If the correlation between height and weight of a large group of people is 0.75​, find the coefficient of determination​ (as a​ percent) and explain what it means. assume that height is the predictor and weight is the​ response, and assume that the association between height and weight is linear.

Independent variable is the predictor variable which is the height and dependent variable is the response variable which is weight in this scenario.

The square of correlation coefficient gives the coefficient of determination. It is denoted by R² (R squared).

We are given:
R = 0.75

So,
R²  = 0.75²

R² = 0.5625

R²  = 56.25 %
The coefficient of determination tells how much of the trend of dependent data can be explained by the independent data using the linear regression model. So in the given case, Height can explain 56.25% of the trend in the weight.