Residuals and r^2

Residual

The difference between the observed value and the predicted value of a dependent variable in a regression model. Residuals indicate how well a model fits the data.

Residual plot

A graphical representation of the residuals against the predicted values, used to assess the fit of a regression model and identify patterns or non-linearity. These help show how well regression line describes data by seeing if there are any obvious patterns or if the residuals are not close to the horizontal axis.

Standard deviation of residuals

A measure of the dispersion of residuals in a regression analysis, indicating how much the residuals vary from the average residual. It provides insight into the model's overall prediction accuracy. (s)

b formula

r(S_y/S_x)

a formula

mean of y - b(mean of x)

r²

is a graphical tool for evaluating how well a linear model fits the data. It is in a percentage form and describes how much percent of the variations is explained by a specific regression (linear, quadratic, cubic, etc.). Is the coefficient of determination. Found by squaring correlation coefficient.

Influential observations

are data points that substantially affect the slope of the regression line. These observations can impact the fit of the model and skew the results, making them critical to identify.

Association does not imply causation

An association between an x and y value, even if it is very strong, is not by itself good evidence that changes in x actually cause changes in y.

Direct causation

is a relationship where changes in one variable directly result in changes in another variable, indicating a clear cause-and-effect link between them.

Nonsense causation

is a misleading relationship where two variables appear to be related but are actually influenced by a third factor, leading to erroneous conclusions about cause and effect.

Lurking variable

is a hidden factor that affects both x and y, potentially creating a spurious association between them.

Reverse regression

is a statistical method used to determine if the dependent and independent variables can be swapped, examining how well the independent variable predicts the dependent variable and vice versa.