(Intercept) scale(crim) scale(rm) scale(age) Original regression model > print(coef(lm(scale(medv)~scale(crim)+scale(rm)+scale(age), data=Boston))) We now apply the same model three times using the differently scaled data sets (Boston, Boston.2, Boston.3) - note the identical coefficient results: We can then compare their values to see which ones are the most important for prediction. It won't matter anymore what unit is used (crim vs crim/1000) for the data, the coefficients will end up the same. To asses the relative importance of variables we first need to perform scaling which will make all the variables comparable. Number of rooms seems way more important as we're measuring variables differently. However, in the original model there is quite a different story. If we compare the variables based on those coefficients it will seem that the crime rate is much much more important (-211.02 vs only 8.03) than the number of rooms(which is not realistic). So compare this model and the original one. > Boston.3 Boston.3$crim print(coef(lm(medv~crim+rm+age, data=Boston.3))) Then there is a big change for the rm and age coefficients. They are all scaled versions from the ones in the original model, but what if we measure for example, the crime rate per 1000? > Boston.2 Boston.2$medv print(coef(lm(medv~crim+rm+age, data=Boston.2))) The regression coefficients are totally different. Now, let's say we measure price in the dollars instead of thousands of dollars. It means that for example, that for increase in one room the medv price rises for 8.03 thousand dollars.

If we want to calculate the price for any house we just use formula: medv = -0.21102311*crim + 8.03283820*rm - 0.05224283*age So we see that the coefficients for those three predictors are -0.211, 8.03 and -0.05. Original regression model > print(coef(lm(medv~crim+rm+age, data=Boston))) The dataset for this is called Boston and it is in the MASS package > library(MASS) Let's say we want to predict median value of house expressed in thousands of $ ( medv) based on its age, number of rooms ( rm) and the crime rate ( crim) in its neighborhood.

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