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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