Q2 Regression- What is the predicted cholesterol level?
Given the data presented in Discussion Question 1 for this week, determine the cholesterol level of someone who drank two and a half cups of coffee a day. To get the answer, plot a regression line in StatCrunch and post your answers from StatCrunch for the following:
a) What is the intercept? (or –what would be your cholesterol level while ingesting no caffeine?)
The intercept is 665.71429
b) What is the slope? (or, what is what we call b in the linear regression equation?)
The slope is -0.69892857
c) What is the cholesterol level of someone who drank two and a half cups of coffee a day (given that 1 cup of coffee equals 100 mg of caffeine)?
The cholesterol level of someone who drank two and a half cups of coffee a day would be 490.98 mg/dL.
Simple linear regression results:
Dependent Variable: Cholesterol level (mg/dL)
Independent Variable: caffeine (mg)
Cholesterol level (mg/dL) = 665.71429 - 0.69892857 caffeine (mg)
Sample size: 7
R (correlation coefficient) = -0.72796194
R-sq = 0.52992859
Estimate of error standard deviation: 155.77582
Parameter estimates:
Parameter |
Estimate |
Std. Err. |
Alternative |
DF |
T-Stat |
P-value |
Intercept |
665.71429 |
131.6546 |
≠ 0 |
5 |
5.0565213 |
0.0039 |
Slope |
-0.69892857 |
0.29438863 |
≠ 0 |
5 |
-2.3741697 |
0.0636 |
Analysis of variance table for regression model:
Source |
DF |
SS |
MS |
F-stat |
P-value |
Model |
1 |
136780.32 |
136780.32 |
5.6366817 |
0.0636 |
Error |
5 |
121330.54 |
24266.107 |
||
Total |
6 |
258110.86 |
Predicted values:
X value |
Pred. Y |
s.e.(Pred. y) |
95% C.I. for mean |
95% P.I. for new |
250 |
490.98214 |
73.597159 |
(301.79463, 680.16965) |
(48.105541, 933.85874) |
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