EBK BUSINESS STATISTICS
7th Edition
ISBN: 8220102743984
Author: STEPHAN
Publisher: PEARSON
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Is it possible to predict the annual number of business bankruptcies by the number of
firm births (business starts) in the United States? The following data published by the
U.S. Small Business Administration, Office of Advocacy, are pairs of the number of
business bankruptcies (1,000s) and the number of firm births (10,000s) for a six-year
period.
Business Bankruptcies
(1,000)
34.3
Firm Births
(10,000)
58.1
35.0
55.4
38.5
57.0
40.1
58.5
35.5
57.4
37.9
58.0
i) Based on the output given, use these data to develop the equation of the
regression model to predict the number of business bankruptcies by the
number of firm births.
ii) Explain the values of r and r.
iii) Predict the number of business bankruptcies if the number of firm births is
54.0 (10,000s).
iv) Do the data support the existence of a linear relationship between the number
of firm births and the number of business bankruptcies? Test using a = 0.05.
OUTPUT
Model Summary
Std. Error of the
Estimate
Adusted R
Model
R
R Square…
Consider data on every game played by the Brooklyn Nets in 2014 (82 games) that includes the
variables
margin; - the Net's margin of victory (number of points the Nets scored minus the number of
points their opponent scored) for game i, and
• home; - a dummy variable equal to 1 when the Nets are the home team (game i was played in
their home arena) and equal to 0 when they are the away team (game i was played in the
opponent's arena).
I use the least-squares method to estimate the following regression model
margin = a + ßhome; + ei
Below is the Stata output corresponding to the estimated regression line:
regress margin home if team==== "Brooklyn Nets"
Source
Model
Residual
Total
margin
home
_cons
SS
1459.95122
15252.0488
16712
df
1
80
Coef. Std. Err.
MS
81 206.320988
8.439024 3.049595
-5.219512 2.156389
1459.95122
190.65061
t
Number of obs
F (1, 80)
Prob > F
R-squared.
Adj R-squared =
Root MSE
P>|t|
2.77 0.007
-2.42 0.018
82
7.66
0.0070
0.0874
0.0760
13.808
[95% Conf. Interval]…
Suppose researchers at an abdominal transplant clinic are concerned about the rate of graft loss due to diabetes status prior to receiving a donor kidney. Research has shown that gender discordance, or receiving a gender from a donor of an opposite gender may increase the risk of both exposure and outcome after transplant. Assume the following tables represent the stratified analysis of the potential confounding variable. (9 points)
Gender Discordance
Graft Failure
No Graft Failure
Total
Diabetes II
23
10
33
No Diabetes II
4
44
48
Total
27
54
81
Gender Concordance
Graft Failure
No Graft Failure
Total
Diabetes II
9
34
43
No Diabetes II
12
87
99
Total
21
121
142
A) Calculate the stratum specific estimates for the odds ratios in each strata.
B) Observe the difference in the odds ratios. Based on observation alone, what are we likely to conclude regarding the relationship between outcome and exposure…
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- Consider data on every game played by the Brooklyn Nets in 2014 (82 games) that includes the variables margin, - the Net's margin of victory (number of points the Nets scored minus the number of points their opponent scored) for game i, and • home; - a dummy variable equal to 1 when the Nets are the home team (game i was played in their home arena) and equal to 0 when they are the away team (game i was played in the opponent's arena). I use the least-squares method to estimate the following regression model margin = a + ßhome; + ei Below is the Stata output corresponding to the estimated regression line: regress margin home if team===== "Brooklyn Nets" . Source Model Residual Total margin home _cons SS 1459.95122 15252.0488 16712 df 1459.95122 1 80 190.65061 None of the above 81 206.320988 Coef. Std. Err. 8.439024 3.049595 -5.219512 2.156389 MS t Number of obs F(1, 80) Prob > F R-squared O The Nets lost more games than they won in 2014 P>|t| 2.77 0.007 -2.42 0.018 Adj R-squared = Root…arrow_forwardA medical student at a community college in city Q wants to study the factors affecting the systolic blood pressure of a person (Y). Generally, the systolic blood pressure depends on the BMI of a person (B) and the age of the person A. She wants to test whether or not the BMI has a significant effect on the systolic blood pressure, keeping the age of the person constant. For her study, she collects a random sample of 150 patients from the city and estimates the following regression function: Y= 15.50 +0.90B + 1.10A. (0.48) (0.35) The test statistic of the study the student wants to conduct (Ho: B, =0 vs. H4: B, #0), keeping other variables constant is. (Round your answer to two decimal places.) At the 5% significance level, the student will v the null hypothesis. Keeping BMI constant, she now wants test whether the age of a person (A) has no significant effect or a positive effect on the person's systolic blood pressure. So, the test statistic associated with the one-sided test the…arrow_forwardSuppose you want to test whether girls who attend a girls’ high school do better in math than girls who attend coed schools. You have a random sample of senior high school girls from a state in the United States, and score is the score on a standardized math test. Let girlhs be a dummy variable indicating whether a student attends a girls’ high school. (i) What other factors would you control for in the equation? (You should be able to reasonably collect data on these factors.) (ii) Write an equation relating score to girlhs and the other factors you listed in part (i). (iii) Suppose that parental support and motivation are unmeasured factors in the error term in part (ii). Are these likely to be correlated with girlhs? Explain. (iv) Discuss the assumptions needed for the number of girls’ high schools within a 20-mile radius of a girl’s home to be a valid IV for girlhs. (v) Suppose that, when you estimate the reduced form for girlshs, you find that the coefficient on numghs (the number…arrow_forward
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