A professor of Anatomy wanted to develop a multiple regression models to predict
ID: 3325613 • Letter: A
Question
A professor of Anatomy wanted to develop a multiple regression models to predict the students' grades in her fourth-year medical course. She decides that the two most important factors are the student's grade point average in the first three years and the student's major. She proposes the model y = 0 + 1x1 + 2x2 + 3x3 + , where y = Fourth-year medical course final score (out of 100), x1 = G.P.A. in first three years (range from 0 to 12), x2 = 1 if student's major is medicine and 0 if not, and x3 = 1 if student's major is biology and 0 if not. The computer output is shown below.
THE REGRESSION EQUATION IS
y = 9.14 + 6.73x1 + 10.42x2 + 5.16x
Predictor
Coef
StDev
T
Constant
9.14
7.10
1.287
x1
6.73
1.91
3.524
x2
10.42
4.16
2.505
x3
5.16
3.93
1.313
S = 15.0
RSq = 44.2%
ANALYSIS OF VARIANCE
Source of Variation
df
SS
MS
F
Regression
3
17098
5699.333
25.386
Error
96
21553
224.510
Total
99
38651
a. Predict the final grade (out of 100) in the fourth-year medical course for a medical student who has a 10.95 G.P.A. in their first three years (range from 0 to 12).
ANS: Y(hat) = __________________
b. Predict the final grade (out of 100) in the fourth-year medical course for a biology major student who has a 10.95 G.P.A. in their first three years (range from 0 to 12).
ANS: ___________
c. Predict the final grade (out of 100) in the fourth-year medical course for an anatomy major student who has a 10.95 G.P.A. in their first three years (range from 0 to 12).
ANS: Y9hat) = ________________
d. Do these results allow us to conclude at the 1% significance level that the model is useful in predicting the fourth-year medical course final grade?
ANS:
Ho = ________________________
H1 = ________________________
Rejection region: ______________
Test statistic: _________________
Conclusion: __________________
e. Do these results allow us to conclude at the 1% significance level that on average medical majors outperform those whose majors are not medical or biology?
ANS:
Ho = ________________________
H1 = ________________________
Rejection region: ______________
Test statistic: _________________
Conclusion: __________________
f. Do these results allow us to conclude at the 1% significance level that on average biology majors outperform those whose majors are not medical or biology?
ANS:
Ho = ________________________
H1 = ________________________
Rejection region: ______________
Test statistic: _________________
Conclusion: __________________
g. Do these results allow us to conclude at the 1% significance level that grade point average in first three years is linearly related to the fourth-year medical final grade?
ANS:
Ho = ________________________
H1 = ________________________
Rejection region: ______________
Test statistic: _________________
Conclusion: __________________
h. Interpret the coefficient b2.
ANS: This can be interpreted as _________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
i. Interpret the coefficient b3.
ANS: This can be interpreted as _________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
Predictor
Coef
StDev
T
Constant
9.14
7.10
1.287
x1
6.73
1.91
3.524
x2
10.42
4.16
2.505
x3
5.16
3.93
1.313
Explanation / Answer
a) y(hat) = 9.14 + 6.73x1 + 10.42x2 + 5.16x3
= 9.14 + 6.73(10.95) + 10.42(0) + 5.16(0) = 82.8335
b) y(hat) = 9.14 + 6.73x1 + 10.42x2 + 5.16x3
= 9.14 + 6.73(10.95) + 10.42(0) + 5.16(1) = 87.9935
c) y(hat) = 9.14 + 6.73x1 + 10.42x2 + 5.16x3
= 9.14 + 6.73(10.95) + 10.42(1) + 5.16(0) = 93.2535
d)
H0: the model is not useful in predicting the fourth-year medical course final grade
H1: the model is useful in predicting the fourth-year medical course final grade
Let the los be alpha = 5%
rejection region: F-value > 2.6994 (=F critical value)
Test statistic F = 25.386
Here F value > F Critical value, so we reject H0
conclusion: the model is useful in predicting the fourth-year medical course final grade
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