Question

In: Computer Science

USING MATLAB: Using the data from table below fit a fourth-order polynomial to the data, but...

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

Solutions

Expert Solution

`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.

venereology answered 11 months ago
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