Using the SPSS data below, run a binary logistic regression to determine the odd

Question

Using the SPSS data below, run a binary logistic regression to determine the odds of a student taking Algebra 2 (alg2) based on their gender (gender), level of motivation (motivation), and parents’ level of education (parEduc). How might these results be used by a HS mathematics supervisor to increase enrollment in Algebra 2?

4.50

gender faed maed alg1 alg2 geo trig calc mathgr grades mathach mosaic visual visual2 satm ethnic religion ethnic2 item01 item02 item03 item04 item05 item06 item07 item08 item09 item10 item11 item12 item13 item14 item04r item05r item08r item11r competence motivation mathcrs maedRevis faedRevis item06r item10r pleasure parEduc 1 10 10 0 0 0 0 0 0 4 9.00 31.0 8.75 7.00 500 2 1 2 1 4 3 1 4 2 2 1 #NULL! 2 1 3 3 3 4 1 4 4 #NULL! 2.83 0 3.00 3.00 3.00 3.00 3.25 10.00 1 2 2 0 0 0 0 0 0 5 10.33 56.0 4.75 4.00 460 3 2 3 3 4 3 #NULL! 1 2 3 3 3 1 1 4 2 3 #NULL! 4 2 4 3.50 #NULL! 0 1.00 1.00 3.00 4.00 3.50 2.00 1 2 2 0 0 0 0 0 1 6 7.67 25.0 4.75 3.00 420 2 2 99 1 1 1 4 4 4 1 2 4 1 1 3 2 2 1 1 3 4 2.50 1.83 0 1.00 1.00 1.00 4.00 2.00 2.00 0 3 3 1 0 0 0 0 0 3 5.00 22.0 1.00 1.00 400 1 1 1 1 1 1 2 4 3 1 3 4 3 4 4 3 1 3 1 2 1 1.75 2.33 1 1.00 1.00 2.00 2.00 1.50 3.00 1 #NULL! 3 0 0 0 0 0 0 3 -1.67 17.5 2.25 2.00 450 2 1 2 1 4 1 4 4 4 1 4 1 1 4 2 2 3 1 1 1 1 1.00 1.33 0 1.00 #NULL! 1.00 4.00 3.00 3.00 1 3 2 0 0 0 0 0 1 5 1.00 23.5 1.00 0.00 250 3 2 2 1 1 1 4 4 4 1 4 1 1 4 1 2 4 1 1 1 1 1.00 1.17 0 1.00 1.00 1.00 4.00 2.50 2.50 0 9 6 1 1 1 0 0 0 6 12.00 28.5 2.50 2.00 480 1 2 1 #NULL! 1 3 1 1 3 3 1 3 1 1 3 3 2 4 4 4 4 3.50 #NULL! 3 2.00 3.00 2.00 4.00 2.25 7.50 1 5 3 1 0 0 0 0 0 4 8.00 29.5 3.50 3.00 430 1 3 1 1 1 3 2 4 2 1 2 3 2 1 3 3 3 3 1 3 4 2.75 2.33 1 1.00 2.00 3.00 3.00 2.50 4.00 1 3 3 1 0 0 0 0 1 7 13.00 28.0 3.50 2.00 490 1 98 2 3 1 #NULL! 1 1 2 2 2 4 2 1 3 2 2 4 4 3 4 #NULL! 2.83 1 1.00 1.00 3.00 3.00 2.25 3.00 