SOLVE A$,$ B$,$ AND C PLEASE $12$

Suppose a bridge's displacement due to vibration as a function of time follows the equation

$y(t)=a_{1}sin(t)+a_{2}cos(t).$

$7$

$($a$)$ Estimate $a_1$ and $a_2$ using linear least squares fitting to the data below $($and$,$ e$.$g$.,$ solving the normal equations$)$ if it is known that $=0\mathrm{.}7$

$($b$)$ Find RSS$,R^2,$ adjusted $R^2,$ and AIC score for this fit.

$($c$)$ Based on your regression model, estimate $)=(7.$

$($d$)$ Write Python code to estimate $$ along with $a_1$ and $a_2$ using nonlinear least squares fitting.

$t,1,2,3,4,5$

$y,71,160,175,107,-11$