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estimated regression coefficients

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What is known as the characteristic line of modern investment analysis is simply the regression line obtained from the following model:

rit = αi + βi rmt + et

Where rit = the rate of return on the ith security in time t; rmt = the rate of return on the market portfolio in time t; et = stochastic disturbance term. In this model beta i is known as the beta coefficient of the ith security, a measure of market (or systematic) risk of a security.

On the basis of 240 monthly rates of return for the period 1956- 1976, Fogler and Ganapathy obtained the following characteristic line for IBM stock in relation to the market portfolio index developed at the University of Chicago (standard errors in parenthesis):

^rit = 0.7264 + 1.0598rmt

(se) (0.3001) (0.0728)

r2 = 0.4710; F(1,238) = 211.896

Interpret the estimated regression coefficients.

Explain the meaning of the estimated r2 value.

A security whose beta coefficient is greater than one is said to be a volatile or aggressive security. Was IBM a volatile security in the time period under study? Conduct an appropriate test to answer the question.

Is the intercept coefficient significantly different from zero? If it is, what is its practical meaning? Again conduct an appropriate test to answer the question

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Solution Preview

Interpret the estimated regression coefficients.

The regression equation says that if the rate on return on market portfolio goes up by 1%, the return on the IBM stock goes up by 1.0598%. The alpha value simply says that when the rate of return on the market portfolio is zero, the return on the IBM stock is 0.7264

Explain the meaning of the estimated r2 value.

The value of r-square is 0.4710 which means that out of the total variance in the return on IBM stock 47.10% is explained by the regression equation build using the return on the market ...

Solution Summary

The estimated regression coefficients are assessed.

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1. Thirty-two data points on Y and X are employed to estimate the parameters in the linear relation Y = a + bX. The computer output from the regression analysis is

a. The equation of the sample regression line is: = __________________________.
b. There are ______ degrees of freedom for the t-test. At the 5% level of significance, the critical t-value for the test is ______________.
c. At the 5% level of significance, __________ (is, not) significant, and ________ (is, is not) significant.
d. At the 2% level of significance, the critical t-value for a t-test is ___________. At the 2% level of significance, _________ (is, is not) significant, and _________ (is, is not) significant.
e. The p-value for indicates that the exact level of significance is ______ percent, which is the probability of _________________________________________.
f. At the 5% level of significance, the critical value of the F-statistic is _______. The model as a whole ___________ (is, is not) significant at the 5% level.
g. If X equals 240, the fitted (or predicted) value of Y is ____________________________.
h. The percentage of the total variation in Y that is NOT explained by the regression is ________.

2. Schools with larger enrollments might have more resources, making their students better prepared and more valuable to employers and, subsequently, commanding a higher salary. Of course, smaller schools may give students more personal attention, which develops better skills and could yield a higher salary for smaller schools. Studying the relationship between mean base salary and enrollment might help us understand this relationship better. (Use bschools2002.xls)

a. Uses excel to perform a regression of mean base salary vs. enrollment. Write the estimated regression equation.
b. Use your regression equation to estimate the mean base salary for a school that enrolls 800 students.
c. Use your regression equation to estimate the mean base salary for a school that enrolls 1,800 students.
d. Interpret the p-value of the independent variable.

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