which of the following regressions represents the strongest positive linear relationship between $x$ and…

which of the following regressions represents the strongest positive linear relationship between $x$ and $y$?\n\nregression 1\n$y = ax + b$\n$a = 9.1$\n$b = 11.8$\n$r = 0.2804$\n\nregression 2\n$y = ax + b$\n$a = -18.5$\n$b = -1.2$\n$r = -0.8314$\n\nregression 3\n$y = ax + b$\n$a = 3.4$\n$b = 12.9$\n$r = 0.5692$\n\nregression 4\n$y = ax + b$\n$a = -6$\n$b = 0.3$\n$r = -0.5086$\n\nanswer\nregression 1\nregression 2\nregression 3\nregression 4

which of the following regressions represents the strongest positive linear relationship between $x$ and $y$?\n\nregression 1\n$y = ax + b$\n$a = 9.1$\n$b = 11.8$\n$r = 0.2804$\n\nregression 2\n$y = ax + b$\n$a = -18.5$\n$b = -1.2$\n$r = -0.8314$\n\nregression 3\n$y = ax + b$\n$a = 3.4$\n$b = 12.9$\n$r = 0.5692$\n\nregression 4\n$y = ax + b$\n$a = -6$\n$b = 0.3$\n$r = -0.5086$\n\nanswer\nregression 1\nregression 2\nregression 3\nregression 4

Answer

Explanation:

Step1: Identify positive linear relationships

A positive linear relationship requires a positive correlation coefficient ($r > 0$). $$r_1 = 0.2804, \quad r_3 = 0.5692$$

Step2: Compare the strength of positive correlations

Strength is determined by the proximity of $r$ to $1$. $$0.5692 > 0.2804$$

Step3: Select the regression with the highest $r$

Regression 3 has the highest positive $r$ value among the options. $$r = 0.5692$$

Answer:

Regression 3