Question

The equation for predicting average steps per day from steps taken on Monday is: Y' = 5000 + .4(X). The correlation between Monday and average steps per day = .80. Interpret this correlation (2 points - make sure you give me both a scientific and a colloquial explanation).

What is the coefficient of determination (1 point)? Interpret this value (1 point).

Answer 1

Given:

The equation for predicting average steps per day from steps taken on Monday is: Y' = 5000 + .4(X).

The correlation between Monday and average steps per day = .80.

r = 0.80 = 80%

There is strong positive relationship between the steps take on Monday & average steps per day.

Positive correlation : When one variable increases as the other variable increases, or one variable decreases while the other decreases.

Here if there is increase in number of steps per day there will be increase in steps on Monday & vice versa.

Means increase in one variable will result in increase in second variable(80%)

The coefficient of determination :

r^2 = (0.80)^2 = 0.64

So the coefficient of determination is 0.64 = 64%

Interpretation : The coefficient of determination, r^2 indicate a strong positive relationship between two variables.