Question

Compare the preceding four simple linear regression models to determine which model is the preferred model. Use the Significance F values, p-values for independent variable coefficients, R-squared or Adjusted R-squared values (as appropriate), and standard errors to explain your selection.

	Regression1		Regression 2		Regression 3		Regression 4
Significant F Values	2.31E-31		1.06E-36		2.70E-07		0.079243652
p-values for independent variable coefficients	2.31E-31		1.06E-36		2.70E-07		0.079243652
R squared	0.601403011		0.662202192		0.16417861		0.020666911
Standard Errors-y	0.850103399		0.633569376		1.81204468		0.649109434
Standard Errors-x	0.139580202		0.181911517		0.25245326		0.038379067

Answer 1

We prefer regressions with lower p-value and f-value. Both the regressions have very low f-value and p-value, so both the regressions are significant with significant independent variable.
So until now we are unable to decide which regression to prefer.
Now, we prefer the regression with lower standard errors. Regression 1 has lower standard error for x while regression 2 has lower standard error for y.
So we still can't decide which one to prefer.
Now, we know that a better regression will have high R squared value.
Regression 2 has much higher R squared value than regression 1.
So regression 2 is preferred.
Thank you