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 following data on $y=SDF$ content $(|\%$ in soybean residue and the two predictors $x_1$ :

extrusion temperature $($in ${?}^{o}C),x_2$ : screw speed $($in rpm$).$

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

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

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

$1.$ 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.

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

$3.$ Find the standard error ${}^{?}$ and adjusted $R$ square $R_a^2$ from output.