0 8 2 0 0 0 0 0 0 5 3.67 27.5 3.75 3.00 300 2 1 2 1 3 1 4 4 4 1 3 3 2 4 3 4 2 1 1 2 1 1.50 2.00 0 1.00 3.00 1.00 3.00 2.25 5.00 0 3 4 1 1 1 1 1 0 6 21.00 27.0 11.00 9.50 500 4 99 2 4 4 4 3 1 4 4 1 4 4 2 4 4 3 2 4 4 3 3.75 3.67 5 2.00 1.00 1.00 1.00 2.25 3.50 0 8 9 1 1 1 1 1 1 8 23.67 26.5 4.75 4.00 700 1 98 1 3 4 4 2 1 2 3 2 4 2 1 3 3 3 3 4 3 4 4.00 3.00 5 3.00 3.00 3.00 3.00 3.25 8.50 1 2 2 1 0 0 0 0 0 5 4.00 13.0 1.00 1.00 380 3 2 3 1 4 1 3 4 2 1 1 4 1 1 4 3 4 2 1 4 4 2.50 2.50 1 1.00 1.00 3.00 4.00 3.75 2.00 0 6 3 1 0 0 0 0 0 2 9.00 18.0 1.00 0.00 450 2 1 3 3 4 3 2 1 1 4 1 4 1 1 4 3 3 3 4 4 4 3.75 3.50 1 1.00 2.00 4.00 4.00 3.75 4.50 1 2 3 1 1 0 0 0 0 3 5.33 25.0 4.75 4.00 400 1 1 1 4 4 3 2 1 3 3 1 4 1 1 3 3 3 3 4 4 4 3.75 3.33 2 1.00 1.00 2.00 4.00 3.25 2.50 0 #NULL! 3 1 1 1 0 0 1 7 19.67 33.0 13.50 9.50 590 2 2 1 3 4 3 2 1 3 4 2 4 1 2 4 3 3 3 4 3 3 3.50 3.33 3 1.00 #NULL! 2.00 4.00 3.25 3.00 0 3 3 1 0 1 0 0 0 7 7.67 33.0 -0.25 1.00 430 1 2 1 4 4 3 2 1 3 3 1 4 1 1 4 3 3 3 4 4 4 3.75 3.50 2 1.00 1.00 2.00 4.00 3.25 3.00 0 9 7 1 0 1 0 0 0 5 14.33 27.0 6.00 5.00 500 2 1 2 3 4 3 2 1 1 4 2 3 1 1 3 3 4 3 4 3 4 3.50 3.17 2 2.00 3.00 4.00 4.00 4.00 8.00 0 3 3 1 1 1 0 0 1 6 14.33 26.0 9.75 9.50 510 3 2 3 3 4 3 1 2 2 4 1 4 1 1 4 2 3 4 3 4 4 3.50 3.50 3 1.00 1.00 3.00 4.00 3.50 3.00 1 8 3 1 1 1 1 0 1 8 19.67 25.0 8.75 9.50 500 4 3 4 3 2 1 2 2 4 3 2 3 3 2 4 3 2 3 3 3 3 2.50 3.17 4 1.00 3.00 1.00 2.00 1.75 5.50 0 5 5 1 0 1 0 0 0 5 17.00 41.0 -0.25 1.00 580 1 3 1 4 4 4 1 1 3 3 1 3 1 1 4 4 3 4 4 4 4 3.75 3.83 2 2.00 2.00 2.00 4.00 3.25 5.00 1 2 3 0 0 0 0 0 0 3 7.67 27.0 7.25 6.00 450 1 99 1 2 4 3 1 2 1 4 2 1 1 1 3 2 4 4 3 3 4 2.75 3.00 0 1.00 1.00 4.00 4.00 4.00 2.50 0 9 7 1 1 1 1 0 0 5 19.67 22.0 4.75 5.00 500 1 98 1 4 4 3 1 1 3 3 2 3 2 1 4 3 3 4 4 3 4 3.50 3.50 4 2.00 3.00 2.00 3.00 3.00 8.00 1 2 2 0 0 0 0 0 0 4 6.67 53.0 1.00 5.00 450 1 1 1 3 3 2 2 2 1 1 2 2 2 2 3 3 3 3 3 3 3 2.50 2.67 0 1.00 1.00 4.00 3.00 3.25 2.00 1 6 6 1 1 