Question

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 equals=0.762. Using alpha α equals=​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?

Answer 1

For the given sample, the degrees of freedom are, n-2, i.e. 6. And of 6 degrees of freedom, the critical value is 0.707.

And the given value of the correlation coefficient, 0.762, is greater than the critical value so there is a linear correlation between weight and chest size.

The proportion of the variation in weight can be explained by the linear relationship between weight and chest​ size, we'll find out R² for that.

R² tells you about the measure of fit and in linear cases can be defined as the square of the correlation coefficient.

R² = (0.762)² = 0.5806

So, 59.06% of the variation in weight can be explained by the linear relationship between weight and chest size.