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

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

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

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

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

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

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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Expert Solution

orchestra answered 2 years ago

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