which of the following regressions represents the weakest linear relationship between x and y?\nregression…

which of the following regressions represents the weakest linear relationship between x and y?\nregression 1\n$y = ax + b$\n$a = - 18.5$\n$b = 10.5$\n$r = - 0.9373$\nregression 2\n$y = ax + b$\n$a = 18.6$\n$b = 3.9$\n$r = 0.8865$\nregression 3\n$y = ax + b$\n$a = - 11.6$\n$b = - 16.4$\n$r = - 0.6453$\nregression 4\n$y = ax + b$\n$a = - 4.5$\n$b = - 10.2$\n$r = - 0.7281$\nanswer\nregression 1\nregression 2\nregression 3\nregression 4

which of the following regressions represents the weakest linear relationship between x and y?\nregression 1\n$y = ax + b$\n$a = - 18.5$\n$b = 10.5$\n$r = - 0.9373$\nregression 2\n$y = ax + b$\n$a = 18.6$\n$b = 3.9$\n$r = 0.8865$\nregression 3\n$y = ax + b$\n$a = - 11.6$\n$b = - 16.4$\n$r = - 0.6453$\nregression 4\n$y = ax + b$\n$a = - 4.5$\n$b = - 10.2$\n$r = - 0.7281$\nanswer\nregression 1\nregression 2\nregression 3\nregression 4

Answer

Explanation:

Step1: Recall the concept of correlation coefficient

The strength of a linear relationship is determined by the absolute value of the correlation coefficient ( r ). The closer ( |r| ) is to ( 1 ), the stronger the linear relationship. The closer ( |r| ) is to ( 0 ), the weaker the linear relationship.

Step2: Calculate the absolute values of ( r ) for each regression

  • For Regression 1: ( |r|=|- 0.9373| = 0.9373 )
  • For Regression 2: ( |r|=|0.8865| = 0.8865 )
  • For Regression 3: ( |r|=|-0.6453| = 0.6453 )
  • For Regression 4: ( |r|=|-0.7281| = 0.7281 )

Step3: Compare the absolute values

We compare ( 0.9373), (0.8865), (0.6453) and (0.7281). Since (0.6453<0.7281 < 0.8865<0.9373)

Answer:

Regression 3