please solve them manually

course : control system engineering

a) Fit a straight line (linear model, f(x)=ax+b) to the data sown in the below table b) Compute the total standard deviation (Sy) and the standard error of the estimate (Sy/x). Appendix si=i=1n(yiAiaisj)2Si=(yiy)2ss=n1Sisi=n2SpThesumofthesquaresofresidualsBWdataandregressionmodelThesumofthesquaresofresidualsBWdataandthemeanthestandarderroroftheestimateStandardDeviationoftheData Consider the following function: f(x)=x2+5x12 a) Use analytical methods to show the function has an optimum (i.e. using differentiation ) b) Check if the optimum is a maximum or minimum. c) Employ the Newton's method to find the maximum of the function f(x) using X0=2 and s=1%) Appendix: Newton Method - The optimum value of f(x) can be found by locating the root of its derivative f(x) xi+1=xif(xi)f(xi)