Baby weights, Part III. We considered the variables smoke and parity, one at a time, in modeling birth weights of babies in Exercises 9.1 and 9.2. A more realistic approach to modeling infant weights is to consider all possibly related variables at once. Other variables of interest include length of pregnancy in days (gestation), mother’s age in years (age), mother’s height in inches (height), and mother’s pregnancy weight in pounds (weight). Below are three observations from this data set.
| bwt | gestation | parity | age | height | weight | smoke | |
| 1 | 120 | 284 | 0 | 27 | 62 | 100 | 0 |
| 2 | 113 | 282 | 0 | 33 | 64 | 135 | 0 |
| 1236 | 117 | 297 | 0 | 38 | 65 | 129 | 0 |
The summary table below shows the results of a regression model for predicting the average birth weight of babies based on all of the variables included in the data set.
| Estimate | Std. Error | t value | Pr(t) | |
| (Intercept) | -80.41 | 14.35 | -5.60 | 0.0000 |
| gestation | 0.44 | 0.03 | 15.26 | 0.0000 |
| parity | -3.33 | 1.13 | -2.95 | 0.0033 |
| age | -0.01 | 0.09 | -0.10 | 0.9170 |
| height | 1.15 | 0.21 | 5.63 | 0.0000 |
| weight | 0.05 | 0.03 | 1.99 | 0.0471 |
| smoke | -8.40 | 0.95 | -8.81 | 0.0000 |
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Write the equation of the regression model that includes all of the variables.
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Interpret the slopes of
gestationandagein this context. -
The coefficient for
parityis different than in the linear model shown in Exercise 9.2. Why might there be a difference? -
Calculate the residual for the first observation in the data set.
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The variance of the residuals is 249.28, and the variance of the birth weights of all babies in the data set is 332.57. Calculate the and the adjusted . Note that there are 1,236 observations in the data set.