Quantitative Reasoning Outcomes Assessment Although more and more women are beco
ID: 3064808 • Letter: Q
Question
Quantitative Reasoning Outcomes Assessment 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 ofmale and female physicians in each. Specialty Dermatology Emergency medicine |5098 20429 Neurology Radiology Pediatrics Ob/Gynecology Female | Male 3482 6506 289510088 12187574 5200 4280 3470 2135 2800 4030 Suppose we would like to predict the number of male specialists from number of female specialists with the specialty data provided in the table. Answer each of the following questions (a) What does the correlation coefficient calculated in (b) tell you about the relationship between the number of male specialists and the number of female specialists? Describe the form, strength, and direction of the relationship. [1 point] (b) Interpret the slope of the regression model in (c). [1 point] (c) Interpret the residual calculated in (f). Is the model underestimate or overestimate the number of male specialists in Radiology? [1 point] (d) Identify the assumptions for the proposed model. [1 point] (e) What are the limitations for prediction with a model (Hint: [2 points]Explanation / Answer
a)
r = 0.318147
positive , weak
b) slope = 1.408
it means that if the number of female increase by 1
the number of male increase by 1.408
c)
residual = yi - yi^
for radiology
y^ = 3002.56638 + 1.4081047 * 1218
= 4717.17
this model underestimate as residual is positive
Regression Statistics Multiple R 0.318147782 R Square 0.101218012 Adjusted R Square -0.078538386 Standard Error 6361.344876 Observations 7 ANOVA df SS MS F Significance F Regression 1 22786169.69 22786169.69 0.563084334 0.486809538 Residual 5 202333543.2 40466708.63 Total 6 225119712.9 Coefficients Standard Error t Stat P-value Lower 95% Intercept 3002.566383 6909.249964 0.434571972 0.681988393 -14758.22607 female 1.40810476 1.876498598 0.750389455 0.486809538 -3.41558845