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	-15.0062	37.9327	-0.3956	0.6942
gestation	0.4798	0.1365	3.5162	0.001

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Residual standard error: 15.1696 on 48 degrees of freedom

Multiple R-squared: 0.2048, Adjusted R-squared: 0.1883

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 224 days?

3. The recorded birth weight for a baby with a gestation of 224 days was 92 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 95% confidence interval for the slope, ?1β1. (  ,  )

Answer 1

1)

Birth weight =-15.0062+0.4798*Gestation

2)

predicted value =-15.0062+0.4798**224=

92.4690

3)

residual =actual-predicted =92-92.4690 =

-0.4690

4)

20.48% of the variation,,,,,in birth weight rate can........to Gestation

3)
test statistic =		3.5162
4)
degree of freedom =(n-2)=48
5)
p value =	0.001
6)
there is a very strong evidence,,,,,,,,

7)

degree of freedom =n-p-1=				48
estimated slope b=				0.479800
standard error of slope=sb=				0.136500
for 95 % confidence and 48df critical t=				2.0106
95% confidence interval =b1 -/+ t*standard error=					(0.2053,0.7543)