Chapter 12.6, Problem 102E

a.

To determine

Use the centered model to estimate the coefficients of the uncentered model.

Find the predicted value of y for $x=285°\text{F}$.

Fit the model $Y={\beta }_0^{*}+{\beta }_1^{*}{x}^{\prime }+{\beta }_{11}^{*}{\left(x^{\prime }\right)}^2+\in$ by using the standardized variable $x^{\prime }=\frac{x-\overline{x}}{s_x}$, where $s_x$ is the standard deviation of x.

b.

To determine

Find the predicted value of y for $x=285°\text{F}$.

c.

To determine

Use the standardized model to estimate the coefficients of the unstandardized model,$Y={\beta }_0+{\beta }_{1}x+{\beta }_{11}{x}^2+\in$.

d.

To determine

Identify the relationship between $S{S}_E$ and $R^2$ for the standardized and unstandardized models.

e.

To determine

Fit a model with the standardized response variable $y^{\prime }=\frac{y-\overline{y}}{s_y}$ to $x^{\prime }$.

Identify the relationship between $S{S}_E$ and $R^2$ for the standardized and unstandardized models.