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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
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asked 2021-06-08

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.

Answers (1)

2021-06-09
The regression line is y=628.6287753-0.6136894x.
Intervals are:
\(\displaystyle\overbrace{{\beta_{{{0}}}}}\pm{s}_{{\beta_{{{0}}}}}\dot{{\lbrace}}{t}_{{{22}}}{\left({0.025}\right)}={628.62878}\pm{13.42758}\dot{{\lbrace}}{2.074}={628.62878}\pm{27.8488}\)
\(\displaystyle\overbrace{{\beta_{{{1}}}}}\pm{s}_{{\beta_{{{1}}}}}\dot{{\lbrace}}{t}_{{{22}}}{\left({0.025}\right)}=-{0.61369}\pm{0.01761}\dot{{\lbrace}}{2.074}=-{0.61369}\pm{0.0365}\)
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