1 1 0 1 7 14.33 27.0 9.75 8.00 520 2 1 2 3 4 4 2 1 3 3 2 3 1 1 3 2 3 3 4 3 4 3.75 2.83 4 2.00 2.00 2.00 4.00 3.25 6.00 1 5 3 1 0 0 0 0 0 5 10.67 31.0 7.25 7.00 490 3 2 3 3 4 3 3 2 3 3 2 3 1 2 2 3 3 2 3 3 3 3.00 2.67 1 1.00 2.00 2.00 4.00 3.25 4.00 1 3 6 1 0 1 0 0 0 6 14.33 29.0 2.25 5.00 510 4 99 4 4 4 3 3 1 1 2 3 3 1 1 3 3 3 2 4 2 4 3.50 2.67 2 2.00 1.00 4.00 4.00 3.75 4.50 0 3 2 1 1 0 0 0 1 5 14.33 26.0 2.25 2.00 480 1 1 1 3 4 4 1 1 1 3 1 4 1 1 4 3 2 4 4 4 4 4.00 3.50 2 1.00 1.00 4.00 4.00 3.50 2.50 1 5 3 1 0 0 0 0 1 6 14.33 22.0 1.00 1.00 450 1 2 1 4 4 3 2 1 2 3 2 3 1 2 3 3 3 3 4 3 3 3.25 3.17 1 1.00 2.00 3.00 4.00 3.50 4.00 0 2 3 0 0 0 0 0 0 3 9.00 31.0 13.50 8.00 400 3 1 98 2 3 2 3 1 3 4 2 3 1 1 3 3 2 2 4 3 4 3.25 2.83 0 1.00 1.00 2.00 4.00 2.75 2.50 1 2 3 1 1 1 1 0 1 7 17.00 27.0 9.75 8.00 550 2 1 2 2 4 4 2 1 1 3 2 4 1 1 3 2 4 3 4 3 4 4.00 2.67 4 1.00 1.00 4.00 4.00 4.00 2.50 0 9 5 1 1 1 0 0 0 6 23.67 34.0 9.50 9.50 710 1 3 1 3 4 2 2 2 3 2 2 4 1 1 4 3 3 3 3 3 4 3.25 3.00 3 2.00 3.00 2.00 4.00 3.25 7.00 0 5 7 1 1 1 1 0 0 4 18.33 24.5 9.75 9.50 600 4 98 4 4 4 4 1 1 2 4 1 4 1 1 3 4 3 4 4 4 4 4.00 3.83 4 2.00 2.00 3.00 4.00 3.50 6.00 0 8 8 1 1 1 1 0 1 7 15.67 23.0 6.00 5.00 650 3 2 3 3 4 3 2 2 4 2 2 3 1 1 3 3 2 3 3 3 4 3.25 2.83 4 3.00 3.00 1.00 4.00 2.75 8.00 1 4 2 1 0 0 0 0 1 8 17.00 32.5 2.25 2.00 550 1 1 1 3 4 3 3 2 2 2 2 3 2 2 3 2 3 2 3 3 3 3.00 2.50 1 1.00 2.00 3.00 3.00 3.25 3.00 0 8 6 1 1 1 1 0 0 6 15.67 29.5 9.75 8.00 470 1 99 1 3 3 3 3 2 3 2 2 3 2 2 1 1 2 2 3 3 3 3.00 2.00 4 2.00 3.00 2.00 3.00 2.50 7.00 0 3 3 1 0 1 0 0 0 7 7.67 33.0 -0.25 3.00 470 1 1 1 3 4 3 1 1 2 4 1 4 1 1 4 3 4 4 4 4 4 3.75 3.67 2 1.00 1.00 3.00 4.00 3.75 3.00 1 2 2 1 1 1 1 1 1 7 22.67 24.0 3.75 3.00 600 1 2 1 3 4 4 1 1 2 4 4 4 1 1 4 4 3 4 4 1 4 4.00 3.33 5 1.00 1.00 3.00 4.00 3.50 2.00 1 4 2 1 1 0 0 0 1 7 14.33 11.0 6.00 5.00 530 2 1 2 4 4 3 3 1 3 2 4 4 1 1 4 4 3 2 4 1 4 3.75 2.83 2 1.00 2.00 2.00 4.00 3.25 3.00 0 2 2 1 1 1 0 0 0 5 21.00 