An Experiment to Measure the Macroscopic Magnetic Relaxation Time in Crystals

An experiment to measure the macroscopic magnetic relaxation time in crystals $$\text { ( } \mu \mathrm { sec } )$$ as a function of the strength of the external biasing magnetic field (KG) yielded the following data $\begin{array}{l}\begin{array} { l l l l l l l } \hline x & 11.0 & 12.5 & 15.2 & 17.2 & 19.0 & 20.8 \\\hline y & 187 & 225 & 305 & 318 & 367 & 365 \\\hline\end{array}\\\\\begin{array} { l l l l l l } \hline x & 22.0 & 24.2 & 25.3 & 27.0 & 29.0 \\\hline y & 400 & 435 & 450 & 506 & 558 \\\hline\end{array}\end{array}$ The summary statistics are $$\sum x _ { i } = 223.2 , \sum y _ { i } = 4116 , \sum x _ { i } ^ { 2 } = 4877.50 , \sum x _ {i } y _ { i } = 90,096.1$$ and $\sum y _ { i } ^ { 2 } = 1,666,782$ Compute the following:
a. A 95% CI for expected relaxation time when field strength equals 18.
b. A 95% PI for future relaxation time when field strength equals 18.
c. Simultaneous confidence intervals for expected relaxation time when field strength equals 15, 18, and 20; your joint confidence coefficient should be at least 97%.