04 Jun Question 1. Following table gives the miles-per-gallon for four
Question
1. Following table gives the miles-per-gallon for four brands of cars using three different grades
of gasoline. If the Total Sum of Squares equals 270, using the Two-Way ANOVA (at ? = 5%),
analyze if there is a significant difference in the means of miles/gallon by (a) Brands of Cars;
and (b) Grades of Gasoline? (10 points)
Cars
A
B
C
D
Regular
18
22
30
26
Gasoline
MidGrade Premium
20
23
24
27
32
32
28
30
2. There are three brands of TVs in the market. Samsung sells 35% of the market, Sony 40%,
and all other brands 25%. Sony announced a special deal for the Holiday Season. To check on
sales, a sample of 300 TVs sold was examined. It showed that 135 TVs sold were Sony, 95
were Samsung, and the rest were other brands. Using Chi-square test, can we say that market
shares of these brands changed significantly as a result of Sonys special deal? State your null
hypothesis, and interpret your results.
(10 points)
3. Estimate the demand curve from the following data where Y is quantity demanded and X is
price.
Number of Observation = 101
Yi = 16,160
2
(Yi-Yhat) = 1,960
(Xi-Xbar)2 = 40,000
6,400
(Xi-Xbar)(Yi-Ybar) = 12,000
(Use only two decimal places to write your answers)
Xi = 30,130
(Yi-Ybar)2 =
(4pts each= 20 points)
Estimate the following:
a. Regression line and interpret it.
b. Make ANOVA Table. Write Ho. Calculate F-value and interpret your results.
c. Calculate measure of goodness of fit and interpret your results
d. Calculate t-statistic for b1
e. What will be the quantity demanded if Price is 400? Calculate 95% confidence
interval of your predicted value.
Bonus: Calculate coefficient of correlation between x and y and test the hypothesis Ho:
?
= 0 against 0. OR Calculate ?xy, ?x and ?y.
(2 points).
xy
4. Following table shows results from a survey testing the use of social networking sites by
adults in three countries.
(10
points)
Countries
UK
Russia
USA
344
201
500
Use Social Networking
YES
NO
456
399
500
Perform Chi-square pairwise comparisons at 5% margin of error to test which pair of countries
differed in their use of social networking sites. Which country did the most networking?
5. Given below is a liner expenditure equation for 1000 families in its simplified version:
Y = 9.12 + 0.36 Income + 3.21 CPI + 1.45 Family Size + 2.33 Race + 0.82 Area
0.81
(1.66) (2.22)
(3.11)
(2.62)
(2.21)
(1.99)
F = 218
R2 =
Where Y is expenditure (thousand $); Income (thousand $); CPI change in consumer price
index (%), Family-size 2 to 5; Race (0 = Asian, 1 = African-American, 2= Hispanic, 3 = White),
and
Area (0 = Township, 1 = Suburb, 2 = Metropolitan).
Calculate the expected expenditure of an African-American family comprising of 4 family
members, earning $50 thousand, living in a metropolitan area where the cost of living
(measured by CPI) increased by 3 percent in one year.
SHORT QUESTION: (10 points)
1/ You are given the following output from model estimation:
Variables
Price Increase_Same Model
(000)
Gender
Number of Competitive Models
Number of Recalls_Same
Model
Constant
Nagelkerke R-sq = 0.66
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