question\nwhich of the following regressions represents the weakest linear relationship between x and…

question\nwhich of the following regressions represents the weakest linear relationship between x and y?\nregression 1\n$y = ax + b$\n$a = 12.3$\n$b = 16.9$\n$r = 0.7329$\nregression 2\n$y = ax + b$\n$a=-9.5$\n$b = 19.8$\n$r=-0.3089$\nregression 3\n$y = ax + b$\n$a = 8.9$\n$b = 12.5$\n$r = 0.8607$\nregression 4\n$y = ax + b$\n$a = 17.9$\n$b=-10.5$\n$r = 0.6017$\nanswer\nregression 1\nregression 3\nregression 2\nregression 4

question\nwhich of the following regressions represents the weakest linear relationship between x and y?\nregression 1\n$y = ax + b$\n$a = 12.3$\n$b = 16.9$\n$r = 0.7329$\nregression 2\n$y = ax + b$\n$a=-9.5$\n$b = 19.8$\n$r=-0.3089$\nregression 3\n$y = ax + b$\n$a = 8.9$\n$b = 12.5$\n$r = 0.8607$\nregression 4\n$y = ax + b$\n$a = 17.9$\n$b=-10.5$\n$r = 0.6017$\nanswer\nregression 1\nregression 3\nregression 2\nregression 4

Answer

Explanation:

Step1: Recall the concept of correlation coefficient

The correlation coefficient $r$ measures the strength and direction of a linear relationship. The closer $|r|$ is to 0, the weaker the linear relationship.

Step2: Calculate the absolute - value of each $r$

For Regression 1: $|r_1| = |0.7329|=0.7329$; for Regression 2: $|r_2| = | - 0.3089| = 0.3089$; for Regression 3: $|r_3| = |0.8607| = 0.8607$; for Regression 4: $|r_4| = |0.6017| = 0.6017$.

Step3: Compare the absolute - values

We have $0.3089<0.6017<0.7329<0.8607$. Since the $|r|$ value for Regression 2 is the smallest among them, Regression 2 represents the weakest linear relationship.

Answer:

Regression 2