Regression Models

Answer in word format. Question 1-40

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: 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? (5 points)

Question 2: Is the statistical significance of the model as a whole acceptable for a 95% level of confidence? How do you know? (5 points)

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? (5 points)

Question 4: What is the regression equation for the model? (5 points)

Question 5: What is the predicted birth length of a newborn whose father is 75.3 inches tall? (5 points)

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? (5 points)

Question 7: Is the statistical significance of the model as a whole acceptable for a 95% level of confidence? How do you know? (5 points)

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? (5 points)

Question 10: What is the predicted birth length of a newborn whose mother is 61.5 inches tall? (5 points)

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? (5 points)

Question 12: Is the statistical significance of the model as a whole acceptable for a 95% level of confidence? How do you know? (5 points)

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? (5 points)

Question 14: What is the regression equation for the model? (5 points)

Question 15: What is the predicted birth length of a newborn whose nearest sibling weighs 7.0 lbs.? (5 points)

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)

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? (5 points)

Question 23: Is the statistical significance of the model as a whole acceptable for a 95% level of confidence? How do you know? (5 points)

Question 24: What is the value of F associated with this regression model? (5 points)

Question 25: What is the regression equation for the model? (5 points)

Question 26: Are both independent variables in this model significant? How do you know? (5 points)

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? (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 all three 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)

The following table may help you organize your answers.

Scenario	r	r2	Adj. r2	Sig. F	p-value	p-value	p-value
1
2
3
4
5
6
7