Question

In: Statistics and Probability

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

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 51.7814 48.867 1.0596 0.2946
gestation 0.2428 0.1745 1.3911 0.1706
---
Residual standard error: 16.5836 on 48 degrees of freedom
Multiple R-squared: 0.0388, Adjusted R-squared: 0.0187

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 282 days?

3. The recorded birth weight for a baby with a gestation of 282 days was 128 ounces. Complete the following sentence:

The residual for this baby is _______. This means the birth weight for this baby is higher than  the birth weight predicted by the regression model.

4. Complete the following sentence:

3.88 % of the variation in Birth weight can be explained by the linear relationship to Gestation age.

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_____evidence of a linear relationship between the explanatory and response variables.

7. Calculate a 95% confidence interval for the slope, ?1β1. (  ,   )

***need help with #7 please***

Solutions

Expert Solution

1) birth weight=51.7814+0.2428*gestation  
2) birth weight=51.7814+0.2428*282=   120.251
3) residual = 128-120.251=   7.749
4)  
test stat=0.2428/0.1745=   1.3911
df = 48  
p value=0.1706  
6) not enough evidence  

7)

confidence interval for slope                      
                      
n =   50                  
alpha,α =    0.05                  
estimated slope=   0.2428                  
std error =    0.1745                  
                      
Df = n-2 =   48                  
t critical value =    2.0106   [excel function: =t.inv.2t(α,df) ]              
                      
margin of error ,E = t*std error =    2.0106   *   0.1745   =   0.35086  
                      
95%   confidence interval is ß1 ± E                   
lower bound = estimated slope - margin of error =    0.2428   -   0.3509   =   -0.1081  
upper bound = estimated slope + margin of error =    0.2428   +   0.3509   =   0.5937  


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