Question

Birth weight and gestational age. The Child Health and Development Studies considered pregnancies among women in the San Francisco East Bay area. Researchers took a random sample of 50 pregnancies and used statistical software to construct a linear regression model to predict a baby's birth weight in ounces using the gestation age (the number of days the mother was pregnant). A portion of the computer output and the scatter plot is shown below. Round all calculated results to four decimal places.

Coefficients	Estimate	Std. Error	t value	Pr(>|t|)
Intercept	-41.8889	40.2659	-1.0403	0.3034
gestation	0.5876	0.1456	4.0345	0.0002

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Residual standard error: 15.5902 on 48 degrees of freedom

Multiple R-squared: 0.2532, Adjusted R-squared: 0.2377

1. Use the computer output to write the estimated regression equation for predicting birth weight from length of gestation.

Birth weight =  +  * gestation

2. Using the estimated regression equation, what is the predicted birth weight for a baby with a length of gestation of 284 days?

3. The recorded birth weight for a baby with a gestation of 284 days was 135 ounces. Complete the following sentence:

The residual for this baby is  . This means the birth weight for this baby is  ? higher than the same as lower than  the birth weight predicted by the regression model.

4. Complete the following sentence:

% of the variation in  ? Birth weight Gestation age Babies Pregnancy  can be explained by the linear relationship to  ? Birth weight Gestation age Babies Pregnancy .

Do the data provide evidence that gestational age is associated with birth weight? Conduct a t-test using the information given in the 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, there is  ? little evidence some evidence strong evidence very strong evidence extremely strong evidence  of a linear relationship between the explanatory and response variables.

7. Calculate a 99% confidence interval for the slope, ?1β1. (  ,  )

Answer 1

1)

Birth weight =-41.8889+0.5876*Gestation

2)

predicted value =-41.8889+0.5876**284=

124.9895

3)

residual =actual-predicted =118-114.79 =

10.0105

4)

25.32% of the variation,,,,,in birth weight rate can........to Gestation

3)
test statistic =		4.0345
4)
degree of freedom =(n-2)=48
5)
p value =	0.0002
6)
there is a extremely strong evidence,,,,,,,,

7)

degree of freedom =n-p-1=				48
estimated slope b=				0.5876
standard error of slope=sb=				0.1456
for 99 % confidence and 48df critical t=				2.6822
99% confidence interval =b1 -/+ t*standard error=					(0.1971,0.9781)