Birth weight and gestational age. The ChildHealth and Development Studies considered pregnancies among womenin the San Francisco East Bay area. Researchers took a randomsample of 50 pregnancies and used statistical software to constructa linear regression model to predict a baby's birth weight inounces using the gestation age (the number of days the mother waspregnant). A portion of the computer output and the scatter plot isshown below. Round all calculated results to four decimalplaces.
| Coefficients | Estimate | Std. Error | t value | Pr(>|t|) |
| Intercept | -68.5476 | 37.1411 | -1.8456 | 0.0711 |
| gestation | 0.6716 | 0.135 | 4.9762 | 0 |
| --- |
| Residual standard error: 16.6653 on 48 degrees of freedom |
| Multiple R-squared: 0.3403, Adjusted R-squared: 0.3266 |
1. Use the computer output to write the estimated regressionequation for predicting birth weight from length of gestation.
Birth weight =Ă‚Â Ă‚Â +Ă‚Â Ă‚Â * gestation
2. Using the estimated regression equation, what is thepredicted birth weight for a baby with a length of gestation of 283days?
3. The recorded birth weight for a baby with a gestation of 283days was 125 ounces. Complete the following sentence:
The residual for this baby is  . This means the birthweight for this baby is  ? higher than the same as lowerthan  the birth weight predicted by the regressionmodel.
4. Complete the following sentence:
% of the variation in  ? Birth weight Gestation ageBabies Pregnancy  can be explained by the linearrelationship to  ? Birth weight Gestation age BabiesPregnancy .
Do the data provide evidence that gestational age is associatedwith birth weight? Conduct a t-test using the information given inthe R output and the hypotheses
?0:?1=0H0:β1=0 vs. ??:?1≠0HA:β1≠0
3. Test statistic =
4. Degrees of freedom =
5. P-value =
6. Based on the results of this hypothesis test, thereis  ? little evidence some evidence strong evidence verystrong evidence extremely strong evidence  of a linearrelationship between the explanatory and response variables.
7. Calculate a 90% confidence interval for the slope, ?1β1.(  ,  )
