Question

A random sample of 200 women who were at least 21 years old, of Pima Indian heritage and living near Phoenix, Arizona, were tested for diabetes according to World Health Organization criteria. The model below is used for predicting their plasma glucose concentration based on their diastolic blood pressure (in mmHg), age (in years), and whether or not they are diabetic. Which of the following statements is false?

	Estimate	Std. Err.	t	P(t > |t|)
intercept	76.00	12.24	6.2	3e-09
bloodpressure	0.35	0.18	1.9	0.05
age	0.43	0.20	2.1	0.04
diabetes_Yes	26.57	4.37	6.1	6e-09

Residual standard error: 27 on 196 degrees of freedom

Multiple R-squared: 0.28, Adjusted R-squared: 0.27

F-statistic: 25 on 3 and 196 DF, p-value: 1e-13

• The model as a whole is significant, even though one of the variables (blood pressure) may not be.
• The predicted difference in blood glucose levels of two 25 year old females who don't have diabetes one of whom has a blood pressure of 70mmHg and the other 75 mmHG is 0.35 * 5 = 1.75.
• The model predicts that women without diabetes have blood glucose levels that are on average 26.57 higher than those who have diabetes, given that they are similar in terms of their blood pressure and age.
• The model explains 28% of variability in blood glucose levels of these women.

Answer 1

• The model as a whole is significant, even though one of the variables (blood pressure) may not be.

  this statement is correct because p value of blood pressure is 0.05

• The predicted difference in blood glucose levels of two 25 year old females who don't have diabetes one of whom has a blood pressure of 70mmHg and the other 75 mmHG is 0.35 * 5 = 1.75.

  this is true because predicted value when bp is 75 is 139.57 - predicted value when bp is 70is 137.82 = 1.75

• The model predicts that women without diabetes have blood glucose levels that are on average 26.57 higher than those who have diabetes, given that they are similar in terms of their blood pressure and age.

  this is false statement

• The model explains 28% of the variability in blood glucose levels of these women. this statement is correct because of Multiple R-squared: 0.28