Question

X are X1 = X3 = y Total Derived Employment, GNP Implicit Price Deflater, X2 Gross National Product, Unemployment, 24 Size of Armed Forces, X5 Noninstitutional Population Age 14 and Over, Year. The objective is to predict y by a linear combination of a constant and the six x's: y aBo + Bkxk. 26 = 6 1 (a) Use the MATLAB backslash operator to compute Bo,B1, ..., B6. This involves augmenting X with a column of all l’s, corresponding to the constant term. (b) Compare your B’s with the certified values [3]. (c) Use errorbar to plot y with error bars whose magnitude is the difference between y and the least squares fit. (d) Use corrcoef to compute the correlation coefficients for X without the column of 1's. Which variables are highly correlated? (e) Normalize the vector y so that its mean is zero and its standard deviation is one. You can do this with y = y mean(y); y = y/std(y) Do the same thing to the columns of X. Now plot all seven normalized vari- ables on the same axis. Include a legend.

DATASET

 y       x1      x2      x3       x4       x5     x6
60323    83.0   234289   2356     1590    107608  1947
61122    88.5   259426   2325     1456    108632  1948
60171    88.2   258054   3682     1616    109773  1949
61187    89.5   284599   3351     1650    110929  1950
63221    96.2   328975   2099     3099    112075  1951
63639    98.1   346999   1932     3594    113270  1952
64989    99.0   365385   1870     3547    115094  1953
63761   100.0   363112   3578     3350    116219  1954
66019   101.2   397469   2904     3048    117388  1955
67857   104.6   419180   2822     2857    118734  1956
68169   108.4   442769   2936     2798    120445  1957
66513   110.8   444546   4681     2637    121950  1958
68655   112.6   482704   3813     2552    123366  1959
69564   114.2   502601   3931     2514    125368  1960
69331   115.7   518173   4806     2572    127852  1961
70551   116.9   554894   4007     2827    130081  1962

Answer 1

`Hey,

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

clc

clear all

close all

A=[60323 83.0 234289 2356 1590 107608 1947

61122 88.5 259426 2325 1456 108632 1948

60171 88.2 258054 3682 1616 109773 1949

61187 89.5 284599 3351 1650 110929 1950

63221 96.2 328975 2099 3099 112075 1951

63639 98.1 346999 1932 3594 113270 1952

64989 99.0 365385 1870 3547 115094 1953

63761 100.0 363112 3578 3350 116219 1954

66019 101.2 397469 2904 3048 117388 1955

67857 104.6 419180 2822 2857 118734 1956

68169 108.4 442769 2936 2798 120445 1957

66513 110.8 444546 4681 2637 121950 1958

68655 112.6 482704 3813 2552 123366 1959

69564 114.2 502601 3931 2514 125368 1960

69331 115.7 518173 4806 2572 127852 1961

70551 116.9 554894 4007 2827 130081 1962];

y=A(:,1);

L=[ones(size(A,1)),A(:,2:7)];

R=y(:);

disp('Coefficients are')

beta=L\R

err=abs(y-L*beta);

errorbar(y,err)

y=y-mean(y);

y=y/std(y);

figure;

hold on;

for i=2:7

x=A(:,i);

x=x-mean(x);

x=x/std(x);

plot(x,y);

end

legend('x1 vs y','x2 vs y','x3 vs y','x4 vs y','x5 vs y','x6 vs y')

MATLAB R2020a - academic use HOME FA Search Documentation Prad OOO Figure 1 File Edit View Insert Insert Tools Desktop Window Help Figure 2 Tools Desktop Window Help File Edit View Insert Hew Ope un an dvand x 104 72 1.5 7 AB/si e x1 vs y x2 vs y x3 vs y x4 vs y x5 vs y x6 vs y E 1 6.8 Current Nam scral scral scra scra scral seas seca 0.5 Value 16x7 double 22x1 double 16x1 double 7 16x22 double 16x1 double 16x1 double 16x1 double 6.6 0 seca -0.5 62 -1 6 2 4 6 8 10 12 14 16 -1.5 -2 -1.5 -1 -0.5 0 0.5 1.5 2 Seca 6.4 seca seco selec selec selec serie shift shin shoc side_len.m sieve.m Simp.m simple_gui2.m simple_gui2.prj simps.m simpson_comp.m SimpsonComp.m SimpsonComp.prj simpsons.m Simp ThreeEight.m sine_series.m sinhRec.m sinN.m sinoperations.m crap_cse.prj (Document) X 1圈圈圈圈圈圈圈圈圈圈 34 x=x/std(x); 35 - plot(x,y); 36 - end 37 - legend('x1 vs y','x2 vs y','x3 vs y','x4 vs y','x5 vs y', 'x6 vs y') Command Window New to MATLAB? See resources for Getting Started. 0.000015061872271 -0.000000035819179 -0.000002020229804 -0.000001033226867 -0.000000051104106 0.001829151464613 fx >>

Kindly revert for any queries

Thanks.