# Correlation Coefficient

A study from a Colombian research center is about to publish a pilot study regarding a new coffee plant that they believe can reduce total cholesterol in humans. They gave increasing doses (cups of coffee) to a test patient over several weeks and recorded the following data:

caffeine (mg)     Cholesterol level (mg/dL)
100     684
200     547
300     200
400     399
500     415
600     400
700     58

Evaluate the claim that the caffeine from this new plant reduces cholesterol by plotting caffeine levels (x) versus the cholesterol levels (y) in StatCrunch (copy and paste your graph and attach as a Word doc).

a.    What is the correlation coefficient r and what does it mean in this case?
b.    What is the coefficient of determination and what does it mean in this case?
c.    Is there a statistically significant correlation between caffeine intake and cholesterol levels in this case?

d) What is the intercept? (or -what would be your cholesterol level while ingesting no caffeine?)
e) What is the slope? (or, what is what we call b in the linear regression equation?)
f) How many cups of coffee must you drink to lower your total cholesterol to 150 mg/dL (given that 1 cup of coffee equals 100 mg of caffeine)?

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