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# DATASET y x1 x2 x3 x4 x5 x6 60323 83.0 234289 2356 1590 107608 1947 61122...

## Question

###### DATASET y x1 x2 x3 x4 x5 x6 60323 83.0 234289 2356 1590 107608 1947 61122...

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`
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.

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