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Scattergrams, hypothesis, confidence interval

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1.7 Based on the data for the years 1962 to 1977 for the United States, Dale Bails and Larry Peppers17 obtained the following demand function for automobiles:

Yt = 5807 + 3.24Xt r2 = 0.22

Se = (1.634)

Where Y = retail sales of passenger cars (thousands) and X = the real disposable income (billions of 1972 dollars).
Note: The se for b1 is not given.
a. Establish a 95% confidence interval for B2.
b. Test the hypothesis that this interval includes B2 = 0. If not, would you accept this null hypothesis?
c. Compute the t value under H0: B2 = 0. Is it statistically significant at the 5 percent level? Which t test do you use, one tailed or two tailed, and why?

2.7 The characteristic line of modern investment analysis involves running the following regression:

rt = B1 + B2r mt + ut

where r = the rate of return on a stock or security
rm = the rate of return on the market portfolio represented by a broad market index such as S&P 500, and
t = tine

In investment analysis, B2 is known as the beta coefficient of the security and is used as a measure of market risk, that is, how developments in the market affect the forunes of a given company.

Based on 240 monthly rates of return for the period 1956 to 1976, Fogler and Ganapathy obtained the following results for IBM stock. The market index used by the authors is the market portfolio index developed at the University of Chicago.

rt = 0.7264 = 1.0598r mt

se = (0.3001) (0.0728) r2 = 0.4710

a. Interpret the estimated intercept and slope.
b. How would you interpret r2?
c. A security whose beta coefficient is greater than 1 is called a volatile or aggressive security. Set up the appropriate null and alternative hypothesis and test them using the t test. Note: Use a =5

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Solution Summary

Interpret the estimated intercept and slope in this posting.