Develop a regression model to help them to predict the birthweight of a baby bas
ID: 3253246 • Letter: D
Question
Develop a regression model to help them to predict the birthweight of a baby based on the variables in the data supplied. The model could then be used to predict birthweight to identify babies at risk in future.
By using the forward stepwise method, develop a multiple regression model to predict the birthweight.
Step 1: Gestation only
Step 2: Gestation and Smoke
Step 3: Gestation, Smoke and Pre-pregnancy Weight
Step 4: Gestation, Smoke, Pre-pregnancy Weight and Height
Step 5: Gestation, Smoke, Pre-pregnancy Weight, Height and Status
Step 6: Gestation, Smoke, Pre-pregnancy Weight, Height, Status and Age
a) Interpret the regression coefficients of all six (6) independent variables in the model obtained in Step 6, and comment on the statistical significance of each.
b) Use Excel to obtain the correlation matrix for the following variables: Gestation, Pre-pregnancy Weight, Height, Age and Birthweight. Do you think multi-collinearity is a problem in the regression model? Are the correlation coefficients consistent with the regression coefficients obtained in the model in Step 6? Discuss briefly.
c) Focusing on Steps 3 and 4, discuss fully how the introduction of Height in Step 4 affects the regression coefficient of Pre-pregnancy Weight.
d) Based on the results in (a) to (c), explain which independent variables should be included or excluded to formulate the final model. State the final model.
e) Comment on the overall adequacy of the final model.
f) Consider an indigenous mother who is a smoker, 20 years of age, and 160cm tall with a pre-pregnancy weight of 58kg and gestational age of 267 days. What is the expected weight of the child, using the finalmodel you have developed in (d)?
Dataset: https://www.dropbox.com/s/mb19h4ddhi7u3q2/Birthweights.xlsx?dl=0
,,hExplanation / Answer
Step1: The minitab output is
Regression Analysis: Birthweight (grams) versus Gestation (days)A1
The regression equation is
Birthweight (grams) = 185 + 12.1 Gestation (days)A1
Predictor Coef SE Coef T P
Constant 185.2 384.9 0.48 0.630
Gestation (days)A1 12.096 1.386 8.72 0.000
S = 523.330 R-Sq = 7.1% R-Sq(adj) = 7.0%
Step 2:
Regression Analysis: Birthweight (gra versus Gestation (days), Smoke
The regression equation is
Birthweight (grams) = 664 + 10.7 Gestation (days)A1 - 236 Smoke
Predictor Coef SE Coef T P
Constant 663.8 382.0 1.74 0.083
Gestation (days)A1 10.703 1.368 7.82 0.000
Smoke -235.80 33.48 -7.04 0.000
S = 511.037 R-Sq = 11.5% R-Sq(adj) = 11.3%
Step3:
Regression Analysis: Birthweight versus Gestation (d, Smoke, ...
The regression equation is
Birthweight (grams) = 418 + 10.3 Gestation (days)A1 - 230 Smoke
+ 6.04 Pre-pregnancy weight (kg)
Predictor Coef SE Coef T P
Constant 418.2 386.0 1.08 0.279
Gestation (days)A1 10.311 1.365 7.55 0.000
Smoke -230.16 33.33 -6.91 0.000
Pre-pregnancy weight (kg) 6.043 1.698 3.56 0.000
S = 508.073 R-Sq = 12.6% R-Sq(adj) = 12.3%
Step 4
Regression Analysis: Birthweight versus Gestation (d, Smoke, ...
The regression equation is
Birthweight (grams) = - 1573 + 10.2 Gestation (days)A1 - 237 Smoke
+ 2.05 Pre-pregnancy weight (kg) + 13.8 Height (cm)
Predictor Coef SE Coef T P
Constant -1573.1 545.2 -2.89 0.004
Gestation (days)A1 10.221 1.348 7.58 0.000
Smoke -236.73 32.94 -7.19 0.000
Pre-pregnancy weight (kg) 2.051 1.850 1.11 0.268
Height (cm) 13.841 2.709 5.11 0.000
S = 501.790 R-Sq = 14.8% R-Sq(adj) = 14.5%
Step 5
Regression Analysis: Birthweight versus Gestation (d, Smoke, ...
The regression equation is
Birthweight (grams) = - 1409 + 9.65 Gestation (days)A1 - 233 Smoke
+ 1.99 Pre-pregnancy weight (kg) + 13.9 Height (cm)
- 180 Status
Predictor Coef SE Coef T P
Constant -1409.1 548.0 -2.57 0.010
Gestation (days)A1 9.655 1.365 7.07 0.000
Smoke -233.13 32.89 -7.09 0.000
Pre-pregnancy weight (kg) 1.993 1.846 1.08 0.280
Height (cm) 13.865 2.702 5.13 0.000
Status -180.05 73.91 -2.44 0.015
S = 500.550 R-Sq = 15.3% R-Sq(adj) = 14.9%
Step 6
Regression Analysis: Birthweight versus Gestation (d, Smoke, ...
The regression equation is
Birthweight (grams) = - 1450 + 9.67 Gestation (days)A1 - 232 Smoke
+ 1.87 Pre-pregnancy weight (kg) + 13.9 Height (cm)
- 181 Status + 1.11 Age
Predictor Coef SE Coef T P
Constant -1449.7 557.6 -2.60 0.009
Gestation (days)A1 9.669 1.366 7.08 0.000
Smoke -232.42 32.96 -7.05 0.000
Pre-pregnancy weight (kg) 1.865 1.874 1.00 0.320
Height (cm) 13.949 2.712 5.14 0.000
Status -180.62 73.96 -2.44 0.015
Age 1.111 2.782 0.40 0.690
S = 500.762 R-Sq = 15.4% R-Sq(adj) = 14.8%
Interpretation : For Gestation (days)A1
The unit change in Gestation (days)A1 the change in mean of dependent variable (Birthweight (grams)) is same as coefficient of Gestation (days)A1 that is 9.669 when other variables are constants.
Interpretation : Smoke
The unit change in Smoke the change in mean of dependent variable (Birthweight (grams)) is same as coefficient of Smoke that is -232.42 when other variables are constants.
Interpretation : Pre-pregnancy weight (kg)
The unit change in Pre-pregnancy weight (kg) the change in mean of dependent variable (Birthweight (grams)) is same as coefficient of Pre-pregnancy weight (kg) that is 1.865 when other variables are constants.
Similarly interprete of other variables.
Singificance of variables:
P values of Pre-pregnancy weight (kg) and age are greater than 0.05
So that the variables Pre-pregnancy weight (kg) and age are not significance and we can exclude them from the model.
c) The regression equation for step 3 is
Birthweight (grams) = 418 + 10.3 Gestation (days)A1 - 230 Smoke + 6.04 Pre-pregnancy weight (kg)
The regression equation for step 4 is
Birthweight (grams) = - 1573 + 10.2 Gestation (days)A1 - 237 Smoke + 2.05 Pre-pregnancy weight (kg) + 13.8 Height (cm)
From the above twomodels coefficient of Pre-pregnancy weight reduces from 6.04 to 2.05 that is change in the coefficient is very large
Also the sign of intercept is changes from positive to negative.
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