In newspapers or magazines, find reports describing the relationship between two variables. Is the correlation coefficient or any other measure used to assess the degree of the relationship? Is the relationship described in terms of a line? Have they violated any of the cautions for correlation and regression? At a particular university the correlation between the average rating students give the instructor on end-of-term course evaluations and the average grade received by students in the class is r = .43 with p < .01. A professor complains that this statistically significant correlation proves that high instructor ratings can be "bought" by giving students higher grades. Why is this conclusion unjustified? What alternative explanation might there be for the significant correlation? A sample of students entering a major university completed a long survey asking about their attitudes, high school activities, academic plans, etc. Students also reported their SAT Verbal and Math scores. Subsequently it was possible to obtain the true scores received by these students as reported by the Educational Testing Service. The following variables are available in the downloadable dataset for 170 students: Sex: 1 = Male, 2 = Female SATV: SAT-Verbal score as reported by the student on the survey SATM: SAT-Math score as reported by the student on the survey TRUESATV: SAT-Verbal score as reported to the university by ETS TRUESATM: SAT-Math score as reported to the university by ETS If you did not already do so for the exercises in previous chapters, construct two new variables: VDIFF = SATV - TRUESATV MDIFF = SATM - TRUESATM VDIFF is the amount a student overstates (if positive) or understates (if negative) his or her SAT-Verbal score. MDIFF has the same interpretation for SAT-Math scores. Use these variables to answer the questions below. For each question, compute the correlation, estimate the best-fitting line, test its slope against the null hypothesis of zero, and construct a 95-percent confidence interval. What is the relationship between SATV and SATM? Does TRUESATV predict SATV, the score reported by the student? If students report truthfully then the slope should equal 1. Does 1 appear in the confidence interval for the slope? Does TRUESATM predict SATM, the score reported by the student? If students report truthfully then the slope should equal 1. Does 1 appear in the confidence interval for the slope? Is there a relationship between VDIFF and TRUESATV? Does overstating of one's SATV score increase or decrease as one's true score increases? Is there a relationship between MDIFF and TRUESATM? Does overstating of one's SATM score increase or decrease as one's true score increases? Is there a relationship between VIDFF and MDIFF?   If you are using a statistical computer package with Seeing Statistics, select some variables from the sample files that came with the program. Use your computer statistical package to test the relationship between pairs of continuous or quantitative variables that interest you. Here are some suggestions: JMP Use the GALTON.JMP dataset to determine if the average height of a child's parents, Parent HT, predicts the child's height, Child HT. If tall parents always had tall children and short parents always had short children, then the slope would be near 1. Is 1 in the 95-percent confidence interval? (Historical note: Galton collected these data and made an early use of the line-fitting techniques described in this chapter. Because children tended not to be as tall or as short as their parents but instead tended to "regress toward the mean" height, the technique has since been called "regression." Minitab Use PULSE.MTW to estimate the line predicting WEIGHT from HEIGHT. About how much does each additional inch weigh? Do the regression separately for males and females. Do you get the same slope for HEIGHT for each sex? StatView Use the TreeData to determine the relationship between TrunkGirth and Weight.
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