Question

I need help with parts A B D E and F. Please show hand work for solving A and B while D and E should be matlab codes. How do i pick the right graph for part F?

5 2 4 6 Linear spline: s fi+ (x-x) 2) Given the points 40 78 125 256 348 425 X1-x a) Write the correct linear spline equation to interpolate for x 4.72, simplifying where appropriate to get to the slope-intercept form. (4 pts) b) Perform the interpolation using the equation of (a) above. Show work (3 pts) d) Use a MATLAB built-in function to find the slope and intercept of a straight line regression (4 pts) xxs intapl e) Write the MATLAB code to plot the "shape-preserving" cubic spline along with the data points on the same plot. (5 pts) yy=intryl (x, y 4 f) Check the appropriate box to indicate which of the following y -4.5x+54.2x2- 108.5x +102 two figures represents a curve fit according to (4 pts) Explain your decision briefly. be as el I has a third deafee so t curve 4

Answer 1

2 40 78 2-S 2St 348 L42S spline e Lihear * Kgz ly.72. = .72 ies beth yo 2SE - Y = 5 K1-Ho. Y 253 548-256) (X-4) (S-4) 1 + 25乙 ニ 9202-4 I12 Spline eauatton g22 4.72 %2 - 322.24 9222-112 ret erpslated valof at is 322 24 qz472

Q. C & Q.D

MATLAB CODE------------

clc;
clear all
x=[1 2 3 4 5 6]
y=[40 78 125 256 348 425]
P=polyfit(x,y,3);
fprintf('Cubic interpolated equation is y=%d*x^3+%d*x^2+%d*x+%d\n\n\n',P)
ynew=polyval(P,x)

plot(x,y,'*')
hold on
x=1:0.01:6;
y=-4.52778*x.^3+54.2381*x.^2-108.52*x+102;
plot(x,y)
hold off
fprintf('\nLinear Regression results\n')
% Code for linear regression to find slope and intercept
P1=polyfit(x,y,1);
slope=P1(1)

intercept=P1(2)

RESULTS#############################################OUTPUT--------------------------------

x =

   1   2   3   4   5   6

y =

    40    78   125   256   348   425

Cubic interpolated equation is y=-4.52778*x^3+54.2381*x^2+-108.52*x+102


ynew =

    43.190    65.690   142.333   245.952   349.381   425.452


Linear Regression results
slope =  87.704
intercept = -100.49

500 400 300 200 100 1 2 3 A 5 6

F) Answer to F

Interpolated curve will not pass exactly through given data points hence curve 1 is correct.

Also from above matlab graph you can see