Question

(14 points) 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	9.0539	38.9964	0.2322	0.8174
gestation	0.4005	0.1408	2.8441	0.0065

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Residual standard error: 15.824 on 48 degrees of freedom

Multiple R-squared: 0.1442, Adjusted R-squared: 0.1264

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 288 days?

3. The recorded birth weight for a baby with a gestation of 288 days was 117 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 =9.0539+0.4005*Gestation

2)

predicted value =9.0539+0.4005**288=

124.3979

3)

residual =actual-predicted =118-114.79 =

-7.3979

4)

14.42% of the variation,,,,,in birth weight rate can........to Gestation

3)
test statistic =		2.8441
4)
degree of freedom =(n-2)=48
5)
p value =	0.0065
6)
there is a very evidence,,,,,,,,

7)

degree of freedom =n-p-1=				48
estimated slope b=				0.400500
standard error of slope=sb=				0.140800
for 99 % confidence and 48df critical t=				2.6822
99% confidence interval =b1 -/+ t*standard error=					(0.0228,0.7782)