Final answer:
The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables, while R-squared (r²) is the proportion of variance in the dependent variable that can be predicted from the independent variable. The beta coefficient (β) measures how much a stock's price is expected to change with the stock market.
Step-by-step explanation:
Understanding R-Squared and Beta in Statistics
The correlation coefficient, denoted as r, measures the strength and direction of a linear relationship between two variables. It is a value between -1 and 1 where a positive r suggests that as one variable increases, the other tends to increase as well, while a negative r suggests an inverse relationship. The coefficient of determination, represented as r² (or R-squared), is the square of r. It is usually expressed as a percentage and represents the proportion of variance in the dependent variable that is predictable from the independent variable.
A beta coefficient (β) is typically used in the context of finance as a measure of how much a stock's price is expected to change in response to a change in the overall stock market. It is a component of the Capital Asset Pricing Model (CAPM), which calculates the expected return of an asset based on its beta and expected market returns.
In the context of simple linear regression, we could say that the slope of the regression line represents beta. It is an indication of how much the dependent variable is expected to change for a one-unit change in the independent variable.