Medical researchers conducted a study designed to evaluate the relationship between blood pressure (y), age (x1), and cholesterol (x2). They proposed a linear model. A total of 126 individuals were randomly sampled, and blood pressure, age, and cholesterol were recorded for each. The regression summary appears here:
The regression equation is
Blood Pressure = 45.5 + 1.03 Age + 0.032 Cholesterol
Predictor Coef SE Coef T P
Constant 45.54 50.73 0.90 0.371
Age 1.02866 0.03920 26.24 0.000
Cholesterol 0.0323 0.4071 0.08 0.937
S = 5.30434 R-Sq = 85.0% R-Sq(adj) = 84.7%
Analysis of Variance
Source DF SS MS F P
Regression 2 19600.5 9800.2 348.32 0.000
Residual Error 123 3460.7 28.1
Total 125 23061.2
Predicted Values for New Observations
New
Obs Fit SE Fit 95% CI 95% PI
1 75.301 0.741 (73.833, 76.769) (64.699, 85.903)
2 75.624 4.219 (67.273, 83.975). (62.209, 89.040)XX
3 74.272 0.772 (72.744, 75.800) (63.662, 84.882)
XX denotes a point that is an extreme outlier in the predictors.
Values of Predictors for New Observations
New
Obs Age Cholesterol
1 25.0 25
2 25.0 135
3 24.0 125
What is a 95% confidence interval on the mean blood pressure for all 25-year-olds with a cholesterol level of 135?
◦
(73.833, 76.769)
◦
(67.273, 83.975)
◦
(72.744, 75.800)
◦
(62.209, 89.040)
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