Residual Plots Unit #8 - Statistics

Residuals The difference between actual data points and ones predicted by the regression line (line of best fit). 𝒆=𝒚− 𝒚 Residuals are strongly influenced by outliers. If the residuals are small, the model is good. The bigger the residuals the less accurately the model can predict outcomes.

Finding Residuals 𝑦− 𝑦 From the equation (predicted outcomes) x y 𝒚 Residual (e) 1 2 2.7 -0.7 5 4.2 0.8 3 7 5.7 1.3 4 6 7.2 -1.2 9 8.7 0.3 10 10.2 -0.2 x y 𝒚 Residual (e) 𝑦− 𝑦 From the graph From the equation (predicted outcomes)

Residual Plots Graph the x-value and the residual value to see how good our regression line models the data. Look for 3 things for the model to be appropriate Equal number of points above the x-axis and below No obvious patterns (linear, exponential or fan) Small values for the residuals (y-axis)

What do these Residual Plots tell us? All of these show residual plots for bad models. What is the biggest problem with each of the graphs? Patterns indicate that we shouldn’t use a linear model

Residual Plot Does the Residual Plot indicate that our model (regression line) is a good predictor for this data? Explain. YES! equal number of points above & below the x-axis no pattern all residuals ≤ 𝟏.𝟓

Create a Residual Plot e x x y 𝒚 Residual (e) 1 2 2.7 -0.7 5 4.2 0.8 3 5.7 1.3 4 6 7.2 -1.2 9 8.7 0.3 10 10.2 -0.2 x