5.3 Linear Regression Models

Calculate a predicted response value using a linear regression model.

• If the form of the relationship between x and y appears linear, we can approximate the relationship between x and y using a linear regression model, which is a linear equation that uses an explanatory variable, x, to predict the response variable, y.
• In a linear regression model, the predicted response value, denoted by y, is calculated as y=+ab x, where a is the y-intercept, b is the slope of the regression line, and x is the explanatory variable.
• Extrapolation is predicting a response value using a value for the explanatory variable that is beyond the interval of x-values used to determine the regression line. The predicted value is less reliable the further the estimate is extrapolated.
• Interpolation is predicting a response value using a value for the explanatory variable that is within the interval of x-values used to determine the regression line.