Question

# Birth weight and gestational age. The Child Health and Development Studies considered pregnancies among women in...

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
 --- 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. (  ,  )

1)

 Birth weight =-41.8889+0.5876*Gestation

2)

 predicted value =-41.8889+0.5876**284= 124.99

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)