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

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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 =  +  * 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.(  ,  )