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?
Rsquare 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
Rsq = 0.52992859
Estimate of error standard deviation: 155.77582
Parameter estimates:
Parameter 
Estimate 
Std. Err. 
Alternative 
DF 
TStat 
Pvalue 
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 
Fstat 
Pvalue 
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?
Rsquare 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 Pvalue=0.0636 is greater than the table value 0.05. Besides, our correlation coefficient value also support this as our absolute value of Rvalue= 0.72796194=  0.72796194 is less than the table value 0.754 at df=5.
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