8.1 Baby weights, Part I. The Child Health and Development Studies investigate a

Question

8.1 Baby weights, Part I. The Child Health and Development Studies investigate a range of
topics. One study considered all pregnancies between 1960 and 1967 among women in the Kaiser
Foundation Health Plan in the San Francisco East Bay area. Here, we study the relationship
between smoking and weight of the baby. The variable smoke is coded 1 if the mother is a
smoker, and 0 if not. The summary table below shows the results of a linear regression model for
predicting the average birth weight of babies, measured in ounces, based on the smoking status of
the mother.

The variability within the smokers and non-smokers are about equal and the distributions are
symmetric. With these conditions satisfied, it is reasonable to apply the model. (Note that we
don't need to check linearity since the predictor has only two levels.)

(a) Write the equation of the regression line.
(b) Interpret the slope in this context, and calculate the predicted birth weight of babies born to
smoker and non-smoker mothers.
(c) Is there a statistically significant relationship between the average birth weight and smoking?

Estimate Std. Error t value Pr(>|t|) (Intercept) 123.05 0.65 189.60 0.0000 smoke -8.94 1.03 -8.65 0.0000

Explanation / Answer

A)

The regression is given by:

Average Birth weight = Estimate(intercept) + estimate(slope) * Smoke = 123.05 - 8.94 * Smoke

B) Predicted Average birth weight for smoker mother ( for them Smoke=1) = 123.05 - 8.94 *1 = 114.11 ounces

Predicted Average birth weight for non-smoker mother ( for them Smoke=1) = 123.05 - 8.94 *0 = 123.05 ounces

Interpretation of slope :

So the difference in the predicted average birth weight of babies for smoker mother and non-smoker mother = 114.11 - 123.05 = -8.94 = estimate of smoke. So it signifies the difference in weight of baby between smoker mothe rand non-smoker mother.

C) As the p-value for estimate of smoke (slope of the regreesion line) is 0.0000 which is much less than 0.05 = alpha. So we can conclude that the slope of the regression line is significant. So there is staiistically significant relationship between birth weight of baby and smoking

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