We will examine the correlation between Sugar content and Caloric value in a variety of popular cereals. All measurements for the data are per serving.

Above is a scatter-plot of data describing two nutritional characteristics of many popular cereals: Sugar (grams) and Calories per serving. The two metrics are related with an estimated Pearson correlation of \(0.5154008\).

This correlation value carries a p-value of \({0.0012959}\), indicating that the correlation between Calories and Sugar content is statistically significant. Moreover, the \(95\)% confidence interval for this correlation is \((0.2249563, 0.721728)\), indicating a 95% confidence that the true correlation lies between these lower and upper bounds.

Once again, above is another plot of the data; this time, a Bayesian correlation analysis plot. The Bayesian correlation test yielded that the likelihood of a positive correlation between Sugar and Calories is greater than \(0\) with a \(99.8\)% chance. This agrees with the P-value of the Pearson correlation calculation above, although the Pearson test was slightly more confident in the positive correlation.

Likewise, the confidence \(95\)% intervals of the Pearson and Bayesian correlation tests were similar, being \((0.2249563, 0.721728)\) and \((0.20, 0.72)\) respectively. The Bayesian confidence interval is slightly wider, but not appreciably so.