Correlation between coffee and cholesterol

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:

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?

Coefficient r value is -0.72796194 and it means there is faily strong negative relationship between caffeine(x) and cholesterol levels(y). In other words, as amount of caffeine increases the cholesterol level go down.

2. What is the coefficient of determination and what does it mean in this case?

R-square value is 0.52992859. It means nearly 53% (0.52992859 x 100=52.992859%≈ 53%) of variation we see in the cholesterol level can be explain by the H. The proportion of variance, r square value, or coefficient of determination tells us that the proportion of variance in the variable y are associated with variable x. Basically the proportion of variance is shared by two variables. Therefore, nearly 53% of the cholesterol level can be explained by caffeine intake.

Simple linear regression results:

Dependent Variable: Cholesterol level (mg/dL)

Independent Variable: Caffein (mg)

Cholesterol level (mg/dL) =665.71429 - 0.69892857 Caffein (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

 

 

 

3. What is the coefficient of determination and what does it mean in this case?

R-square value is 0.52992859. It means nearly 53% (0.52992859 x 100=52.992859%≈ 53%) of variation we see in the cholesterol level can be explain by the H. The proportion of variance, r square value, or coefficient of determination tells us that the proportion of variance in the variable y are associated with variable x. Basically the proportion of variance is shared by two variables. Therefore, nearly 53% of the cholesterol level can be explained by caffeine intake.

4. Is there a statistically significant correlation between caffeine intake and cholesterol levels in this case?

No, there is not a statistically significant correlation between caffeine intake and cholesterol levels in this case because our P-value=0.0636 is greater than the table value 0.05. Besides, our correlation coefficient value also support this as our absolute value of R-value= -0.72796194= | 0.72796194| is less than the table value 0.754 at df=5.

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