7.1 Residuals and Residual Plots Learning Goal: Interpret residual plots. Recognize linear and non-linear form in a residual plot Introduction: In this activity we will learn another method for determining whether a line is a good fit for the data. It involves a new way to look at prediction errors. 1) Here we have data from a sample of 16 fetuses. AC is the fetus's abdominal circumference in millimeters. GAWKS is the gestational age of the fetus in weeks. The scatterplot of the data with the least squares regression line is on the left (r=0.99). On the right is a residual plot. Residual is another name for the prediction error (recall: error = y - D). So, this graph shows the prediction error, along with the AC, for each fetus in the data set. gestational age (weeks) Residuals vs. Abdominal circumference (cm) Residuals 40 35 30 OHN 25 20 -1 15 -2 10 50 100 150 200 250 300 350 50 100 150 200 250 300 350 Abdominal circumference (mm ) Abdominal circumference (mm) predicted GAWKS = 5.18 + 0.097 (Abdominal circumference) a) One fetus had an abdominal circumference of 331 mm when they were 39.8 weeks old. Calculate the predicted GAWKS for this fetus and then find the prediction error. Circle them in both graphs. b) In both graphs circle the fetuses for whom the regression line predicts the GAWK almost exactly. c) If a fetus has a negative residual, is the data point above or below the regression line? Why does this make sense