1. AP Statistics Chapter 27 Notes “Inference for Regression”

2. Scatter plots Review  To enter the data –  STAT, EDIT, X’s in L1, Y’s in L2  To see the picture –  2 nd, Y=, Turn on plot 1, Set it on scatter plot for L1 and L2, Zoom, #9 ZoomStat  To find the equation –  STAT, CALC, #8 LinReg (a + bx) L1, L2  To look at a residuals plot –  2 nd, Y=, Change L2 to RESID (which is in 2 nd, STAT after you calculate the regression equation) NOTE: Go into the catalog (2 nd, 0) and turn Diagnostics On to get the r and r 2 values.

3. Scatter plots Review  1. Make a scatter plot. Label the axes and at least two points.  2. Find the regression equation.  3. Find r. What does it tell you?  4. Find r 2. What does it tell you?  5. Look at the residuals plot. What does it tell you? GPA ACT score 3.2524 2.8721 2.6618 3.3322 2.8722 3.2122 2.7618 3.9128 3.5529 2.5518 2.4420 3.2224 3.0121 3.4424 3.2225

4. Inference for Regression  Different samples will give different regression equations and thus, different slope and y-intercept values.  We will use the slope from our sample to:  1. Check for a significant relationship between x and y  2. Make a confidence interval for the true slope for the entire population

5. Hypothesis Testing for the Slope of the Regression Line  If there is a relationship between x and y, the slope of the regression line would not be zero.  Thus, Ho:Ha:  The hypothesis test to test the null hypothesis is a t- test with n – 2 degrees of freedom. No relationship exists between x and y A relationship exists between x and y

6. Example  The given data is a random sample of GPAs and ACT scores for students at a certain high school as collected by a school counselor. Based on this sample, is there evidence of a linear relationship between GPA and ACT scores for students at this high school? GPA ACT score 3.2524 2.8721 2.6618 3.3322 2.8722 3.2122 2.7618 3.9128 3.5529 2.5518 2.4420 3.2224 3.0121 3.4424 3.2225

7. The Solution Process  1. State the hypotheses. Ho: slope is 0(there is no relationship between x and y) Ha: slope is not 0 (there is a relationship between x and y)  2. Check the conditions. - The scatter plot of the data should look linear - The residual plot should show random scatter with no pattern - The data should be randomly selected - The histogram of the residuals should be unimodal and roughly symmetric or the Normal probability plot should look fairly straight  3. Test the hypotheses and state your conclusion. (STAT, TESTS, F)  4. Create and interpret a 95% confidence interval for the slope of the regression line. (STAT, TESTS, G)