of 1 given any value of the explanatory variable.
B)The regression equation is linear in the explained and explanatory variables.
C) The sample outcomes on the explanatory variable are all the same value.
D) The error term has the same variance given any value of the explanatory variable.

Question 11

The explained sum of squares for the regression function, , is defined as _____.

A)
B)
C)

D)

Question 12

In the equation , what is the estimated value of ?

A)
B)
C)

D)

Question 13

In the equation , c denotes consumption and i denotes income. What is the residual for the 5^th observation if =$500 and =$475?

A)$975
B)$300
C) $25
D) $50

Question 14

In the regression of y on x, the error term exhibits heteroskedasticity if _____.

A)it has a constant variance
B)Var(y|x) is a function of x
C) x is a function of y
D) y is a function of x

Question 15

If the residual sum of squares (SSR) in a regression analysis is 66 and the total sum of squares (SST) is equal to 90, what is the value of the coefficient of determination?

A)0.73
B)0.55
C) 0.27
D) 1.2

Question 16

In the equation is the _____.

A)dependent variable
B)independent variable
C) slope parameter
D) intercept parameter

Question 17

If the total sum of squares (SST) in a regression equation is 81, and the residual sum of squares (SSR) is 25, what is the explained sum of squares (SSE)?

A)64
B)56
C) 32
D) 18

Question 18

In a regression equation, changing the units of measurement of only the independent variable does not affect the _____.

A)​dependent variable
B)​slope
C) ​intercept
D) ​error term

Question 19

Simple regression is an analysis of correlation between two variables.​

Question 20

The error term in a regression equation is said to exhibit homoskedasticty if _____.

A)it has zero conditional mean
B)it has the same variance for all values of the explanatory variable
C) it has the same value for all values of the explanatory variable
D) if the error term has a value of one given any value of the explanatory variable

Question 21

R² is the ratio of the explained variation compared to the total variation.

Question 22

There are n-1 degrees of freedom in Ordinary Least Square residuals.

Question 23

The sample covariance between the regressors and the Ordinary Least Square (OLS) residuals is always positive.

Question 24

In general, the constant that produces the smallest sum of squared deviations is always the sample average.​

Question 25

The variance of the slope estimator increases as the error variance decreases.