7.2 Standard Error for Regression Lines Learning Goal: Use residuals and standard error to assess the fit of a linear model. Use the standard error to make a prediction interval Introduction: If data has a linear form, then we know that the least-squares regression line is the line that best fits the data. We also know that there will still be errors in the predictions from this regression line. The correlation coefficient gives us one way to measure how well the regression line fits the data. In this activity, we will learn another way to describe this. 1) Here we again have data from a sample of 16 fetuses. AC is the abdominal circumference in millimeters. GAWKS is the gestational age of the fetus in weeks. gestational age (weeks) AC GAWK Prediction Error 40 62 12.8 11.2 1.6 35 101 15.7 15.0 0.7 30 104 14.2 15.3 -1.1 25 129 17.8 17.7 0.1 20 141 19.1 18.9 0.2 15 10 166 20 21.3 1.3 50 100 150 200 250 300 350 176 22.2 22.2 0.0 Abdominal circumference ( mum ) Linear regression results: 221 24.4 26.6 2.2 221 26.7 26.6 0.1 predicted GAWK = 5.18 + 0.097(AC) Sample size: 16 266 28.8 31.0 -2.2 R (correlation coefficient) = 0.98974067 274 31.4 31.8 0.4 R-sq = 0.97958659 269 33.5 31.3 2.2 Estimate of error standard deviation: 315 36 35.7 0.3 Se = 1.4098154 331 39.8 37.3 2.5 a) Suppose that a fetus has an abdominal 341 38.4 38.3 0.1 circumference of 150mm, what is its 383 41.5 42.3 -0.8 predicted GAWK? Show your work. b) We cannot compute the error (the residual) for this prediction. Why not