Interpreting Coefficient of Determination

Flashcards focusing on the key concepts related to the coefficient of determination and linear regression interpretation.

Coefficient of Determination

Also known as r squared, it measures the proportion of variation in the response variable explained by the explanatory variable.

Residual

The difference between the observed value and the predicted value in a regression model.

Sum of Squared Residuals

The sum of the squares of the residuals, used to evaluate the fit of a regression model.

Least Squares Regression Line

A statistical method for finding the line of best fit by minimizing the sum of squared residuals.

R Squared Interpretation

The percentage of variation in the response variable explained by the linear relationship with the explanatory variable; for example, 90.3% in the context of attendance predicting test scores.

Correlation

A measure of the strength and direction of a linear relationship between two variables, denoted as r.

R value

The correlation coefficient, which represents the strength and direction of a linear relationship.

Y hat (Ŷ)

The predicted value of the response variable in a regression model.

Slope

In a linear regression model, the coefficient that represents the change in the predicted value for each one-unit change in the explanatory variable.

Y Intercept

The constant term in a regression equation, representing the predicted value of Y when X is zero.

Interpretation Template for R Squared

'X% of the variation in the response variable can be explained by the linear relationship with the explanatory variable.'

Positive/Negative Relationship

Determined by the sign of the slope in a regression model; a positive slope indicates a positive relationship, while a negative slope indicates a negative relationship.

Square Root Relationship

To find the correlation (r), take the square root of r squared; r = √(r²).

Model without Explanatory Variable

A model that uses the mean of the response variable as a prediction, unable to account for variability due to the explanatory variable.

Reduction Percentage

The percent by which the sum of squared residuals is decreased when using a more accurate model compared to a baseline model.