Question

Which explanatory variable has a stronger relationship with the response variable y?

Here are the scatter plots for two sets of bivariate data with the same response variable. The first compares the variables x & y. The second compares the variables w & y

[Graphs generated by this script: width="300";height="300";xmin=-5;xmax=5;ymin=-5;ymax=5;axes(1,1);marker="dot"; line([0.54,-0.41596638655462],[0.54,-0.41596638655462]); line([1.5,-1.890756302521],[1.5,-1.890756302521]); line([1.02,0.11344537815126],[1.02,0.11344537815126]); line([3.396,-2.7415966386555],[3.396,-2.7415966386555]); line([2.436,-1.3424369747899],[2.436,-1.3424369747899]); line([0.372,0.58613445378151],[0.372,0.58613445378151]); line([0.612,-0.58613445378151],[0.612,-0.58613445378151]); line([-1.764,0.71848739495798],[-1.764,0.71848739495798]); line([-2.292,1.436974789916],[-2.292,1.436974789916]); line([2.94,-2.2310924369748],[2.94,-2.2310924369748]); line([0.732,-0.34033613445378],[0.732,-0.34033613445378]); line([-1.26,1.1533613445378],[-1.26,1.1533613445378]); line([-4.5,4.5],[-4.5,4.5]); line([0.492,-0.41596638655462],[0.492,-0.41596638655462]); line([1.452,-0.5672268907563],[1.452,-0.5672268907563]); line([2.172,-1.890756302521],[2.172,-1.890756302521]); line([2.412,-1.5882352941176],[2.412,-1.5882352941176]); line([1.644,-0.7563025210084],[1.644,-0.7563025210084]); line([1.14,-0.58613445378151],[1.14,-0.58613445378151]); line([1.572,-0.47268907563025],[1.572,-0.47268907563025]); line([0.612,0.32142857142857],[0.612,0.32142857142857]); line([-0.18,0.41596638655462],[-0.18,0.41596638655462]); line([-0.3,0.018907563025213],[-0.3,0.018907563025213]); line([2.196,-1.4936974789916],[2.196,-1.4936974789916]); line([1.524,-0.54831932773109],[1.524,-0.54831932773109]); line([0.612,-1.6071428571429],[0.612,-1.6071428571429]); line([-0.084,-0.41596638655462],[-0.084,-0.41596638655462]); line([3.492,-2.1365546218487],[3.492,-2.1365546218487]); line([4.5,-2.968487394958],[4.5,-2.968487394958]); line([3.66,-3.3655462184874],[3.66,-3.3655462184874]); line([-2.46,2.2121848739496],[-2.46,2.2121848739496]); line([0.996,-1.0021008403361],[0.996,-1.0021008403361]); line([-0.156,0.20798319327731],[-0.156,0.20798319327731]); line([3.276,-2.2689075630252],[3.276,-2.2689075630252]); line([0.444,-0.90756302521008],[0.444,-0.90756302521008]); line([4.476,-4.5],[4.476,-4.5]); line([1.836,-0.64285714285714],[1.836,-0.64285714285714]);]       [Graphs generated by this script: width="300";height="300";xmin=-5;xmax=5;ymin=-5;ymax=5;axes(1,1);marker="dot"; line([2.3076923076923,0.41832348199893],[2.3076923076923,0.41832348199893]); line([1.2692307692308,-0.81004836109618],[1.2692307692308,-0.81004836109618]); line([0.51923076923077,-0.29742074153681],[0.51923076923077,-0.29742074153681]); line([2.8846153846154,-0.76652337452982],[2.8846153846154,-0.76652337452982]); line([0.40384615384615,2.3334228909189],[0.40384615384615,2.3334228909189]); line([2.5384615384615,-2.8121977431488],[2.5384615384615,-2.8121977431488]); line([2.8846153846154,1.5789897904353],[2.8846153846154,1.5789897904353]); line([0.80769230769231,-0.97447608812466],[0.80769230769231,-0.97447608812466]); line([4.5,1.356528747985],[4.5,1.356528747985]); line([-0.28846153846154,0.34578183772166],[-0.28846153846154,0.34578183772166]); line([2.4807692307692,2.1544868350349],[2.4807692307692,2.1544868350349]); line([-4.3846153846154,-3.6826974744761],[-4.3846153846154,-3.6826974744761]); line([0.23076923076923,-0.92611499193982],[0.23076923076923,-0.92611499193982]); line([1.1538461538462,2.1835034927458],[1.1538461538462,2.1835034927458]); line([2.5384615384615,-2.1835034927458],[2.5384615384615,-2.1835034927458]); line([-1.4423076923077,2.7154755507792],[-1.4423076923077,2.7154755507792]); line([-0.63461538461539,2.9911337990328],[-0.63461538461539,2.9911337990328]); line([0.057692307692307,-1.4048898441698],[0.057692307692307,-1.4048898441698]); line([1.9615384615385,1.975550779151],[1.9615384615385,1.975550779151]); line([0.11538461538461,0.90677055346588],[0.11538461538461,0.90677055346588]); line([1.4423076923077,3.3683503492746],[1.4423076923077,3.3683503492746]); line([2.1346153846154,0.76168726491134],[2.1346153846154,0.76168726491134]); line([-1.1538461538462,-3.9825362708221],[-1.1538461538462,-3.9825362708221]); line([-1.4423076923077,0.10397635679742],[-1.4423076923077,0.10397635679742]); line([-4.5,-4.1953250940355],[-4.5,-4.1953250940355]); line([1.7307692307692,0.99865663621709],[1.7307692307692,0.99865663621709]); line([1.4423076923077,2.1109618484686],[1.4423076923077,2.1109618484686]); line([-1.7884615384615,-2.7396560988716],[-1.7884615384615,-2.7396560988716]); line([-1.7307692307692,-3.1603976356797],[-1.7307692307692,-3.1603976356797]); line([2.7692307692308,4.5],[2.7692307692308,4.5]); line([0.34615384615384,-4.5],[0.34615384615384,-4.5]); line([-0.11538461538462,2.4688339602364],[-0.11538461538462,2.4688339602364]); line([2.4230769230769,0.81004836109618],[2.4230769230769,0.81004836109618]); line([1.7884615384615,-0.70365394948952],[1.7884615384615,-0.70365394948952]); line([1.7307692307692,-2.8944116066631],[1.7307692307692,-2.8944116066631]); line([-1.1538461538462,-0.59725953788286],[-1.1538461538462,-0.59725953788286]); line([1.7307692307692,2.1109618484686],[1.7307692307692,2.1109618484686]);]

Which explanatory variable has a stronger relationship with the response variable y?


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