y Side College freshmen involved in a dating relationship agreed to participate in a nine month long study Every two weeks participants answered a detailed questionnaire about their relationship and their emotional well being Over the course of the study 26 of the participants experienced a breakup The average distress of these 26 participants at the time of breakup 0 weeks and over the following 10 weeks was assessed from their questionnaire answers The table shows the findings in a scientific publication Time since brea kup wee ks Aver age distr ess unit less score 0 2 6 10 3 3 3 1 2 9 2 6 CSV Excel JMP Mac TXT Minitab14 18 Minitab18 PC TXT R SPSS TI CrunchIt 1 P Eastwick et al Mispredicting distress following romantic breakup Revealing the time course of the affective forecasting error Journal of Experimental Social Psychology 44 2008 pp 800 807 doi 10 1016 j jesp 2007 07 001 Macmillan Learning As a pedagogical exercise find the correlation r step by step You may wish to round off to two decimal places in each step First obtain the mean and standard deviation of each variable Let x represent time since breakup in weeks and y represent average distress Ox 4 00 sx 3 84 y 3 00 sy 0 26 O x 4 00 sx 4 43 y 3 00 sy 0 30 x 4 50 sx 3 84 y 2 98 sy 0 26 O x 4 50 sx 4 43 y 2 98 sy 0 30 Second compute the four standardized values for each variable O Zx Zy 15 07 0 07 8 37 0 03 5 02 0 02 18 42 0 08 Zx Zy 4 50 0 33 2 50 0 13 0 08 1 50 5 5 0 38 O Zx Zy 1 01 1 09 0 56 0 42 0 34 0 25 1 24 1 26 Zx Zy 1 01 1 09 0 56 0 42 0 34 0 25 1 24 1 26 Finally use the formula for r Use your calculator or software to obtain r and check that you get the same result as in your hand calculations up to roundoff error