Although more and more women are becoming physicians each year, it is well known
ID: 3217845 • 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:
3
a) Give the correlation coefficient, r between the number of female specialists and the number of male specialists. Again, you do not need to show the computations.
b) What does the correlation coefficient r tell you about the relationship between the number of male specialists and the number of female specialists? Describe the relationship in terms of (1) the form (linear or curved), (2) the strength (strong or weak), and (3) the direction (positive or negative) of the relationship. Write complete sentences while answering the question.
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
3 a.
Step 1: Find XY , X2 and Y2 as it was done in the table below.
Step 2: Find the sum of every column to get:
X=14301 , Y=50557 , XY=172623770 , X2=49158943 , Y2=646737127
Step 3: Use the following formula to work out the correlation coefficient.
r = nXYXY/sqrt[nX2(X)2][nY2(Y)2]= 71726237701430150557/sqrt[749158943143012][7646737127505572]0.9253
b.
Step 1: Find XY and X2 as it was done in the table below.
Step 2: Find the sum of every column:
X=14301 , Y=50557 , XY=172623770 , X2=49158943
Step 3: Use the following equations to find a and b:
a=YX2XXY/nX2(X)2=505574915894314301172623770/749158943143012119.175
b=nXYXY/nX2(X)2=71726237701430150557/749158943(14301)23.477
Step 4: Substitute a and b in regression equation formula
y = a + bx= 119.175 + 3.477x Yes its linear
c.As r is near to 1 its strong
d. As r is positive it is positive
X Y XY XX YY 3482 7500 26115000 12124324 56250000 5098 20440 104203120 25989604 417793600 2895 10088 29204760 8381025 101767744 459 1241 569619 210681 1540081 1218 7674 9346932 1483524 58890276 181 399 72219 32761 159201 968 3215 3112120 937024 10336225Related Questions
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