Residuals and Residual Plots Most likely a linear

Residuals and Residual Plots Most likely a linear regression will not fit the data perfectly. distance The residual (e) for each data point is the ____________ prediction from the data point to the regression line. It is the error in _________. observed y value To find the residual (e) of a data point, take the ____________ predicted value and subtract the _____________ (y value from the linear regression). zero That is, Σ e = The sum of the residuals is equal to _____. Residual Plot Residuals can be plotted on a scatterplot called a ______________. x value · The horizontal x-axis is the same ____________ as the original graph. residual · The vertical y-axis is now the ____________. LOOKING AT RESIDUAL PLOTS: ·When a set of data has a linear pattern, its random pattern residual plot will have a ______________. ·If a set of data does not have a linear pattern, its NOT be random residual plot will ____________, but rather, shape will have a _______. HOW TO USE RESIDUAL PLOTS: ·If the residual plot is RANDOM: Use Linear Regression ·If the residual plot is NON-random: DO NOT USE Linear Regression Consider some other type of regression.

Perfectly Linear Data Draw a scatterplot from the given data. Enter x-values into L 1. Enter y-values into L 2. Use a calculator to find the linear regression for this data. Lin. Reg y=ax+b a= b= r 2= r= Linear regression equation: Draw the linear regression on the same graph as the scatter plot (left). Enter linear regression into Y 1. How does the linear regression fit the data? Use the table feature on the calculator to fill in the center column on the residual table (top right). Complete the table. Create a residual plot (right). What do you notice about the residual plot?

Linear Data A scatterplot and linear regression line are already drawn from the given data. Enter x-values into L 1. Enter y-values into L 2. Use a calculator to find the linear regression for this data. Lin. Reg y=ax+b a= b= r 2= r= Linear regression equation: Enter linear regression into Y 1. How does the linear regression fit the data? Use the table feature on the calculator to fill in the center column on the residual table (top right). Complete the table. Create a residual plot (right). What do you notice about the residual plot?

Non-Linear Data A scatterplot and linear regression line are already drawn from the given data. Enter x-values into L 1. Enter y-values into L 2. Use a calculator to find the linear regression for this data. Lin. Reg y=ax+b a= b= r 2= r= Linear regression equation: Enter linear regression into Y 1. Use the table feature on the calculator to fill in the center column on the residual table (top right). How does the linear regression fit the data? Complete the table. Create a residual plot (right). What do you notice about the residual plot?