Question

In: Statistics and Probability

A researcher wants to test if women’s glucose level is associated with age, number of pregnancies...

  1. A researcher wants to test if women’s glucose level is associated with age, number of pregnancies and BMI. The response variable is the plasma glucose concentration at 2 hours in an oral glucose (mg/dL) tolerance test, and the explanatory variables are:   Age: years, Pregnant: number of pregnancies, Obesity: Yes vs. No

The researcher fitted a linear model and the results are listed below:

Source

Degrees of Freedom

Sum of Squares

Mean Squares

F value

Pr > F

Model

60000

< .0001

Error

400

120000

Parameter

Estimate

Standard Error

t Value

Pr > ½t½

Intercept

85.36

4.099

20.82

<.0001

Age

0.726

0.111

6.55

<.0001

Pregnancy

-0.35

0.387

-0.78

0.4330

Obese Yes vs. No

17.38

3.133

5.55

<.0001

  1. Calculate R2 and interpret the R2. Is R2 a good model fitting statistic for multiple linear regression? Why or why not?

  1. Is the overall model significant? Answer this question with the statistical evidence.

  1. Interpret the regression coefficients and the significance of each referring to the statistical evidence.

  1. What are the linear model assumptions and how to test or examine if the model assumptions hold?

  1. Identify outliers, high leverage or influential data point based on below model diagnostic statistics:

Studentized Residual

Hat value (mean Hat: 0.0075)

Cook’s D

1

-0.65

0.001

0.00011

2

-3.5

0.008

0.0015

3

2.4

0.03

0.025

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