AIM 1: Explain how regression analysis in econometrics measures the relationship between dependent and independent variables.

1、Joe Harris is interested in why the returns on equity differ from one company to another. He chose several company-specific variables to explain the return on equity, including financial leverage and capital expenditures. In his model:

A) return on equity is the independent variable, and financial leverage and capital expenditures are dependent variables

B) return on equity is the dependent variable, and financial leverage and capital expenditures are independent variables.

C) return on equity is the explanatory variable, and financial leverage and capital expenditure are the explained variables.

D) return on equity, financial leverage, and capital expenditures are all independent variables.

The correct answer is B

The dependent variable is return on equity. This is what he wants to explain. The variables he uses to do the explaining (i.e., the independent variables) are financial leverage and capital expenditures.

2、The purpose of regression is to:

A) explain the variation in the dependent variable.

B) explain the variation in the independent variable.

C) get the largest R2 possible.

D) explain the mean of the independent variable.

The correct answer is A

The goal of a regression is to explain the variation in the dependent variable.

3、The capital asset pricing model is given by: Ri =Rf + Beta ( Rm -Rf) where Rm = expected return on the market, Rf = risk-free market and Ri = expected return on a specific firm. The dependent variable in this model is:

A) Rf.

B) Rm.

C) Rm - Rf.

D) Ri.

The correct answer is D

The dependent variable is the variable whose variation is explained by the other variables. Here, the variation in ri is explained by the variation in the other variables, rf and rm.

4、The independent variable in a regression equation is called all of the following EXCEPT:

A) predicted variable.

B) explanatory variable.

C) exogenous variable.

D) predicting variable.

The correct answer is A

The dependent variable is the predicted variable.

5、A regression analysis has the goal of:

A) measuring how the properties of the variables regress towards each other.

B) estimating how changes in independent variables affect a dependent variable.

C) estimating how changes in dependent variable affect an independent variable.

D) measuring the tendency of both independent and dependent variables to regress towards their respective means.

The correct answer is B

A regression analysis has the goal of measuring how changes in one variable, called a dependent or explained variable, can be explained by changes in one or more other variables called the independent or explanatory variables.

AIM 2: Define and interpret the results of a scattegram.

1、Which of the following statements regarding scatter plots is most accurate? Scatter plots:

A) are used to examine the third moment of a distribution (skewness).

B) are used to examine the fourth moment of a distribution (kurtosis).

C) illustrate the relationship between two variables.

D) illustrate the scatterings of a single variable.

The correct answer is C

A scatter plot is a collection of points on a graph where each point represents the values of two variables. They are used to examine the relationship between two variables.

2、If the correlation between two variables is ?1.0, the scatter plot would appear along a:

A) straight line running from southwest to northeast.

B) a curved line centered in the scatter plot. 

C) a curved line running from southwest to northeast. 

D) straight line running from northwest to southeast.

The correct answer is D

3、In the scatter plot below, the correlation between the return on stock A and the market index is:

A)    negative.

B)    positive.

C)   zero.

D)   not discernable using the scatter plot.

The correct answer is B

In the scatter plot, higher values of the return on stock A are associated with higher values of the return on the market, i.e. a positive correlation between the two variables.

AIM 3: Define and interpret the population regression function, regression coefficients, parameters, slope and the intercept.

1、Sera Smith, a research analyst, had a hunch that there was a relationship between the percentage change in a firm’s number of salespeople and the percentage change in the firm’s sales during the following period. Smith ran a regression analysis on a sample of 50 firms, which resulted in a slope of 0.72, an intercept of +0.01, and an R2 value of 0.65. Based on this analysis, if a firm made no changes in the number of sales people, what percentage change in the firm’s sales during the following period does the regression model predict?

A) +0.72%.

B) +1.00%.

C) +0.65%.

D) +0.10%.

The correct answer is B

The slope of the regression represents the linear relationship between the independent variable (the percent change in sales people) and the dependent variable, while the intercept represents the predicted value of the dependent variable if the independent variable is equal to zero. In this case, the percentage change in sales is equal to: 0.72(0) + 0.01 = +0.01.

2、In the estimated regression equation Y = 0.78 - 1.5 X, which of the following is least accurate when interpreting the slope coefficient?

A) If the value of X is zero, the value of Y will be -1.5.

B) The dependent variable declines by -1.5 units if X increases by 1 unit.

C) The dependent variable increases by 1.5 units if X decreases by 1 unit.

D) -1.5 is the elasticity of Y with respect to X.

The correct answer is A

The slope represents the change in the dependent variable for a one-unit change in the independent variable. If the value of X is zero, the value of Y will be equal to the intercept, in this case, 0.78.

3、Paul Frank is an analyst for the retail industry. He is examining the role of television viewing by teenagers on the sales of accessory stores. He gathered data and estimated the following regression of sales (in millions of dollars) on the number of hours watched by teenagers (in hours per week):

Salest = 1.05 + 1.6 TVt

Which of the following is the most accurate interpretation of the estimated results? If TV watching:

A) goes up by one hour per week, sales of accessories increase by $1.60.

B) goes up by one hour per week, sales of accessories increase by $1.6 million.

C) changes, no change in sales is expected.

D) is zero (that is, every teenager turns off the TV for a week), the expected sales of accessories is $0.

