Instructions for Assignment: Use Excel to construct a spreadsheet for each of the four models (Scenarios), and answer each set of questions for each scenario, then answer
The following table may help you organize your answers.
|
Scenario
|
r
|
r2
|
Adj. r2
|
Sig. F
|
p-value
|
p-value
|
p-value
|
|
1
|
|
|
|
|
|
|
|
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2
|
|
|
|
|
|
|
|
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3
|
|
|
|
|
|
|
|
|
4
|
|
|
|
|
|
|
|
|
5
|
|
|
|
|
|
|
|
|
6
|
|
|
|
|
|
|
|
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7
|
|
|
|
|
|
|
|
|
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
|
22.0
|
58
|
62
|
6.4
|
|
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
|
20.5
|
61
|
70
|
6.0
|
|
10
|
22.1
|
65
|
72
|
6.1
|
|
11
|
20.3
|
63
|
71
|
6.0
|
|
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
|
23.5
|
63
|
72
|
6.3
|
|
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
|
21.2
|
60
|
70
|
6.2
|
|
24
|
24.1
|
66
|
72
|
7.1
|
|
25
|
22.8
|
63
|
68
|
7.1
|
Scenario 1: As a researcher studying how inherited traits influence newborn babies. You have gathered genetic data on newborns', parents and sibling as shown in the table above.
Scenario 1: Perform a simple linear regression analysis to predict a newborn's birth length (in inches) using the father's height as a predictor variable. Conduct your analysis using a 95% level of confidence.
Question 1: Does the regression model confirm a correlation between the dependent variable and the independent variable? How do you know?
Question 2: Is the statistical significance of the model as a whole acceptable for a 95% level of confidence? How do you know?
Question 3: Is the statistical significance of the linear relationship between the dependent and independent variable acceptable for a 95% level of confidence? How do you know?
Question 4: What is the regression equation for the model?
Question 5: What is the predicted birth length of a newborn whose father is 75.3 inches tall?
Scenario 2: Perform a simple linear regression analysis to predict a newborn's birth length (in inches) using the mother's height as a predictor variable. Conduct your analysis using a 95% level of confidence.
Question 6: Does the regression model confirm a correlation between the dependent variable and the independent variable? How do you know?
Question 7: Is the statistical significance of the model as a whole acceptable for a 95% level of confidence? How do you know?
Question 8: Is the statistical significance of the linear relationship between the dependent and independent variable acceptable for a 95% level of confidence? How do you know?
Question 9: What is the regression equation for the model?
Question 10: What is the predicted birth length of a newborn whose mother is 61.5 inches tall?
Scenario 3: Perform a simple linear regression analysis to predict a newborn's birth length (in inches) using the nearest (in age) sibling's birth weight as a predictor variable. Conduct your analysis using a 95% level of confidence.
Question 11: Does the regression model confirm a correlation between the dependent variable and the independent variable? How do you know?
Question 12: Is the statistical significance of the model as a whole acceptable for a 95% level of confidence? How do you know?
Question 13: Is the statistical significance of the linear relationship between the dependent and independent variable acceptable for a 95% level of confidence? How do you know? (
Question 14: What is the regression equation for the model?
Question 15: What is the predicted birth length of a newborn whose nearest sibling weighs 7.0 lbs.?
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? (5 points)
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?
Question 29: Is the statistical significance of the model as a whole acceptable for a 95% level of confidence? How do you know?
Question 30: What is the value of F associated with this regression model?
Question 31: What is the regression equation for the model?
Question 32: Are both of the independent variables in this model significant? How do you know?
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?
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?
Question 35: Is the statistical significance of the model as a whole acceptable for a 95% level of confidence? How do you know?
Question 36: What is the value of F associated with this regression model?
Question 37: What is the regression equation for the model?
Question 38: Are all three independent variables in this model significant? How do you know?
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?
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.