let' talk about multivariate regressionwhich is little bit more complicated the idea of multivariate regression is thiswhat if there' more than one factor that influences the thing you're trying to predictin our previous exampleswe looked at linear regression we talked about predicting people' heights based on their weightfor example we assumed that the weight was the only thing that influenced their heightbut maybe there are other factors too we also looked at the effect of page speed on purchase amounts maybe there' more that influences purchase amounts than just page speedand we want to find how these different factors all combine together to influence that value so that' where multivariate regression comes in the example we're going to look at now is as follows let' say that you're trying to predict the price that car will sell for it might be based on many different features of that carsuch as the body stylethe brandthe mileagewho knowseven on how good the tires are some of those features are going to be more important than others toward predicting the price of carbut you want to take into account all of them at once so our way forwards here is still going to use the least-squares approach to fit model to your set of observations the difference is that we're going to have bunch of coefficients for each different feature that you have sofor examplethe price model that we end up with might be linear relationship of alphasome constantkind of like your -intercept wasplus some coefficient of the mileageplus some coefficient of the ageplus some coefficient of how many doors it hasonce you end up with those coefficientsfrom least squares analysiswe can use that information to figure outwellhow important are each of these features to my model soif end up with very small coefficient for something like the number of doorsthat implies that the number of doors isn' that importantand maybe should just remove it from my model entirely to keep it simpler this is something that really should say more often in this book you always want to do the simplest thing that works in data science don' over complicate thingsbecause it' usually the simple models that work the best if you can find just the right amount of complexitybut no morethat' usually the right model to go with anywaythose coefficients give you way of actually"hey some of these things are more important than others maybe can discard some of these factors