Today in class we talked about multiple linear regression. So far, it isn’t much more complicated than simple linear regression. The only change is that there are multiple independent variables that determine the dependent variable. There is still one y, but multiple x’s. The multiple l.r. helps make a more accurate line of the data sometimes, it takes into account more of the factors that determine data points. It will be helpful when we want to do more comprehensive linear modeling, we can take into consideration more data and relationships.
We don’t have any new key equations, just slightly revised from the simple l.r. The main change is that instead of n-2 everywhere (like in the denominator of MSE), it is n-(k+1). This is because the subtraction from n is the number of betas, and in simple l.r. it was easy to do the general case–we would never have more than 2 betas.
We haven’t focused on any R code yet, so doing other specific examples beside the BAC with weight and beers will help me better understand it. We also talked more about R^2 and adjusted R^2. The main difference is that the adjusted version will penalize you for having more variables, the original one will not. From that, we can draw the conclusion that R^2 will always be greater than or equal to adjusted R^2.