To judge whether it was worthwhile to fit a parabola in

Question

To judge whether it was worthwhile to fit a parabola in Exercise 84 and not just a straight line, test the null hypothesis β₂ = 0 against the alternative hypothesis β₂  0 at the 0.05 level of significance.

Exercise 84

The following data pertain to the demand for a product (in thousands of units) and its price (in cents) charged in five different market areas:

Fit a parabola to these data by the method suggested in Exercise 83.

Exercise 83

The regression models that we introduced in Sections 2 and 6 are linear in the x's, but, more important, they are also linear in the β's. Indeed, they can be used in some problems where the relationship between the x's and y is not linear. For instance, when the regression is parabolic and of the form

we simply use the regression equation μ_Y|x = β₀ + β₁x₁ + β₂x₂ with x₁ = x and x₂ = x₂. Use this method to fit a parabola to the following data on the drying time of a varnish and the amount of a certain chemical that has been added:

Also, predict the drying time when 6.5 grams of the chemical is added.