For a sample of eight bears researchers measured the distanc

For a sample of eight bears, researchers measured the distances around the bears\' chests and weighed the bears. Minitab was used to find that the value of the linear correlation coefficient is r=0.886.

Using =0.05, determine if there is a linear correlation between chest size and weight. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size? (Round to three decimal places as needed)

Solution

Since r=0.886

ie., correlation coefficient is 0.886

and proportion of the variation in weight can be explained by the linear relationship between weight and chest size is denoted as R² = 0.886²=0.7849

Hence78.49% proportion of the variation in weight can be explained by the linear relationship between weight and chest size