Correlation Between Coffee And Cholesterol Study From A Col

Correlation Between Coffee And Cholesterola Study From A Colombian

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) and cholesterol level (mg/dL). Evaluate the claim that the caffeine from this new plant reduces cholesterol by plotting caffeine levels (x) versus the cholesterol levels (y). 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? Is there a statistically significant correlation between caffeine intake and cholesterol levels in this case? Click on the link below for help with how to do a Simple Regression and r value test in StatCrunch.

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The investigation into the relationship between caffeine intake from a new Colombian coffee plant and cholesterol levels necessitates a comprehensive statistical analysis, primarily focusing on the correlation between these two variables. Based on the available data, plotting caffeine levels against cholesterol levels reveals the nature and strength of their relationship. The primary statistical measure for this is the correlation coefficient, denoted as r, which quantifies the degree to which the two variables move in tandem.

In this pilot study, caffeine intake (measured in milligrams) represents the independent variable (x), while cholesterol levels (in mg/dL) are the dependent variable (y). Plotting these data points on a scatterplot provides a visual indication of any linear association. If the points tend to slope downward, this suggests a negative correlation, implying higher caffeine intake might be associated with lower cholesterol levels - which supports the hypothesis that the new coffee plant could reduce cholesterol.

The correlation coefficient r ranges between -1 and 1. An r close to -1 indicates a strong negative correlation. Conversely, an r near 0 indicates no linear relationship, and an r close to 1 suggests a strong positive correlation. In this case, suppose the computed r value is -0.85; this would indicate a substantial negative linear association between caffeine intake and cholesterol levels, implying that as caffeine increases, cholesterol tends to decrease.

The coefficient of determination, denoted R², is the square of the correlation coefficient r. It represents the proportion of the variance in the dependent variable (cholesterol levels) that can be explained by the independent variable (caffeine intake). For an r of -0.85, R² would be approximately 0.7225, meaning about 72.25% of the variation in cholesterol levels is accounted for by caffeine consumption. This indicates a strong explanatory power of caffeine intake with respect to cholesterol variation in this dataset.

To assess whether this observed correlation is statistically significant, hypothesis testing is employed. Specifically, a t-test for the correlation coefficient determines if the relationship observed is unlikely to be due to random chance. Typically, setting a significance level (α) of 0.05, a p-value less than 0.05 indicates a statistically significant correlation. If the test yields a p-value of 0.01, for example, one can conclude that the correlation between caffeine intake and cholesterol levels is statistically significant, lending support to the claim that caffeine from this coffee plant might influence cholesterol reduction.

It is important to recognize that correlation does not imply causation. While a strong, statistically significant negative correlation suggests an association, it does not prove that increased caffeine intake directly causes cholesterol reduction. Other factors, experimental controls, and further studies are necessary to establish a causal relationship definitively.

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