Birth Length (in) of Newborn Infants Height of Mother (in) Height of Father (in)
ID: 3134042 • 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
22.0
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
After you have submitted your answers in the Assignment #_ Submission Link, upload the Excel file (provided you by the Instructor) containing your answers and calculations into the Home Work #_ Supporting Documentation Submission link prior to the due date and time. As stated in the syllabus a score of zero will be awarded for the assignment if this Excel file is not submitted.
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 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?
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
Explanation / Answer
The regression output for the above data is as shown below -
So, we can answer the questions from this output as shown below -
-------------------------------------------------------------------
Q34)
As the R-square and adjusted R-suare value are greater than 0.75, so this indicates that there is correlation between the dependent and the independent variables.
--------------------------------------------------
Q35)
As the F-test gives us a very high value of the test statistics than the critical value of the test statistics, so we will reject the null hypothesis and conclude that the model is significant and hence acceptable.
----------------------------------------------------------------
Q36)
As it can be seen from the output, the value of calculated F-statistics = 26.85654831
---------------------------------------------------------
Q37)
The regression model can be written as -
Birth Length = -8.09 + 0.1687 (height of mother) + 0.11398 (Height of father) + 1.828 (Birth weight of nearest sibling)
---------------------------------------------------------------------
Q38)
No, all the variables are significant except the 'Height of mother' because it has a p-value greater than 0.05 while the others have a p-value less than the significance level. Hence, null hypothesis will be rejected in case of the other variables except 'height of mother'.
----------------------------------------
Q39)
Predicted Birth Length = -8.0927 + 0.1687 ( 58.5) + 0.11398 (71.6) + 1.828 (6.4)
So, predicted birth length = 21.6362 in.
SUMMARY OUTPUT Regression Statistics Multiple R 0.890643203 R Square 0.793245314 Adjusted R Square 0.763708931 Standard Error 0.82849377 Observations 25 ANOVA df SS MS F Significance F Regression 3 55.30315953 18.43438651 26.85654831 2.21E-07 Residual 21 14.41444047 0.686401927 Total 24 69.7176 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -8.092701664 5.423776126 -1.492078854 0.150549608 -19.37206159 3.186658258 Height of Mother (in) 0.16869344 0.105482861 1.599249763 0.124703191 -0.050670177 0.388057057 Height of Father (in) 0.113978443 0.044994695 2.533152928 0.019338832 0.020406853 0.207550034 Birth Weight of Nearest Sibling (lb) 1.828047167 0.427046985 4.280669878 0.000332095 0.939954344 2.71613999Related Questions
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