Question

# The file sapphire lists observed values of Young’s modulus (g) measured at various temperatures (T ) for sapphire rods (Ku 1969). Fit a linear relatio

Confidence intervals

The file sapphire lists observed values of Young’s modulus (g) measured at various temperatures (T ) for sapphire rods (Ku 1969). Fit a linear relationship $$\displaystyle{g}=\beta_{{{0}}}+\beta_{{{1}}}{t}$$, and form confidence intervals for the coefficients. Examine the residuals.

$$\displaystyle\overbrace{{\beta_{{{0}}}}}\pm{s}_{{\beta_{{{0}}}}}\dot{{\lbrace}}{t}_{{{22}}}{\left({0.025}\right)}={628.62878}\pm{13.42758}\dot{{\lbrace}}{2.074}={628.62878}\pm{27.8488}$$
$$\displaystyle\overbrace{{\beta_{{{1}}}}}\pm{s}_{{\beta_{{{1}}}}}\dot{{\lbrace}}{t}_{{{22}}}{\left({0.025}\right)}=-{0.61369}\pm{0.01761}\dot{{\lbrace}}{2.074}=-{0.61369}\pm{0.0365}$$