The following problem should be implemented in MATLAB or Python and submitted to the Canvas website of the class for evaluation. Write a summary of the method you used in writing your code, explain the algorithms and syntax you have used. In your write$-$up$,$ provide the answer to any specific question asked as well as a sample of running your codes and the inputs$/$outputs$.$ Also, include your entire code in the pdf file.

Problem $1$

$17\mathrm{.}3$ Use least$-$squares regression to fit a straight line to

$\backslash$table$[[x,0,2,4,6,9,11,12,15,17,19],[y,5,6,7,6,9,8,7,10,12,12]]$

Along with the slope and intercept, compute the standard error of the estimate and the correlation coefficient. Plot the data and the regression line. Then repeat the problem, but regress $x$ versus $y$ that is$,$ switch the variables. Interpret your results.

Problem $2$

$17\mathrm{.}15$ The following data are provided

$\backslash$table$[[x,1,2,3,4,5],[y,2\mathrm{.}2,2\mathrm{.}8,3\mathrm{.}6,4\mathrm{.}5,5\mathrm{.}5]]$

You want to use least$-$squares regression to fit this data with the following model,

$y=a+bx+\frac{c}{x}$

$[$note: pseudo inverse can help with this.$]$

Problem $3$: Do problem $18\mathrm{.}2$ below only. Use Equation $18\mathrm{.}4$ from your book.

$18\mathrm{.}1$ Estimate the common logarithm of $10$ using linear interpolation.

$($a$)$ Interpolate between $log8=0\mathrm{.}9030900$ and $log12=1\mathrm{.}0791812.$

$($b$)$ Interpolate between $log9=0\mathrm{.}9542425$ and $log11=1\mathrm{.}0413927.$ For each of the interpolations, compute the percent relative error based on the true value.

$18\mathrm{.}2$ Fit a second$-$order Newton's interpolating polynomial to estimate $log10$ using the data from Prob. $18\mathrm{.}1$ at $x=8,9,$ and $11.$ Compute the true percent relative error.

Can you please create a Matlab code for these problem plz