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

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

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.

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.

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

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

A) The residuals are normally distributed.

B) The variance of the residuals is constant.

C) The independent variable is correlated with the residuals.

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The assumption is that the independent variable is uncorrelated with the residuals.

HuskyGrad2010

The assumptions underlying linear regression include all of the following EXCEPT the:

A) disturbance term is normally distributed with an expected value of 0.

B) independent variable is linearly related to the residuals (or disturbance term).

C) disturbance term is homoskedastic and is independently distributed.

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The independent variable is uncorrelated with the residuals (or disturbance term).
The other statements are true. The disturbance term is homoskedastic because it has a constant variance. It is independently distributed because the residual for one observation is not correlated with that of another observation. Note: The opposite of homoskedastic is heteroskedastic. For the examination, memorize the assumptions underlying linear regression!

HuskyGrad2010

Linear regression is based on a number of assumptions. Which of the following is least likely an assumption of linear regression?

A) Values of the independent variable are not correlated with the error term.

B) There is at least some correlation between the error terms from one observation to the next.

C) The variance of the error terms each period remains the same.

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When correlation (between the error terms from one observation to the next) exists, autocorrelation is present. As a result, residual terms are not normally distributed. This is inconsistent with linear regression.

HuskyGrad2010

Which of the following statements about linear regression analysis is most accurate?

A) The coefficient of determination is defined as the strength of the linear relationship between two variables.

B) An assumption of linear regression is that the residuals are independently distributed.

C) When there is a strong relationship between two variables we can conclude that a change in one will cause a change in the other.

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Even when there is a strong relationship between two variables, we cannot conclude that a causal relationship exists. The coefficient of determination is defined as the percentage of total variation in the dependent variable explained by the independent variable.

HuskyGrad2010

Assume you perform two simple regressions. The first regression analysis has an R-squared of 0.80 and a beta coefficient of 0.10. The second regression analysis has an R-squared of 0.80 and a beta coefficient of 0.25. Which one of the following statements is most accurate?

A) Explained variability from both analyses is equal.

B) The influence on the dependent variable of a one-unit increase in the independent variable is the same in both analyses.

C) Results from the first analysis are more reliable than the second analysis.

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The coefficient of determination (R-squared) is the percentage of variation in the dependent variable explained by the variation in the independent variable. The R-squared (0.80) being identical between the first and second regressions means that 80% of the variability in the dependent variable is explained by variability in the independent variable for both regressions. This means that the first regression has the same explaining power as the second regression.