23.0 6.50 6.00 610 4 1 4 2 4 2 2 3 1 3 3 4 1 1 2 2 2 3 2 2 4 3.00 2.33 3 1.00 1.00 4.00 4.00 3.50 2.00 1 2 2 0 0 0 0 0 1 6 6.33 26.0 1.00 0.00 500 1 1 1 2 4 3 2 1 4 3 3 4 1 1 2 2 3 3 4 2 4 3.75 2.33 0 1.00 1.00 1.00 4.00 3.00 2.00 1 3 6 1 0 1 0 0 1 6 3.67 22.5 6.00 5.00 350 1 2 1 4 2 4 1 1 3 4 1 2 2 1 3 4 1 4 4 4 4 3.50 3.83 2 2.00 1.00 2.00 3.00 2.00 4.50 0 10 10 1 1 0 0 0 0 7 10.33 20.5 3.50 3.00 450 2 1 2 3 4 3 4 1 3 3 3 4 1 2 3 3 3 1 4 2 3 3.50 2.50 2 3.00 3.00 2.00 4.00 3.25 10.00 1 8 8 1 1 1 1 1 1 8 23.67 28.0 3.50 6.00 550 1 1 1 3 4 3 2 1 1 4 1 4 1 1 4 3 4 3 4 4 4 3.75 3.50 5 3.00 3.00 4.00 4.00 4.00 8.00 1 2 3 1 0 0 0 0 1 7 4.00 16.0 1.00 1.00 400 2 1 2 4 4 3 3 1 2 2 3 3 1 1 3 2 3 2 4 2 4 3.50 2.50 1 1.00 1.00 3.00 4.00 3.50 2.50 1 4 6 1 1 0 0 0 0 6 17.00 30.0 -0.25 0.00 520 1 2 1 3 4 3 1 1 2 4 1 3 1 1 3 3 3 4 4 4 4 3.50 3.50 2 2.00 2.00 3.00 4.00 3.50 5.00 1 10 9 1 1 1 0 0 0 6 6.33 23.5 -0.25 0.00 410 1 3 1 2 4 2 4 1 3 1 3 3 1 1 2 2 3 1 4 2 4 3.25 1.67 3 3.00 3.00 2.00 4.00 3.25 9.50 1 2 3 1 0 0 0 0 0 5 3.67 20.5 -0.25 4.00 520 1 1 1 3 4 2 3 2 1 4 1 4 1 1 2 3 3 2 3 4 4 3.25 3.00 1 1.00 1.00 4.00 4.00 3.75 2.50 1 3 5 1 0 0 0 0 0 5 9.00 22.5 4.75 4.00 440 1 2 1 4 3 4 3 1 2 4 2 4 2 1 2 2 3 2 4 3 4 4.00 2.83 1 2.00 1.00 3.00 3.00 3.00 4.00 1 8 7 1 1 1 1 0 0 6 20.33 24.0 5.00 4.00 470 1 3 1 3 4 3 3 1 3 3 2 4 1 1 3 3 3 2 4 3 4 3.75 2.83 4 2.00 3.00 2.00 4.00 3.25 7.50 1 2 2 1 0 0 0 0 0 6 13.00 37.0 4.75 2.00 600 4 3 4 4 4 4 2 1 3 4 1 3 1 2 3 3 2 3 4 4 3 3.50 3.50 1 1.00 1.00 2.00 4.00 3.00 2.00 1 2 3 1 0 0 0 0 1 5 12.00 31.0 4.75 4.00 500 98 1 2 2 4 4 3 1 3 1 3 4 1 1 2 2 3 2 4 2 4 4.00 1.83 1 1.00 1.00 2.00 4.00 3.25 2.50 1 6 2 0 0 0 0 0 1 6 17.00 56.0 5.00 4.00 520 2 1 2 3 3 3 2 1 2 2 2 3 2 1 3 2 3 3 4 3 4 3.50 2.67 0 1.00 2.00 3.00 3.00 3.00 4.00 1 5 7 1 1 1 1 1 1 8 23.67 35.5 11.00 8.00 730 3 2 3 3 4 2 2 2 2 3 2 3 1 2 2 3 3 3 3 3 3 2.75 2.83 5 2.00 2.00 3.00 4.00 3.50 6.00 0 2 2 1 1 1 1 0 1 8 21.00 28.0 11.00 9.50 