a. What is the equation of the least-squares regression line relating posttest and pretest scores? Define any variables used.

b. Is a linear model appropriate for describing this relationship? Justify your answer.

c. If we use the least-squares regression line to predict students’ posttest scores from their pretest scores, how far off will our predictions typically be?

Many chess masters and chess advocates believe that chess play develops general intelligence, analytical skill, and the ability to concentrate. According to such beliefs, improved reading skills should result from study to improve chess-playing skills. To investigate this belief, researchers conducted a study. All the subjects in the study participated in a comprehensive chess program, and their reading performances were measured before and after the program. The graphs and numerical summaries that follow provide information on the subjects’ pretest scores, posttest scores, and the difference (Post − Pre) between these two scores.

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Descriptive Statistics: Pretest, Posttest, Post – Pre Variable N Mean Median StDev Min Маx Q1 Q3 Pretest 53 57.70 58.00 17.84 23.00 99.00 44.50 70.50 Posttest 53 63.08 64.00 18.70 28.00 99.00 48.00 76.00 Post – Pre 53 5.38 3.00 13.02 -19.00 42.00 -3.50 14.00