Given the data below with x as the independent variable and y as the

dependent variable:

x $5101520253035404550$

y $17243133373740404241$

$($a$)$ Use least$-$squares regression to fit $($i$)$ a straight line, and $($ii$)$ a parabola without

using polyfit$()/$polyval$()$ in MATLAB or trendline in Excel $($you can use

MATLAB$/$Excel to calculate sums, inverses etc.$).$

$($b$)$ Plot the given data and the best$-$fits in two separate graphs $($one for linear fit and the other for quadratic fit$)$ in either MATLAB or Excel without using

polyfit$()/$polyval$()$ in MATLAB or trendline in Excel

$($c$)$ Calculate the r$2$ value for each fit and determine the superior fit between the two. Is the other one a $$good enough$$ fit? Typically a $95\%$ reduction in the error$/$uncertainty in data with respect to the mean can be used to determine whether a fit is $$good enough$.$

Submit relevant MATLAB$/$Excel printouts along with any hand calculations.