Q$6(8$ points$)$

Q$6(8).$ Apply $R$ to this question, your solution must include $R$ code and $R$ output, Rmarkdown is recommended to present your solution.

Please keep you solution clear and easy to read. Unclear solution will not be graded. Please keep you solution clear and easy to read.

Unclear solution will not be grade. $0$ for manual solution.

Soluble dietary fiber$($SDF$)$ can provide health benefits by lowering blood cholesterol and glucose levels. One artical reported the followin

data on $y=SDF$ content $(\%)$ in soybean residue and the two predictors $x_1$ : extrusion temperature $($in $C),x_2$: screw speed $($in rpm$).$

$y$:$11\mathrm{.}13,10\mathrm{.}98,12\mathrm{.}56,11\mathrm{.}46,12\mathrm{.}38,12\mathrm{.}43,12\mathrm{.}55,10\mathrm{.}59,11\mathrm{.}15,10\mathrm{.}55,9\mathrm{.}25,9\mathrm{.}58,11\mathrm{.}59,10\mathrm{.}68,11\mathrm{.}73,10\mathrm{.}81,12\mathrm{.}68$

$x_1$:$35,25,30,30,30,30,30,25,30,30,30,25,35,35,35,25,30$

$x_2$:$110,130,110,130,110,110,110,110,130,90,90,90,110,90,130,110,110.$

$1(4).$ Fit the data to a regression model $y={}_0+{}_1{x}_1+{}_2{x}_2+{}_3{x}_1^2+{}_4{x}_2^2+{}_5{x}_1{x}_2+lon.$ Write the fitted model.

$2(2).$ Which variable$($s$)$ are NOT significant in predicting $y?$

$3(2).$ Find the standard error hat$()$ and adjusted R square $R_a^2$ from output.