Chapter 2
1. A dependent variable is also known as a(n) _____.
a. explanatory variable
b. control variable
c. predictor variable
d. response variable
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
3. In the equation y = β0 + β1x + u, β0 is the _____.
a. dependent variable
b. independent variable
c. slope parameter
d. intercept parameter
4. In the equation y = β0 + β1x + u, what is the estimated value of β0?
a. y̅ − β1
̂ x̅
b. y̅ + β1x̅
c. ∑(xi−x
̅)(yi−y)
̅
̅
̅
n
i=1
∑(xi)2
n
i=1
d. ∑xy
n
i=1
5. In the equation c = β0 + β1i + u, c denotes consumption and i denotes income. What is the residual for
the 5th observation if c5=$500 and c5
̂=$475?
a. $975
b. $300
c. $25
d. $50
6. What does the equation ŷ = β0
̂+ β1
̂x denote if the regression equation is y = β0 + β1x1 + u?
a. The explained sum of squares
b. The total sum of squares
c. The sample regression function
d. The population regression function
Feedback: The equation ŷ = β0
̂+ β1
̂x denotes the sample regression function of the given regression
model.
7. Consider the following regression model: y = β0 + β1x1 + 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 (x̅, y̅) always lies on the OLS regression line.
8. The explained sum of squares for the regression function, yi= β0+ β1x1+ u1, is defined as _____.
a. ∑(𝑦𝑖− 𝑦̅)2
𝑛
𝑖=1
b. ∑(𝑦𝑖− 𝑦̂)2
𝑛
𝑖=1
c. ∑𝑢𝑖
̂
𝑛
𝑖=1
d.∑(𝑢𝑖)2
𝑛
𝑖=1
9. 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
10. 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
11. Which of the following is a nonlinear regression model?
a. y = β0 + β1x1/2 + u
b. log y = β0 + β1log x +u
c. y = 1 / (β0 + β1x) + u
d. y = β0 + β1x + u
12. 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.
13. 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.
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
15. What is the estimated value of the slope parameter when the regression equation, y = β0 + β1x1 +
u passes through the origin?
a.∑𝑦𝑖
𝑛
𝑖=1
b.∑(𝑦𝑖− 𝑦̅
𝑛
𝑖=1 )
c. ∑𝑥𝑖𝑦𝑖
𝑛
𝑖=1
∑𝑥𝑖2
𝑛
𝑖=1
d. ∑(𝑦𝑖− 𝑦̅)2
𝑛
𝑖=1
16. A natural measure of the association between two random variables is the correlation coefficient.
17. The sample covariance between the regressors and the Ordinary Least Square (OLS) residuals is
always positive.
18. R2 is the ratio of the explained variation compared to the total variation.
19. There are n-1 degrees of freedom in Ordinary Least Square residuals.
20. The variance of the slope estimator increases as the error variance decreases.