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	-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 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 283 days?

3. The recorded birth weight for a baby with a gestation of 283 days was 125 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 90% confidence interval for the slope, ?1β1. (  ,  )

Answer 1

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

Birth weight = -68.5476 + 0.6716 * gestation

2. \the predicted birth weight for a baby with a length of gestation of 283 days is

Birth weight = -68.5476 + 0.6716 *283 =121.5152

3. The recorded birth weight for a baby with a gestation of 283 days was 125 ounces.

The residual for this baby is 125 -121.5152 =3.4848 . This means the birth weight for this baby is lower than  the birth weight predicted by the regression model.

4.

34.03 % of the variation in  Birth weight can be explained by the linear relationship to Gestation

?0:%�1=0H0:β1=0 vs. ??:?1≠0HA:β1≠0

3. Test statistic =4.9762

4. Degrees of freedom =48

5. P-value =0

6. Based on the results of this hypothesis test, there is very strong evidence of a linear relationship between the explanatory and response variables.

7. Calculate a 90% confidence interval for the slope, ?1

t at 90% with 48 df = 1.677

lower limit = 0.676-1.677*0.135=0.4496

upper limit = 0.676+1.677*0.135=0.9024