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 | -15.0062 | 37.9327 | -0.3956 | 0.6942 |

gestation | 0.4798 | 0.1365 | 3.5162 | 0.001 |

--- |

Residual standard error: 15.1696 on 48 degrees of freedom |

Multiple R-squared: 0.2048, Adjusted R-squared: 0.1883 |

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 224 days?

3. The recorded birth weight for a baby with a gestation of 224 days was 92 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. ( , )

Answer #1

1)

Birth weight =-15.0062+0.4798*Gestation |

2)

predicted value =-15.0062+0.4798**224= | 92.4690 |

3)

residual =actual-predicted =92-92.4690 = | -0.4690 |

4)

20.48% of the variation,,,,,in birth weight rate can........to Gestation |

3) | ||||

test statistic = | 3.5162 | |||

4) | ||||

degree of freedom =(n-2)=48 | ||||

5) | ||||

p value = | 0.001 | |||

6) | ||||

there is a very strong evidence,,,,,,,, |

7)

degree of freedom =n-p-1= | 48 | |||||

estimated slope b= | 0.479800 | |||||

standard
error of slope=s_{b}= |
0.136500 | |||||

for 95 % confidence and 48df critical t= | 2.0106 | |||||

95% confidence interval =b1 -/+ t*standard error= |
(0.2053,0.7543) |

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...

A study conducted at Baystate Medical Center in Springfield,
Massachusetts, identified factors that affect the risk of giving
birth to a low-birth-weight baby. Low birth weight is defined as
weighing fewer than 2,500 grams (5 pounds, 8 ounces) at birth.
Low-birth-weight babies have increased risk of health problems,
disability, and death. [Source: Hosmer, D., & Lemeshow, S.
(2000). Applied logistic regression (2nd ed.). Hoboken, NJ: Wiley.]
Suppose that you conduct a similar study focusing on the age,
prepregnancy weight, and...

(1 point) College Graduation
Rates. Data from the College Results Online
website compared the 2011 graduation rate and school size for 92
similar-sized public universities and colleges in the United
States. Statistical software was used to create the linear
regression model using size as the explanatory variable and
graduation rate as the response variable. Summary output from the
software and the scatter plot are shown below. Round all calculated
results to four decimal places.
Coefficients
Estimate
Std. Error
t value
Pr(>|t|)...

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