A study was carried out to relate time to failure (y) of a certain machine component to the variables operating voltage

(x1), motor speed (x2), and operating temperature (x3). The resulting data set consisted of n
20 observations. When the model with the three variables x1, x2, and x3 was fit to the data, the value of error sum of squares was 8212.5. Fitting the second-order interaction model (with quadratic predictors and all products of pairs of variables) gave an error sum of squares of 5027.1. Should at least one of the quadratic or interaction predictors be retained in the model? State and test the relevant hypotheses.