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= | 124.9895 |
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) |
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