Although more and more women are becoming physicians each year, it is well known
ID: 3217844 • Letter: A
Question
Although more and more women are becoming physicians each year, it is well known that men outnumber women in many specialties. Randomly selected specialties are listed below with the numbers of female and male physicians in each.
Specialty
Female
Male
Dermatology
Emergency medicine
Neurology
Pediatric Cardiology
Radiology
Forensic Pathology
Radiation Oncology
3482
5098
2895
459
1218
181
968
7500
20440
10088
1241
7674
399
3215
Suppose we would like to predict the number of male specialists from number of female specialists with the data provided in the table. Answer each of the following questions:
2 Predict the number of male specialists if
a) the number of female specialists is 2000. Show work. What do you call this prediction, interpolation or extrapolation? Explain.
b) the number of female specialist is 6000. Show work. What do you call this prediction, interpolation or extrapolation? Explain.
c) How reliable is this prediction in (2b)? Explain.
Specialty
Female
Male
Dermatology
Emergency medicine
Neurology
Pediatric Cardiology
Radiology
Forensic Pathology
Radiation Oncology
3482
5098
2895
459
1218
181
968
7500
20440
10088
1241
7674
399
3215
Explanation / Answer
Since number of male & female across specialties are highly positively correlated, so we used simple linear regression model for prediction (in excel using data analysis add in):
Equation is
Male= 119.18+3.48*Female + error
2.a) if female = 2000
Male= 119.18+3.48*2000 =7079 Males
This prediction is interpolation. Since the data given i.e. no. of male and female are in the range of analyzed data.
2.b) if female = 6000
Male= 119.18+3.48*6000 =20999Males
This prediction is extrapolation. Since the data given i.e. no. of male and female are Not in the range of analyzed data.
2.c) Since regression is not used for extrapolation so 2.b results are not reliable.
SUMMARY OUTPUT Regression Statistics Multiple R 0.925257 R Square 0.856101 Adjusted R Square 0.827321 Standard Error 2846.784 Observations 7 ANOVA df SS MS F Significance F Regression 1 2.41E+08 2.41E+08 29.74661 0.002817 Residual 5 40520907 8104181 Total 6 2.82E+08 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 119.1752 1689.361 0.070545 0.946495 -4223.47 4461.816 Female 3.476874 0.637485 5.454045 0.002817 1.838166 5.115582Related Questions
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