Question

USING MATLAB:

Using the data from table below fit a fourth-order polynomial to the data, but use a label for the year starting at 1 instead of 1872. Plot the data and the fourth-order polynomial estimate you found, with appropriate labels. What values of coefficients did your program find? What is the LMS loss function value for your model on the data?

Year Built	SalePrice
1885	122500
1890	240000
1900	150000
1910	125500
1912	159900
1915	149500
1920	100000
1921	140000
1922	140750
1923	109500
1925	87000
1928	105900
1929	130000
1930	138400
1936	123900
1938	119000
1939	134000
1940	119000
1940	244400
1942	132000
1945	80000
1948	129000
1950	128500
1951	141000
1957	149700
1958	172000
1959	128950
1960	215000
1961	105000
1962	84900
1963	143000
1964	180500
1966	142250
1967	178900
1968	193000
1970	149000
1971	149900
1972	197500
1974	170000
1975	120000
1976	130500
1977	190000
1978	206000
1980	155000
1985	212000
1988	164000
1990	171500
1992	191500
1993	175900
1994	325000
1995	236500
1996	260400
1997	189900
1998	221000
1999	333168
2000	216000
2001	222500
2002	320000
2003	538000
2004	192000
2005	220000
2006	205000
2007	306000
2008	262500
2009	376162
2010	394432

Answer 1

`Hey,

Note: Brother if you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

clear all
clc
M=load('aa.txt');
n=size(M,1);
x=[13, 18, 28, 38, 40, 43, 48, 49, 50, 51, 53, 56, 57, 58, 64, 66, 67, 68, 68, 70, 73, 76, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 94, 95, 96, 98, 99, 100, 102, 103, 104, 105, 106, 108, 113, 116, 118, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138]+1;
y=[122500, 240000, 150000, 125500, 159900, 149500, 100000, 140000, 140750, 109500, 87000, 105900, 130000, 138400, 123900, 119000, 134000, 119000, 244400, 132000, 80000, 129000, 128500, 141000, 149700, 172000, 128950, 215000, 105000, 84900, 143000, 180500, 142250, 178900, 193000, 149000, 149900, 197500, 170000, 120000, 130500, 190000, 206000, 155000, 212000, 164000, 171500, 191500, 175900, 325000, 236500, 260400, 189900, 221000, 333168, 216000, 222500, 320000, 538000, 192000, 220000, 205000, 306000, 262500, 376162, 394432];
C=polyfit(x,y,4);
disp('Coefficients of 4th order polynomial with 1872 as year 1');
disp(C);
xx=1:1:140;
yy=polyval(C,xx);
plot(x,y,'o',xx,yy);
xlabel('Year starting 1872 as 1');
ylabel('Sale Price');
disp('LMS is');
sum((y-polyval(C,x)).^2)

Kindly revert for any queries

Thanks.