What is the correlation coefficient r and what does it mean in this case? What is the coefficient of determination and what does it mean in this case?

Week Four, Discussion One

Q1 Correlation between coffee and cholesterol

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:

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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).

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

 

 

 

Week Four, Discussion Two

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:

  1. a) What is the intercept? (or –what would be your cholesterol level while ingesting no caffeine?)
    b) What is the slope? (or, what is what we callbin the linear regression equation?)
    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)?

 

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