Reading 11: Correlation and Regression-LOS e, (Part 2)习题精选 2010, produces, between, center

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Session 3: Quantitative Methods: Quantitative
Methods for Valuation
Reading 11: Correlation and Regression

LOS e, (Part 2): Interpret the regression coefficients.

 

 

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

B) The covariance of RCRANTZ and GSTERN is negative.

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

土豆妮

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

B) The covariance of RCRANTZ and GSTERN is negative.

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

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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.

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

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

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

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

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

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

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

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.

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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):

Sales_t = 1.05 + 1.6 TV_t

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) changes, no change in sales is expected.

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

土豆妮

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):

Sales_t = 1.05 + 1.6 TV_t

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) changes, no change in sales is expected.

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

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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.

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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%.

土豆妮

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%.

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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.

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