Chapter 8, Problem 18SE

a.

To determine

Obtain a linear model $y={\beta }_0+{\beta }_{1}x+\epsilon$.

Also obtain a residual plot and comment on the appropriateness of the model.

b.

To determine

Obtain a linear model $y={\beta }_0+{\beta }_1\ln \left(x\right)+\epsilon$.

Also obtain a residual plot and comment on the appropriateness of the model.

c.

To determine

Find the coefficients and their standard deviations for polynomial of degrees 2, 3, 4 and 5.

Obtain residual plot for each of the polynomials.

d.

To determine

Explain the reason of quartic model $y={\beta }_0+{\beta }_{1}x+{\beta }_2{x}^2+{\beta }_3{x}^3+{\beta }_4{x}^4$ is reasonable.