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ECO252 QBA2
FINAL EXAM
April 25, 1998
Name
Hour of Class Registered (Circle)
MWF 10 11 TR 12:30 2:00
I. (16 points) Do all the following.
The following pages show the regression of the variable 'pccons', automobile fuel consumed, against some
of the following independent variables:
'pop'
US population in millions
'year'
Years after 1970 (so 1990 data has 'year' = 20)
'earn'
Average gross real weekly earnings in 1982 dollars
'regpr' Price of regular gasoline in dollars per gallon
'relpr' Relative price of gasoline - a price index for gasoline divided by the Consumer Price Index
1. In regression 2, what coefficients are significant at the 5% level? Why?(3)
2. Which coefficients are significant at the 1% level? Why?(1)
3. Comparing the three regressions, noting t-tests, Rsq, Rsq(adj), which seems best? Why?(2)
4. Compare the first regression against the third using an F test. Do the added variables have additional
explanatory power? (4)
5. Using the first observation, give a confidence and prediction interval for consumption. (3)
6. In the third equation, are the signs of the coefficients as expected? Why?(2)
7. If in 1994 population was 260 million, earnings were $260, regular price was $1.10 and relative price
was .650, what consumption does the second regression predict? (2)
8. (Extra credit) Looking at the Durbin Watson statistics, explain what they seem to show?(3)
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II. Do at least 4 of the following 6 Problems (at least 15 each) (or do sections adding to at least 60 points Anything extra you do helps, and grades wrap around) . Show your work! State H 0 and H1 where
applicable. Use a significance level of 5% unless noted otherwise.
1. The data below shows sales in billions, employees in thousands and R&D expenditures in billions
for a sample of six pharmaceutical corporations..
x1
x2
y
sales
10.0
13.4
empl
43.8
64.7
R&D
3.47
1.35
a) Compute the simple regression equation of sales against employees (6)
b) Compute R 2 . (4)
c) Compute s e .(3)
13.8
49.1
1.20
d) Compute sb0 and do a significance test on b0 . (4)
1.3
18.8
16.7
7.9
82.3
45.2
0.06
1.63
5.30
e) Do a confidence interval for sales when a firm has 40 thousand employees.(4)
 y  74.0,  y  1104.0,  x  293.0,  x  17394,  x  13.01,  x  46.054,
 x y  ?,  x y  188.58,  x x  672.43 and n  6 . You do not need all of these.
2
1
1
2
1 2
2
1
2
2
2
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2. Data from 1) is repeated below.
 y  74.0,  y  1104.0,  x  293.0,  x  17394,  x
 x y  ?,  x y  188.58,  x x  672.43 and n  6 .
2
1
1
2
2
1
2
 13.01,
x
2
2
 46.054,
1 2
a. Do a multiple regression of sales against employment and R&D. (12)
b. Compute R 2 and R 2 adjusted for degrees of freedom. Compare both with values for the previous
problem.(5)
c. Do an F test to see if R&D helps explain sales.(6)
d. Use your equation to predict sales for a firm with 50 thousand employees and $1 billion in R&D
expenditures. (2)
e. Using the method suggested in the text, make your answer to d into prediction and confidence intervals.
(4)
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3. Data from the previous problem is repeated again!
a) Compute the correlation between sales and R&D. Is it significant? (5)
x1
x2
y
sales
10.0
13.4
13.8
1.3
18.8
16.7
empl
43.8
64.7
49.1
7.9
82.3
45.2
R&D
3.47
1.35
1.20
0.06
1.63
5.30
b) Compute a rank correlation between sales and R&D. Is it significant?
Why might we expect rank correlation to be higher that the conventional
correlation? (5)
c) Compute Kendall's W for this data and test it for significance.(6)
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4. Non-union member Confidence in big business and job satisfaction is reported below.
a. Test the hypothesis that these are independent.(7)
b. Test the hypothesis that the proportion who are very confident is the same for the very satisfied and the
moderately satisfied. (4)
c. Test the Hypothesis that one third of those who are very satisfied are very confident. (3)
very
moderately
satisfied
satisfied
dissatisfied
Very Confident
111
52
16
Somewhat Confident
246
142
55
Not Confident
73
51
28
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5. The data below represents samples of consumer ratings of three different displays.
Display
a. Assuming that each column represents a random sample from a normal
1
2
3
population with similar variances, compare the means of the three
55
45
45
populations. (6)
50
30
35
b. Assuming that each row represents the opinions of one individual
35
25
20
do a again, still assuming normality.(8)
45
35
40
c. Under the assumptions in b, compare the means of display 1 and 2
40
30
35
using a 2-sample method. (2)
x
1
 225,
x
2
1
 10375,
x
2
 165,
x
2
2
 5675,
x
3
 175,
x
2
3
 6475.
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6. Data from the pervious problem is repeated.
Display
a. Drop the assumption of normality and compare the medians assuming that
1
2
3
that the columns are random samples. (5)
55
45
45
b. Do the same assuming that each row is 'owned' by one consumer. (5)
50
30
35
c. Since the method used in 6a assumes that variances are similar, test the
35
25
20
first two columns to see if they have similar variances (3)
45
35
40
40
30
35