Computer programming problem$)$

$($a$)$ Find the least squares quadratic polynomial for the data using basis $\backslash$phi $1($t$)=$

$1,\backslash$phi $2($t$)=$ t$,$ and $\backslash$phi $3($t$)=$ t$2.$ Plot the solution and the data points.

ti $-1-0\mathrm{.}75-0\mathrm{.}500\mathrm{.}250\mathrm{.}50\mathrm{.}75$

yi $1\mathrm{.}000\mathrm{.}81250\mathrm{.}751\mathrm{.}001\mathrm{.}31251\mathrm{.}752\mathrm{.}3125$

$($b$)$ Find the least squares linear polynomials for the two sets of data using the

basis $\backslash$phi $1($t$)=50,$ and $\backslash$phi $2($t$)=$ t$1065.$ Notice that the QR decomposition

only needs to be done once. Plot your solutions and the data points.

ti $100010501060108011101130$

$(1)$yi $601061536421639967266701$

$(2)$yi $942293009220915090428800$

$1$