1. Suppose you want to understand the non-linear nature of the relationship between Y; and X;and you estimate a polynomial regression of order r of Y; on X;: Y_{i}=\beta_{0}+\beta_{1} X_{i}+\beta_{2}

X_{i}^{2}+\ldots+\beta_{r} X_{i}^{r}+\varepsilon_{i} For each of the following comparison state: 1) what r you would choose for the estimation;2) what are the null and alternative hypotheses; 3) what type of test you would use; 4) if you choose a Wald test, specify the hypotheses in terms of the matrices R and r; 5) the approximate distribution of the test statistic. a) Linear vs Quadratic Relation ɔ) Linear vs Cubic Relation c) Cubic vs Quartic Relation d) Linear vs Quartic Relation