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Use the following question to comment on its answer below:

What are some ways to identify that a quadratic term is needed in a multiple regression model? Comment on the importance of using quadratic terms in models when it is determined that one is in fact needed. Suppose you are given a quadratic model of the form:

 y=β_0+β_1 x+β_2 x^2+ε

Is the model valid for all values of x? Use examples to support your conclusions.

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"To identify if the quadratic is good for your data, you can take your data and create a scatter plot to look for curved trends, then you could possibly fit a quadratic more accurately than a linear model. I actually use quadratic models all the time at work, we have a metric that is spit out when focusing cameras that creates a upside down U shape (perfect parabola) and to find the peak of the data without noise or outliers, previously we were fitting linear regressions to both sides of our parabola to get the intersection of those lines and then estimating the point of the highest value of this metric. That was not working out that well so we switched and fit a quadratic to it and it does a much better job, finding the highest point without taking in all of the noise from the system.

The quadratic model is only valid for the x values that are inside the sample set. In our book it says that we can interpret β_0 only if the x value is in the sample data set, otherwise we can not conclude it is accurate. The same goes for basing conclusions on the models prediction past the data set on this model. I believe it is more of a technique to clarify current data and less about determining what past or future data will be."

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