A small study is conducted involving 17 infants to investigate the association b
ID: 3242353 • Letter: A
Question
A small study is conducted involving 17 infants to investigate the association between gestational age at birth, measured in weeks, and birthweight, measured in grams. We want to figure out a way to predict the birthweight of an infant with of certain gestational ages, and we want to see if the relationship between the quantities is strong.
Observations:
X (Gestational Age)
Y (Weight)
1
34.7
1895
2
29.3
2030
3
35.7
1440
4
36
2835
5
37.3
3090
6
38
3827
7
38.3
3260
8
38.5
2690
9
38.7
3285
10
39.7
2920
11
39.7
3430
12
40.1
3657
13
40.3
3685
14
40.9
3345
15
41.1
3260
16
41.4
2680
17
42.4
2006
A) What is the value for b
B) What is the Value for a
C) Find the equation of the regression line, and use it to predict birthweight for an infant of at each of the following gestational ages:
37 weeks
40 weeks
42 weeks
D) Find and interpret Pearson’s correlation coefficient r
Observations:
X (Gestational Age)
Y (Weight)
1
34.7
1895
2
29.3
2030
3
35.7
1440
4
36
2835
5
37.3
3090
6
38
3827
7
38.3
3260
8
38.5
2690
9
38.7
3285
10
39.7
2920
11
39.7
3430
12
40.1
3657
13
40.3
3685
14
40.9
3345
15
41.1
3260
16
41.4
2680
17
42.4
2006
Explanation / Answer
The regression equation is
Y (Weight) = - 1081 + 103.85 X (Gestational Age)
Predictor Coef SE Coef T P
Constant -1081 1935 -0.56 0.584
X (Gestational Age) 103.85 50.28 2.07 0.057
S = 634.907 R-Sq = 22.1% R-Sq(adj) = 16.9%
A) What is the value for b
Ans: The value of b is 103.85.
B) What is the Value for a
Ans: The value of a is -1081.
C) Find the equation of the regression line, and use it to predict birthweight for an infant of at each of the following gestational ages:
Ans: The equation of the regression line is
Y (Weight) = - 1081 + 103.85 X (Gestational Age)
At 37 weeks
Y (Weight) = - 1081 + 103.85 *37=2761.45
At 40 weeks
Y (Weight) = - 1081 + 103.85 *40=3073
At 42 weeks
Y (Weight) = - 1081 + 103.85 *42=3280.7
D) Find and interpret Pearson’s correlation coefficient r
Ans: Pearson’s correlation coefficient r = 0.471.
The value of Pearson’s correlation coefficient r is positive. Hence, Y and X has positive association. Also, the value is arround 0.5, hence, it has medium strength in association.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.