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Regression
Q1
A financial analyst wants to know the relationship between the return on Dalton
Company’s stock (Y) and the overall market return (X). He collects the following
annual data for both variables:
Y(%)
11 14 3
17 10 12 6
7
14 13
X(%)
10 12 8
15 9
11 8
10 13 11
∑
∑
∑
=
=
=
,
1222
,
1189
,
1309
2
2
xy
x
y
(a) Find the least squares prediction line for these data. Interpret the slope coefficient
of this model (i.e., explain what the number means, in the context of this particular
problem).
(b) The slope coefficient of this model is called the stock’s beta by investment
analysts. A coefficient greater than 1 means that the stock is sensitive to changes in
the overall market. Test the null hypothesis that Dalton Company’s stock is
insensitive to the market against the alternative hypothesis that it is sensitive. Use
α
= .05.
(c) Market analysts expect overall market return to be 10.5% next year. Find a 90%
prediction interval estimate of the return on Dalton Company’s stock for next year
under the assumption that the overall market forecast is accurate.
(d) What percentage of the total variance in Dalton Company’s stock return is
explained by this model?
(e) What is a 98% confidence interval estimate of the average return on Dalton
Company stock when the annual market return is 14%?
Q2
Consumer Report magazine conducted a study to find out if cheaper brands of
hotdogs have a higher calorie content than the more expensive ones. They take a
sample of 9 different brands of beef hotdogs and measure the variables Y = ”Calorie
content” and X = ”Price per ounce”. The data and part of the analysis is shown in the
following tables.
B
r
a
n
d
s
P
r
i
c
e
C
a
l
o
r
i
e
s
Spike’s Beef
0.15
149
Hungry Hugh’s Jumbo Beef
0.10
184
Great Dinner Beef
0.11
190
RJB Kosher Beef
0.21
158
Wonder Kosher Skinless Beef
0.20
139
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View Full Document Happy Fats Jumbo Beef
0.14
175
Midwest Beef
0.14
148
General Kosher Beef
0.23
152
Wall’s Kosher Beef Low Fat
0.25
111
Predictors
Coef
Stdev
tRatio p
Constant
218.2
17.95
Price
−
364.6
101.2
Notice that some of the numbers in the output are missing.
(a) Interpret the slope coefficient in the context of this particular problem.
(b) It is assumed that the price is not necessarily a good predictor of the calorie
content. Perform a hypothesis test to verify this assumption.
(c) Calculate the Rsquare and interpret the result.
Q3
It is known that GMAT scores can be improved by training for the test. The following
table gives increase in GMAT scores by four students after X hours of training.
Hours of training
10
20
40
80
Average improvement
10
18
35
50
(a) Find the intercept and slope of the regression line by least squares.
(b) Estimate the average improvement after 50 hours of training.
(c) Find a 95% prediction interval for the score improvement after 30 hours of
training.
Q4
A university administered a newly designed entrance test to 25 students randomly
selected from the new freshman class of a school in a study to determine whether a
student’s grade point average (Y ) at the end of the freshman year can be predicted
from this entrance test score (X). In the data set, X ranges from 3.5 to 7.8 and Y
ranges from 1.6 to 4.7. The summary statistics are:
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This note was uploaded on 09/18/2010 for the course BBA ISOM111 taught by Professor Hu during the Fall '08 term at HKUST.
 Fall '08
 HU

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