Correlation Between Coffee And Cholesterol

Correlation Between Coffee And Cholesterol

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?

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:

  • 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 call b in 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)?

Paper For Above instruction

The investigation into the potential impact of a novel coffee plant on human cholesterol levels involves analyzing the relationship between caffeine intake and cholesterol concentration in the blood. Through plotting caffeine consumption against cholesterol levels and performing linear regression analysis, the study seeks to determine whether increased caffeine intake correlates with decreased cholesterol levels, and if this correlation is statistically significant. The core statistical tools employed include the correlation coefficient (r), coefficient of determination (r²), and the regression equation's parameters (intercept and slope). These analyses not only explore the nature of the relationship but also facilitate predictions about cholesterol levels based on caffeine consumption, specifically for individuals consuming approximately 250 mg of caffeine daily, equivalent to 2.5 cups of coffee.

The correlation coefficient (r) measures the strength and direction of the linear relationship between caffeine intake and cholesterol levels. A value of r close to -1 would suggest a strong negative correlation, implying that higher caffeine consumption might be associated with lower cholesterol. Conversely, an r close to 0 would indicate no linear relationship. The coefficient of determination (r²) indicates the proportion of variance in cholesterol levels that can be explained by caffeine intake. For example, an r² of 0.25 would mean that 25% of the variability in cholesterol levels is accounted for by differences in caffeine consumption, with the remaining variability attributable to other factors.

Assessing statistical significance involves hypothesis testing to determine whether the observed correlation is unlikely to have occurred by chance. Typically, a p-value less than 0.05 signifies a statistically significant relationship, suggesting that the correlation observed in the sample reflects a true association in the population.

In the context of the regression analysis, the intercept represents the predicted cholesterol level when caffeine intake is zero, essentially the baseline cholesterol level without caffeine consumption. The slope indicates how much the cholesterol level is expected to change with each additional unit of caffeine consumed, measured here in milligrams. Based on the regression equation, the cholesterol level for someone consuming 250 mg of caffeine (2.5 cups of coffee, given 100 mg per cup) can be predicted by substituting x = 250 into the equation.

Specifically, if the regression equation is written as: y = a + bx, where y is cholesterol level and x is caffeine intake, then the predicted cholesterol level for 250 mg caffeine would be y = a + b*250. This prediction provides valuable insight into how caffeine consumption from the new coffee plant might influence cholesterol levels, aiding in understanding its potential health benefits or risks.

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