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

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.

Find the following:
(a) Compute the sample regressioncoefficients bo and b1.
(b) Compute the estimated variance of the regression.
(c) Compute the standard error of the regression.
(d) Compute the estimated variance of b1.
(e) Compute the standard error of b1.
Year y = book value per share x = earning per share
1980

For the multiple regression equation y = 100 + 20x1 + 3x2 + 120x3:
a. Identify the y-intercept and partial regressioncoefficients.
b. If x1 = 12, x2 = 5, and x3 = 10, what is the estimated value of y?
c. If x3 were to increase by 4, what change would be necessary in x2 in order for the estimated value of y to remain uncha

5) Find the following:
Year y = book value per share x = earning per share
1985 0.81 0.35
1986 1.32 0.57
1987 1.87 0.65
1988 2.48 0.70
1989 2.88 0.50
(a) Compute the sample regressioncoefficients bo and b1.
(b) Compute the estim

13) The commercial division of a real estate firm is conducting a regression analysis of the relationship between gross rents (X) and selling price (Y) for apartment building. Data have been collected on several properties recently sold, and the following output has been obtained in computer run.
a. How many apartment buildings

For the multiple regression equation y-hat = 100 + 20x1 - 3x2 + 120x3
a. identify the y-intercept partial regressioncoefficients
b. if x1 = 12, x2 = 5, and x3 = 10, what is the estimated value of y?
c. if x3 were to increase by 4, what change would be necessary in x2 in order for the estimated value of y to remain unchange

What is the interpretation of the coefficients that emerge from the regression equation. Can you predict a change in the y variable given knowledge of the x variable? How much change would you predict in y for a one unit change in x?

See the attached file.
Predictor Coef StDev
Constant -150 90
X1 2000 500
X2 -25 30
X3 5 5
X4 -300 100
X5 0.60 0.15
Source DF SS MS F
Regression 5 1,500.00
Error 15
Total 20 2,000.0
a. Complete the ANOVA table.
b. Conduct a global test of hypothesis, using the .05 si

A)Show the scatter diagram and explain whether it displays a linear relationship.
b)Enter the regression equation
c)Interpret the coefficients in the regression.
d)Predict the amount of ice cream sold for one day with a temperature of 950C.

1. Compute the Pearson correlation for the following data.
X Y
7 3
3 1
6 5
4 4
5 2
2. Find the regression equation for predicting X from Y for the following set of scores.
X Y
0 9
1 7
2 11

Regression analysis was applied between demand for a product (Y) and the price of the product (X), and the following estimatedregression equation was obtained. Y = 130 - 20 X
Based on the above estimatedregression equation, if the price is increased by 2 units, then demand is expected to
decrease by 90 units
i