Question

Data were collected on annual rain fall (y), and maximum daily temperature (x) in11 sites in Mongolia (Central Asia). The scatterplot ofyagainstxwas approximately linear.The estimated correlation coefficient wasr=−0.92.The regression function is: ˆy= 2970.65−114.75xApproximately, what is the estimated coefficient of determination?

Answer 1

For a simple linear regression, the estimated coefficient of determination (r^{​​​​​​2}) is equal to the square of the correlation coefficient (r) between x and y scores. The coefficient of determination is the proportion of the variance in the dependent variable that is predictable from the independent variable.

The estimated coefficient of determination is r^{​​​​​​2} = (–0.92)² = 0.8464

So, 84.64% of the variability is explained in the dependent variable (y) from the independent variable (x).