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	-106.8033	43.8363	-2.4364	0.0186
gestation	0.8157	0.1584	5.1505	0

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Residual standard error: 15.8922 on 48 degrees of freedom

Multiple R-squared: 0.3559, Adjusted R-squared: 0.3425

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 278 days?

3. The recorded birth weight for a baby with a gestation of 278 days was 115 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. (  ,   )

**I need help with finding 3 and 7**

Answer 1

Result:

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	-106.8033	43.8363	-2.4364	0.0186
gestation	0.8157	0.1584	5.1505	0

---

Residual standard error: 15.8922 on 48 degrees of freedom

Multiple R-squared: 0.3559, Adjusted R-squared: 0.3425

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

Birth weight = -106.8033 + 0.8157 * gestation

2. Using the estimated regression equation, what is the predicted birth weight for a baby with a length of gestation of 278 days?

predicted Birth weight = -106.8033+0.8157*278

= 119.9613

3. The recorded birth weight for a baby with a gestation of 278 days was 115 ounces. Complete the following sentence:

Residual = 115-119.9613

= -4.9613

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:

35.59% of the variation in   Birth weight Babies Pregnancy  can be explained by the linear relationship to 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 = 5.1505

4. Degrees of freedom = 48

5. P-value = 0.0000

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

7. Calculate a 95% confidence interval for the slope, ?1. ( 0.4972 ,1.1342   )

Confidence interval for slope : β1 ± t*se

Critical t value with 48 df at 0.05 level =2.0106

Lower limit = 0.8157-2.0106*0.1584 =0.4972

upper limit = 0.8157+2.0106*0.1584 =1.1342