700 1 1 1 3 3 3 2 1 2 3 2 3 1 1 3 3 3 3 4 3 4 3.50 3.00 4 1.00 1.00 3.00 4.00 3.25 2.00 0 10 9 1 1 1 1 1 1 7 22.33 36.0 7.25 7.00 600 1 2 1 3 4 3 1 1 1 4 1 3 1 1 3 2 4 4 4 4 4 3.50 3.33 5 3.00 3.00 4.00 4.00 4.00 9.50 1 2 3 0 0 0 0 0 0 3 2.33 35.0 3.50 3.00 400 2 1 2 4 4 3 1 1 2 4 1 4 1 1 2 3 3 4 4 4 4 3.75 3.50 0 1.00 1.00 3.00 4.00 3.50 2.50 1 10 5 1 1 1 1 0 1 8 22.33 44.0 7.25 6.00 500 3 2 3 4 4 3 3 2 1 2 3 2 4 1 1 1 3 2 3 2 4 3.00 2.00 4 2.00 3.00 4.00 1.00 3.00 7.50 1 2 2 1 0 0 0 0 1 7 5.00 -4.0 3.50 3.00 400 1 3 1 2 3 2 2 2 3 1 3 3 1 1 1 1 2 3 3 2 4 3.00 1.67 1 1.00 1.00 2.00 4.00 2.75 2.00 1 2 3 0 0 0 0 0 1 5 5.00 24.5 6.00 5.00 410 2 1 1 3 4 2 2 2 1 3 1 3 1 1 3 3 4 3 3 4 4 3.00 3.17 0 1.00 1.00 4.00 4.00 4.00 2.50 1 2 3 1 1 1 0 0 1 8 10.33 25.0 9.75 8.00 450 3 3 3 3 3 3 2 2 3 3 2 3 2 2 3 2 2 3 3 3 3 3.00 2.83 3 1.00 1.00 2.00 3.00 2.50 2.50 0 3 3 0 0 0 0 0 0 3 5.00 51.5 2.25 2.00 300 1 1 1 4 4 3 4 1 1 1 4 4 1 1 2 1 3 1 4 1 4 3.75 1.67 0 1.00 1.00 4.00 4.00 3.75 3.00 1 10 3 1 0 0 0 0 0 7 1.00 25.0 1.00 0.00 250 1 2 1 4 4 4 1 1 2 4 1 4 1 1 4 4 3 4 4 4 4 4.00 4.00 1 1.00 3.00 3.00 4.00 3.50 6.50 0 2 3 1 0 1 0 0 0 4 13.00 30.5 3.50 3.00 510 4 2 4 3 4 2 2 2 3 2 2 3 1 1 3 3 3 3 3 3 4 3.00 2.83 2 1.00 1.00 2.00 4.00 3.25 2.50 1 3 2 0 0 0 0 0 0 4 9.33 29.0 4.75 4.00 480 1 3 1 3 4 3 2 1 1 3 2 4 1 1 4 3 4 3 4 3 4 3.75 3.17 0 1.00 1.00 4.00 4.00 4.00 2.50 1 2 3 1 1 0 0 0 0 7 10.33 20.0 -0.25 0.00 460 99 3 98 4 3 4 2 1 3 3 1 4 3 1 3 3 2 3 4 4 4 4.00 3.33 2 1.00 1.00 2.00 2.00 2.25 2.50 0 9 3 1 1 1 1 1 1 7 23.67 22.0 4.75 4.00 650 1 1 1 4 4 3 2 1 3 3 1 3 1 1 3 3 3 3 4 4 4 3.50 3.33 5 1.00 3.00 2.00 4.00 3.25 6.00 0 5 5 0 0 0 0 0 0 3 5.00 7.5 6.00 8.00 500 1 2 1 3 4 2 1 1 1 3 1 3 1 1 2 2 4 4 4 4 4 3.25 3.00 0 2.00 2.00 4.00 4.00 4.00 5.00 0 9 8 1 1 1 1 1 1 8 23.67 32.0 7.25 7.00 480 1 3 1 4 4 4 3 1 3 3 1 4 1 1 4 2 3 2 4 4 4 4.00 3.17 5 3.00 3.00 2.00 4.00 3.25 8.50 0 3 3 1 1 0 0 0 0 5 14.67 23.0 1.00 1.00 530 1 1 1 4 4 3 1 1 