HuskyGrad2010

Which of the following is least likely an assumption of linear regression? The:

A) expected value of the residuals is zero.

B) residuals are mean reverting; that is, they tend towards zero over time.

C) residuals are independently distributed.

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The assumptions regarding the residuals are that the residuals have a constant variance, have a mean of zero, and are independently distributed.

HuskyGrad2010

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

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

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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.

invic

A regression between the returns on a stock and its industry index gives the following results:

	Coefficient	Standard Error
Intercept	2.1	2.01
Industry Index	1.9	0.31

• Standard error of estimate = 15.1
• Correlation coefficient = 0.849

If the return on the industry index is 4%, the stock’s expected return would be:

A) 7.6%.

B) 11.2%.

C) 9.7%.

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Y = b0 + bX1
Y = 2.1 + 1.9(4) = 9.7%

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The percentage of the variation in the stock return explained by the variation in the industry index return is closest to:

A) 84.9%.

B) 63.2%.

C) 72.1%.

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The coefficient of determination, R2, is the square the correlation coefficient. 0.8492 = 0.721.

invic

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 increases by 1.5 units if X decreases by 1 unit.

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

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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.

invic

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.

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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.

invic

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) +1.00%.

B) +0.72%.

C) +0.65%.

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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.

invic

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, financial leverage, and capital expenditures are all independent variables.

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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.

invic

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

A) predicted variable.

B) predicting variable.

C) explanatory variable.

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The dependent variable is the predicted variable.

invic

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) Ri.

B) Rm - Rf.

C) Rf.

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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.

invic

The purpose of regression is to:

A) get the largest R2 possible.

B) explain the variation in the dependent variable.

C) explain the variation in the independent variable.

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