Birth Length (in) of Newborn Infants Height of Mother (in) Height of Father (in)
ID: 3201497 • Letter: B
Question
Birth Length (in) of Newborn Infants
Height of Mother (in)
Height of Father (in)
Birth Weight of Nearest Sibling (lb)
1
22.0
61
70
6.5
2
23.5
64
72
6.1
3
24.0
64
74
7.3
4
22.1
60
61
6.2
5
18.7
59
60
5.9
6
22.1
64
62
6.7
7
23.0
62
73
6.8
8
24.3
64
76
7.2
9
22.9
63
72
6.1
10
22.1
65
72
6.1
11
20.3
63
71
6
12
24.2
64
76
7.4
13
21.9
65
72
6.2
14
23.4
62
78
6.7
15
26.1
64
77
7.1
16
22.5
63
72
6.8
17
22.7
62
70
6.5
18
22.6
63
69
6.7
19
21.9
63
68
6.2
20
19.6
60
61
5.9
21
19.6
61
64
5.8
22
22.5
64
66
6.2
23
23.7
65
72
6.7
24
24.1
66
72
7.1
25
22.8
63
68
7.1
Scenario 4: Perform a multiple linear regression analysis to predict a newborn’s birth length (in inches) using both the mother’s height (X1) and the father’s height (X2) as the predictor variables. Conduct your analysis using a 95% level of confidence.
Question 16: Does the regression model confirm a correlation between the dependent variable and the independent variables? How do you know? (5 points)
Question 17: Is the statistical significance of the model as a whole acceptable for a 95% level of confidence? How do you know? (5 points)
Question 18: What is the Critical Value of F associated with this regression model?
Question 19: What is the regression equation for the model? (5 points)
Question 20: Are both independent variables in this model significant? How do you know? (5 points)
Question 21: What is the predicted birth length of a newborn whose mother is 59.6 inches tall and the father’s height of 75.1 inches? (5 points)
Birth Length (in) of Newborn Infants
Height of Mother (in)
Height of Father (in)
Birth Weight of Nearest Sibling (lb)
1
22.0
61
70
6.5
2
23.5
64
72
6.1
3
24.0
64
74
7.3
4
22.1
60
61
6.2
5
18.7
59
60
5.9
6
22.1
64
62
6.7
7
23.0
62
73
6.8
8
24.3
64
76
7.2
9
22.9
63
72
6.1
10
22.1
65
72
6.1
11
20.3
63
71
6
12
24.2
64
76
7.4
13
21.9
65
72
6.2
14
23.4
62
78
6.7
15
26.1
64
77
7.1
16
22.5
63
72
6.8
17
22.7
62
70
6.5
18
22.6
63
69
6.7
19
21.9
63
68
6.2
20
19.6
60
61
5.9
21
19.6
61
64
5.8
22
22.5
64
66
6.2
23
23.7
65
72
6.7
24
24.1
66
72
7.1
25
22.8
63
68
7.1
Explanation / Answer
Answer:
Scenario 4: Perform a multiple linear regression analysis to predict a newborn’s birth length (in inches) using both the mother’s height (X1) and the father’s height (X2) as the predictor variables. Conduct your analysis using a 95% level of confidence.
Regression Analysis
Regression Statistics
Multiple R
0.8005
R Square
0.6408
Adjusted R Square
0.6081
Standard Error
1.0322
Observations
25
ANOVA
df
SS
MS
F
Significance F
Regression
2
41.8120
20.9060
19.6237
0.0000
Residual
22
23.4376
1.0653
Total
24
65.2496
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-8.7939
7.8637
-1.1183
0.2755
-25.1022
7.5144
x1
0.2885
0.1496
1.9286
0.0668
-0.0217
0.5986
x2
0.1879
0.0511
3.6792
0.0013
0.0820
0.2938
Question 16: Does the regression model confirm a correlation between the dependent variable and the independent variables? How do you know? (5 points)
Multiple R=0.8005 and Calculated R square =0.6408.
64.08% of variation is explained by independent variables.
Question 17: Is the statistical significance of the model as a whole acceptable for a 95% level of confidence? How do you know? (5 points)
Calculated F=19.6237, P=0.0000 which is < 0.05 level. The model is significant.
Question 18: What is the Critical Value of F associated with this regression model?
F(2,22) value at 95% level =3.44
Question 19: What is the regression equation for the model? (5 points)
y = -0.8.7939+0.2885*x1+0.1879*x2
Question 20: Are both independent variables in this model significant? How do you know? (5 points)
For the variable x1, calculated t=1.9286, P=0.0668 which is > 0.05 level.
Mother’s height (X1) is not significant
For the variable x2, calculated t=3.6792, P=0.0013 which is < 0.05 level.
Father’s height (X2) is significant
Question 21: What is the predicted birth length of a newborn whose mother is 59.6 inches tall and the father’s height of 75.1 inches? (5 points)
y = -8.7939+0.2885*59.6+0.1879*75.1
=22.51199
Predicted birth length =22.51 inches.
Regression Analysis
Regression Statistics
Multiple R
0.8005
R Square
0.6408
Adjusted R Square
0.6081
Standard Error
1.0322
Observations
25
ANOVA
df
SS
MS
F
Significance F
Regression
2
41.8120
20.9060
19.6237
0.0000
Residual
22
23.4376
1.0653
Total
24
65.2496
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-8.7939
7.8637
-1.1183
0.2755
-25.1022
7.5144
x1
0.2885
0.1496
1.9286
0.0668
-0.0217
0.5986
x2
0.1879
0.0511
3.6792
0.0013
0.0820
0.2938
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