2 4 1 4 1 1 4 4 3 4 4 4 4 3.75 4.00 2 1.00 1.00 3.00 4.00 3.50 3.00 0 7 3 1 1 1 1 0 0 4 18.67 24.5 11.00 9.50 550 1 2 1 3 4 1 2 3 4 4 1 2 1 2 3 1 3 3 2 4 3 2.00 3.00 4 1.00 2.00 1.00 4.00 3.00 5.00 0 5 4 1 1 1 0 0 0 7 11.67 23.0 8.50 9.50 500 1 3 1 4 4 4 3 1 4 1 3 3 3 1 2 1 2 2 4 2 4 3.75 2.00 3 2.00 2.00 1.00 2.00 2.25 4.50 0 3 6 1 0 0 0 0 0 4 14.33 30.5 8.50 3.00 460 1 1 1 2 2 2 2 2 3 3 2 3 3 2 3 3 1 3 3 3 3 2.75 2.83 1 2.00 1.00 2.00 2.00 1.75 4.50 0 3 3 1 0 1 0 0 0 5 11.67 13.5 14.75 9.50 470 1 2 1 3 3 2 3 2 3 2 3 3 2 2 3 2 2 2 3 2 3 2.75 2.33 2 1.00 1.00 2.00 3.00 2.50 3.00 0 6 3 1 1 1 1 0 1 7 14.33 30.0 14.75 7.00 520 1 3 1 3 3 3 1 1 3 3 1 4 2 1 3 3 2 4 4 4 4 3.75 3.33 4 1.00 2.00 2.00 3.00 2.50

4.50

Explanation / Answer

We can run the analysis using the open source statisitical package R , as SPSS is a commercial tool

Please see the r code below

# read the data into R dataframe
data.df<- read.csv("D:\downloads\Chegg\log.csv",header=TRUE)
str(data.df)

data.df$alg2 <- as.factor(data.df$alg2)

model <- glm(alg2 ~.,family=binomial(link='logit'),data=data.df)
summary(model)

The results are

Call:
glm(formula = alg2 ~ ., family = binomial(link = "logit"), data = data.df)

Deviance Residuals:
Min 1Q Median 3Q Max  
-1.9077 -0.8979 -0.5250 1.0289 1.7343  

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -3.1235 1.5188 -2.056 0.03973 * ## signficnat for the model
gender -0.6349 0.5390 -1.178 0.23885
motivation 0.6052 0.4412 1.372 0.17013
parEduc 0.3560 0.1265 2.814 0.00489 ** ## signficnat for the model
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 99.313 on 71 degrees of freedom
Residual deviance: 83.601 on 68 degrees of freedom
AIC: 91.601

Number of Fisher Scoring iterations: 4

we see that the variable ParEduc is directly related to the number of students in alg2 , hence one should focus on this variable to increase the odds of enrollment in alg2

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