Question

can someone explain the ols and relationship of age and income. below is the output

DA E , av Normal No Spacing Residuals vs Fitted 40 20 Residuals OOOOO DERBO 0 -20 -40 49 Fitted values Imagss_2018Sage-gss_2018$incom 16) Call: Im(formula = gss_2018$age gss_2018$incom16) Coefficients: (Intercept) gss_2018$incom16below average 49.7037 0.1791 gss_2018$incom16average gss_2018$incom16above average -0.2757 -4.6685 gss_2018$incom 16far above average -2.8837 Call: Im(formula = gss_2018$age gss_2018$incom16) Residuals: Min 10 Median 3Q Max -31.883 -15.035 -0.883 13.965 43.965 (United States) Focus MacBook

Answer 1

Here, linear regression is run between Age and Income using function lm() in R.

Here, multiple R-squared and adjusted R-squared tell us the goodness of fit or the amount of variability Income is capable of explaining in Age. The more it is close to 1 , better is the model and more it is close to 0, poorer is the model. Here,

Multiple R-squared : 0.009128 and adjusted R-squared : 0.0003154 which is approximately 0. Hence, model is worst or cannot explain even 1% variability for Age.

Also, for various indpendent variable like Income16below average, average, above average and far above average, we have the values of corresponding coefficients that explain the model.

Age ~ 49.7037 + 0.1791 * Income16below average -0.2757*  income16average - 4.6685 * income16 above average - 2.8837 * income16far above average

Correponding t-statistics and p-value explain the significance of these individual factors in the model. Here, only income16 above average is significant. Since, only its p-value is less than the signifacnt levels (1%,5%,10%) and makes it important to the model by rejection corresponding Ho of no significance relationship.

Also, the residual plot explains Age is categorial and not linear which cannot have same variability.

Therefore, OLS is not a good idea for this model, since ages form categories or classes, one can run classification or clustering algorithms like decision trees, logistic regression, etc.