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# Beta Value & Regression Analysis

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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

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