# Beta Value & Regression Analysis

I need help with problems 13.49 and 13.79. They are attached here. Thank you in advance!!

13.49 The volatility of a stock is often measured by its

beta value. You can estimate the beta value of a stock by

developing a simple linear regression model, using the per-

centage weekly change in the stock as the dependent vari-

able and the percentage weekly change in a market index as

the independent variable. The S&P 500 Index is a common

index to use. For example, if you wanted to estimate the beta

for Disney, you could use the following model, which is

sometimes referred to as a market model: (%weeklychangeinDisney) = b0 + b11%weeklychangeinS&P500index2 + e

The least-squares regression estimate of the slope is the

estimate of the beta value for Disney. A stock with a beta

value of 1.0 tends to move the same as the overall market. A

stock with a beta value of 1.5 tends to move 50% more than

the overall market, and a stock with a beta value of 0.6 tends

to move only 60% as much as the overall market. Stocks

with negative beta values tend to move in a direction oppo-

site that of the overall market. The following table gives

some beta values for some widely held stocks, using a year's

worth of data ending in May, 2009. Note that in the first 10

months of this time frame the S&P 500 lost approximately

40% of its value and then rebounded by about 10% in the last two months

Company Ticker Symbol Beta

Procter & Gamble PG 0.54

AT&T T 0.73

Disney DIS 1.10

Apple AAPL 1.52

eBay EBAY 1.69

Ford F 2.86

Source: Data extracted from finance.yahoo.com, May 27, 2009.

a. For each of the six companies, interpret the beta value.

b. How can investors use the beta value as a guide for

investing?

13.79 An accountant for a large department store would

like to develop a model to predict the amount of time it takes

to process invoices. Data are collected from the past

32 working days, and the number of invoices processed and

completion time (in hours) are stored in .

(Hint: First, determine which are the independent and

dependent variables.)

a. Assuming a linear relationship, use the least-squares

method to compute the regression coefficients

b. Interpret the meaning of the Y intercept, and the slope,

in this problem.

c. Use the prediction line developed in (a) to predict the

amount of time it would take to process 150 invoices.

d. Determine the coefficient of determination, and inter-

pret its meaning.

e. Plot the residuals against the number of invoices

processed and also against time.

f. Based on the plots in (e), does the model seem appropriate?

g. Based on the results in (e) and (f), what conclusions

can you make about the validity of the prediction made

Data:

Invoices Time

103 1.5

173 2

149 2.1

193 2.5

169 2.5

29 0.5

188 2.3

19 0.3

201 2.7

58 1

110 1.5

83 1.2

60 0.8

25 0.4

60 1.8

190 2.9

233 3.4

289 4.1

45 1.2

70 1.8

241 3.8

163 2.8

120 2.5

201 3.3

135 2

80 1.7

77 1.7

222 3.1

181 2.8

30 1

61 1.9

120 2.6

#### Solution Summary

The solution provides step by step method for the calculation of regression analysis. Formula for the calculation and Interpretations of the results are also included. Attached in Excel and Word.