Chapter 7, Problem 18SE

a.

To determine

Show that if the calculated value x is accurate, then $y=x+\epsilon$.

b.

To determine

Find the least-squares line $y={\widehat{\beta }}_0+{\widehat{\beta }}_{1}x$.

c.

To determine

Show that if the calculated value is accurate, then the true coefficients are ${\beta }_0=0$ and ${\beta }_1=1$.

d.

To determine

Test the null hypotheses ${\beta }_0=0$ and ${\beta }_1=1$.

e.

To determine

Check whether it is plausible that the calculated value is accurate.