Birth Length (in) of Newborn Infants Height of Mother (in) Height of Father (in)
ID: 3177454 • 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
20.4
61
60
7.4
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
21.3
62
71
7.1
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
21.4
63
71
6.2
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
24.1
66
73
6.6
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?
Question 17: Is the statistical significance of the model as a whole acceptable for a 95% level of confidence? How do you know?
Question 18: What is the Critical Value of F associated with this regression model?
Question 19: What is the regression equation for the model?
Question 20: Are both independent variables in this model significant? How do you know?
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?
Scenario 5: Perform a multiple linear regression analysis to predict a newborn’s birth length (in inches) using the father’s height (X1) and the birth weight of the nearest sibling (X2) as the predictor variables. Conduct your analysis using a 95% level of confidence.
Question 22: Does the regression model confirm a correlation between the dependent variable and the independent variables? How do you know?
Question 23: Is the statistical significance of the model as a whole acceptable for a 95% level of confidence? How do you know?
Question 24: What is the value of F associated with this regression model?
Question 25: What is the regression equation for the model?
Question 26: Are both independent variables in this model significant? How do you know?
Question 27: What is the predicted birth length of a newborn whose father’s height of 73.6 inches tall and the nearest sibling’s birth weight is 6.25 lbs?
Scenario 6: Perform a multiple linear regression analysis to predict a newborn’s birth length (in inches) using the mother’s height (X1), and the birth weight of the nearest sibling (X2) as the predictor variables. Conduct your analysis using a 95% level of confidence.
Question 28: Does the regression model confirm a correlation between the dependent variable and the independent variables? How do you know? (5 points)
Question 29: Is the statistical significance of the model as a whole acceptable for a 95% level of confidence? How do you know? (5 points)
Question 30: What is the value of F associated with this regression model? (5 points)
Question 31: What is the regression equation for the model? (5 points)
Question 32: Are both of the independent variables in this model significant? How do you know? (5 points)
Question 33: What is the predicted birth length of a newborn whose mother’s height is 58.5 inches and the nearest sibling’s birth weight is 6.9 lbs? (5 points)
Scenario 7: Perform a multiple linear regression analysis to predict a newborn’s birth length (in inches) using the mother’s height (X1), the father’s height (X2) and the birth weight of the nearest sibling (X3) as the predictor variables. Conduct your analysis using a 95% level of confidence.
Question 34: Does the regression model confirm a correlation between the dependent variable and the independent variables? How do you know? (5 points)
Question 35: Is the statistical significance of the model as a whole acceptable for a 95% level of confidence? How do you know? (5 points)
Question 36: What is the value of F associated with this regression model? (5 points)
Question 37: What is the regression equation for the model? (5 points)
Question 38: Are all three independent variables in this model significant? How do you know? (5 points)
Question 39: What is the predicted birth length of a newborn whose mother’s height is 58.5 inches, a father’s height of 71.6 inches and the nearest sibling’s birth weight is 6.4 lbs? (5 points)
Question 40: Which of the seven regression models is the preferred model, and why? This is not an “opinion” answer; please reference your data to validate your answer. (10 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
20.4
61
60
7.4
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
21.3
62
71
7.1
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
21.4
63
71
6.2
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
24.1
66
73
6.6
24
24.1
66
72
7.1
25
22.8
63
68
7.1
Explanation / Answer
Result:
Multiple questions: First question answered.
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?
R square = 0.722.
72.2% of variation in dependent variable is explained by the 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?
The model is significant, F=2858, P=0.000 which is < 0.05 level.
Question 18: What is the Critical Value of F associated with this regression model?
Critical F(2,22) =3.44
Question 19: What is the regression equation for the model?
Y=-15.4259+0.3896*X1+0.1888*X2
Question 20: Are both independent variables in this model significant? How do you know?
Both independent variables in this model are significant.
For Mother height, t=2.868, P=0.0089 which is < 0.05 level.
For father height, t=4.142 P=0.0004 which is < 0.05 level.
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?
predicted birth length,
y=-15.4259+0.3896*59.6+0.1888*75.1
=21.97
Regression Analysis
R²
0.722
Adjusted R²
0.697
n
25
R
0.850
k
2
Std. Error
0.956
Dep. Var.
Birth Length (in) of Newborn Infants
ANOVA table
Source
SS
df
MS
F
p-value
Regression
52.2776
2
26.1388
28.58
7.64E-07
Residual
20.1200
22
0.9145
Total
72.3976
24
Regression output
confidence interval
variables
coefficients
std. error
t (df=22)
p-value
95% lower
95% upper
Intercept
-15.4259
7.2531
-2.127
.0449
-30.4679
-0.3839
Height of Mother (in)
0.3896
0.1358
2.868
.0089
0.1079
0.6713
Height of Father (in)
0.1888
0.0456
4.142
.0004
0.0943
0.2833
Predicted values for: Birth Length (in) of Newborn Infants
95% Confidence Interval
95% Prediction Interval
Height of Mother (in)
Height of Father (in)
Predicted
lower
upper
lower
upper
Leverage
59.6
75.1
21.9738
20.6052
23.3425
19.5642
24.3835
0.476
Regression Analysis
R²
0.722
Adjusted R²
0.697
n
25
R
0.850
k
2
Std. Error
0.956
Dep. Var.
Birth Length (in) of Newborn Infants
ANOVA table
Source
SS
df
MS
F
p-value
Regression
52.2776
2
26.1388
28.58
7.64E-07
Residual
20.1200
22
0.9145
Total
72.3976
24
Regression output
confidence interval
variables
coefficients
std. error
t (df=22)
p-value
95% lower
95% upper
Intercept
-15.4259
7.2531
-2.127
.0449
-30.4679
-0.3839
Height of Mother (in)
0.3896
0.1358
2.868
.0089
0.1079
0.6713
Height of Father (in)
0.1888
0.0456
4.142
.0004
0.0943
0.2833
Predicted values for: Birth Length (in) of Newborn Infants
95% Confidence Interval
95% Prediction Interval
Height of Mother (in)
Height of Father (in)
Predicted
lower
upper
lower
upper
Leverage
59.6
75.1
21.9738
20.6052
23.3425
19.5642
24.3835
0.476
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