The correct answer is B

The interpretation of the slope coefficient is the change in the dependent variable (sales in millions of dollars) for a given one-unit change in the independent variable (TV hours per week). The intercept of 1.05 means that 1.05 million dollars worth of accessories is expected to be sold even if TV watching is zero.

4、An analyst is examining the relationship between two random variables, RCRANTZ and GSTERN. He performs a linear regression that produces an estimate of the relationship:

RCRANTZ = 61.4 ? 5.9GSTERN

Which interpretation of this regression equation is least accurate?

A) The covariance of RCRANTZ and GSTERN is negative.

B) If GSTERN increases by one unit, RCRANTZ should increase by 5.9 units.

C) The intercept term implies that if GSTERN is zero, RCRANTZ is 61.4.

D) In this regression, RCRANTZ is the dependent variable and GSTERN is the independent variable.

The correct answer is B

The slope coefficient in this regression is -5.9. This means a one unit increase of GSTERN suggests a decrease of 5.9 units of RCRANTZ. The slope coefficient is the covariance divided by the variance of the independent variable. Since variance (a squared term) must be positive, a negative slope term implies that the covariance is negative.

5、A simple linear regression is run to quantify the relationship between the return on the common stocks of medium sized companies (Mid Caps) and the return on the S& 500 Index, using the monthly return on Mid Cap stocks as the dependent variable and the monthly return on the S& 500 as the independent variable. The results of the regression are shown below:

Use the regression statistics presented above and assume this historical relationship still holds in the future period. If the expected return on the S& 500 over the next period were 11%, the expected return on Mid Cap stocks over the next period would be:

A)    18.4%.

B)    33.8%.

C)   25.6%

D)   20.3%.

The correct answer is A

Y = intercept + slope(X)

Mid Cap Stock returns = 1.71 + 1.52(11) =18.4%

6、Given: Y = 2.83 + 1.5X

What is the predicted value of the dependent variable when the value of an independent variable equals 2?

A) 5.83

B) -0.55

C) 6.50

D) 2.83

The correct answer is A

Y = 2.83 + (1.5)(2)

= 2.83 + 3

= 5.83

7、Paul Frank is an analyst for the retail industry. He is examining the role of television viewing by teenagers on the sales of accessory stores. He gathered data and estimated the following regression of sales (in millions of dollars) on the number of hours watched by teenagers (TV, in hours per week):

Salest = 1.05 + 1.6 TVt

The predicted sales if television watching is 5 hours per week is:

A) $8.00 million.

B) $9.05 million.

C) $2.65 million.

D) $1.05 million.

The correct answer is B

The predicted sales are: Sales = $1.05 + [$1.6 (5)] = $1.05 + $8.00 = $9.05 million.

8、Consider the regression results from the regression of Y against X for 50 observations:

Y = 5.0 - 1.5 X

The standard error of the estimate is 0.40 and the standard error of the coefficient is 0.45. The predicted value of Y if X is 10 is:

A) -10.

B) 10.

C) 20.

D) 4.5.

The correct answer is A

The predicted value of Y is: Y = 5.0 – [1.5 (10)] = 5.0 – 15 = -10

AIM 4: Define and interpret the stochastic error term, noise components.

In a regression analysis, the effects from independent variables that are not included in the model are embodied in the:

A) error term.

B) intercept.

C) scattergram.

D) slope coefficient.

The correct answer is A

The error term embodies the effect of variables omitted from the model.

AIM 6: Define and interpret the sample regression function, regression coefficients, parameters, slope and the intercept.

Which of the following are included in a sample regression function?

?            The intercept.

?            The error term.

?            The slope coefficient.

?            The independent variable.

A) I, II, III, and IV.

B) III and IV only.

C) I and III only.

D) I, III, and IV only.

The correct answer is D

The sample regression function has a residual and not an error term. Although the residual and error term serve a similar purpose in their respective equations, there are distinctions.

AIM 7: Explain the concept of linear regression.

Trudy Baker, FRM and Steven Phillips, FRM are planning to do a regression analysis. They discuss specifying the equation they wish to estimate. Baker proposes the specification E(Yi|Xi) = B0 + (B1) × (Xi2). Phillips proposes the specification (Yi|Xi) = B0 + (B1 × Xi)2. Which, if either, is appropriate using linear regression?

A) Neither the specification of Baker nor that of Phillips.

B) The specification of Phillips but not that of Baker.

C) Both the specification of Baker and Phillips.

D) The specification of Baker but not that of Phillips.

The correct answer is D

Since the specification of Phillips would essentially be B0 + (B12) × (Xi2), this precludes the application of linear regression analysis because there is an exponent on B1, i.e., the specification is nonlinear with respect to the parameters.

AIM 9: Explain the process of ordinary least squares of estimation.

1、Sample regression coefficients are often estimated with a process known as:

A) a scattergram.

B) a population regression function.

C) Ockham's razor.

D) ordinary least squares.

The correct answer is D

Ordinary least squares or OLS is a method for estimating population coefficients. It provides the line that minimizes the squared deviations of the dependent variables in the sample from the sample regression line.

2、As part of a regression analysis, an analyst finds that: Y – b1 × X = -1.8 and b1 = 3.2. Based upon these results, for every unit increase in the independent variable, on average the dependent variable increases by:

A) 1.4.

B) 1.8.

C) 3.2.

D) 5.0.

The correct answer is C

b1 gives the slope coefficient which indicates the average change in the dependent variable given a unit change in the independent variable.

辛苦了！