Imagine That You Had Discovered a Relationship That Would Generate $Y _ { i } = X _ { i } ^ { 2 }$

Essay

Imagine that you had discovered a relationship that would generate a scatterplot very similar to the relationship $Y _ { i } = X _ { i } ^ { 2 }$ , and that you would try to fit a linear regression through your data points. What do you expect the slope coefficient to be? What do you think the value of your regression R² is in this situation? What are the implications from your answers in terms of fitting a linear regression through a non-linear relationship?