Help with an interpolation problem

Given the (fictitious) gasoline price data over 10 years,

Year, x 1986 1988 1990 1992 1994 1996

Price (¢),y 113.5 132.2 138.7 141.5 137.6 144.2

a simple interpolating polynomial is proposed as:

y(x) = c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5

Find and plot the interpolating polynomials of gasoline prices by

(a) Solving system of equations
(b) Using Lagrange polynomial
(c) Using Newton polynomial

(Note: Use the MATLAB command format long e to clearly identify the differences between the values of the coefficients produced by using different methods.)

Here is my code for lagrange:

%Given data points

x=[1986 1988 1990 1992 1994 1996];

y=[113.5 132.2 138.7 141.5 137.6 144.2];

%Find the Lagrange polynomial

[l,L]=lagranp(x,y);

disp(' (1) Lagrange coefficient polynomials:'),L

disp(' (2) Lagrange polynomial coefficients:'),l

%Create an xx vector [0 4] and define xi=1 which is the point of interest

xx=[1986:0.1:1996];

%Interpolate for xx 

yy=polyval(l,xx);

%Plot the polynomial

plot(xx,yy,'r',x,y,'d-'), grid on

xlabel('x'),ylabel('y')

title('Lagrange Plot')

I'm not sure my plot is right because there is two lines one the graph

Here is my code for newton:

%Given data points

x=[1986 1988 1990 1992 1994 1996];

y=[113.5 132.2 138.7 141.5 137.6 144.2];

%Find the Newton polynomial

[n,D]=newtonp(x,y);

disp(' (1) Newton polynomial coefficients:'),n

disp(' (2) Newton divided differences:'),D

%Create an xx vector and point to evaluate the function at

xx=1986:1996;

%Interpolate for xx

yy=polyval(n,xx);

%Plot the polynomial

plot(xx,yy,'b',x,y,'d'), grid on

xlabel('x'),ylabel('y')

title('newton')

I'm pretty sure this is right but I'm not 100% sure

Also I'm not quite sure how to do this for system of equations

[Walter Roberson]

That interpolating polynomial is probably wrong. Where are the second powers and so on?

[Steven]

That's all the information I'm given and all the information I need to solve this problem. I'm not quite sure how to interpolate using system of equations

[Jan]

I'm sure also, that "y(x)= c0 + c1x + c2x + c3x + c4x + c5x" is not a valid interpolation polynomial.

[Walter Roberson]

If we understand c1x to be c subscript 1, multiplied by x, then

y(x) = c0 + (c1 + c2 + c3 + c4 + c5) * x

which would simplify to

y(x) = c0 + c6 * x

when c6 = c1 + c2 + c3 + c4 + c5

This could be done, but you would not be able to meaningfully extract c1, c2, c3, c4, c5 from it.

A different polynomial would make more sense:

y(x) = c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5

[Steven]

Ok, yeah that's what it says in my textbook. I must have typed in the equation wrong sorry. It should read

y(x) = c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5

So would the years correspond to the x values in the equation?

Am I suppose to make a matrix with values of x and a matrix with values of y? But then what am I suppose to set them to?