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Quantitative Methods
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Tracy, senior analyst at CMSSP Capital reviewed Cronin (his junior’s) regression analysis. He asked Cronin how the key inputs to the regression could affect the ultimate results. Cronin explained the effects of some of these inputs and assumptions, Cronin made the following comments:
Comment 1: “The standard error of estimate is an important input for a hypothesis test. Small standard errors result in both tighter confidence intervals and tighter prediction intervals.”
Comment 2: “The estimated value for the variance of the independent variable can also affect hypothesis testing. The higher the assumed variance, the tighter the prediction intervals. However, changes in the assumed variance will have no effect on the confidence interval.”
Cronin is most accurate with respect to:
Kelly Cronin is one of the statistical experts at CMSSP. He is presently using internally-developed software to explain the relationship between a company’s EPS growth and profitable opportunities as measured by the spread between the equity return on new projects and the firm’s cost of equity. After regressing a sample company’s historical EPS on its return spread for the past ten years, Cronin presented the results to his superior, Brendan Tracy. The following table displays the results of the regression:
Using the information provided in Exhibit 1, the confidence interval for the slope coefficient at the 5% significance level is closest to:Exhibit 1: Explaining EPS Growth by Changesin the Return Spread Coefficients Standard error Intercept 1.2070.5522 Return spread 22.9011.992Regression StatisticsStandard error of estimate 1.120 Observations 62 Mean return spread 0.0943 Variance of mean return spread 0.007724Consider the following information, from a particular regression analysis.
df Sum of squares (SS) Regression 10.1856 Residual Errors600.0268 Total 610.2124
The F-test statistic is closest to:
“For our regression model to be valid, a linear relationship must exist between EPS growth and changes in return spread.” This statement implies that:
Kim Richard has been looking at ways to increase efficiency in the construction process especially with regard to fuel consumption. She ran a regression explaining the variation in fuel consumption as a function of distance. The total variation of the dependent variable was 160.85, the explained variation was 80.15, and the unexplained variation was 100.70. She had 60 monthly observations. The standard error of the estimate in the regression is closest to:
Which of the following is the most appropriate description of a parameter?