Question

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.

Answer 1

Explanation:

Given that the correlation between height and weight of a large group of people is 0.75

Coefficient of determination =
`R^2 =0.75^2 =0.5625=56.25%`

Coefficient of determination gives us the strength of association between two variables and how much the variability of the response variable i.e. weight is due to the variability of the predictor variable i.e. height

When there is a linear association correlation coefficient square gives us the reason for the variability and percentage due to the variability in predictor variable

Answer 2

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.