The variables are x=SP500 market monthly log return and y = monthly return of Am

Question

The variables are x=SP500 market monthly log return and y = monthly return of American Express for 48 months beginning in January 2009.
For input into R, the data vectors for monthly market return and monthly stock return are
x=c(-0.08955, -0.116457, 0.081953, 0.089772, 0.051721, 0.000196, 0.071522, 0.033009, 0.0351, -0.01996, 0.055779, 0.017615, -0.037675, 0.028115, 0.057133, 0.014651, -0.085532, -0.055388, 0.066516, -0.048612, 0.083928, 0.036193, -0.002293, 0.063257, 0.022393, 0.031457, -0.001048, 0.028097, -0.013593, -0.018426, -0.021708, -0.058467, -0.074467, 0.102307, -0.005071, 0.008497, 0.04266, 0.039787, 0.030852, -0.007526, -0.064699, 0.038793, 0.012519, 0.019571, 0.023947, -0.019988, 0.002843, 0.007043)
and
y=c(-0.094831, -0.327553, 0.122848, 0.628447, -0.01477, -0.059504, 0.197838, 0.177291, 0.007631, 0.027493, 0.182835, -0.031815, -0.069106, 0.014097, 0.081678, 0.111456, -0.145839, 0.000267, 0.117249, -0.112987, 0.052807, -0.008864, 0.041605, -0.007102, 0.01488, 0.004349, 0.036686, 0.086333, 0.050099, 0.00546, -0.032588, -0.006479, -0.101895, 0.124084, -0.052417, -0.018101, 0.064759, 0.053416, 0.089713, 0.043379, -0.075531, 0.041759, -0.005326, 0.010095, -0.024979, -0.012179, -0.001281, 0.02781)

For the questions below, use 3 decimal places.

The variables are x SP500 market monthly log return and y monthly return of American Express for 48 months beginning in January 2009 For input into R, the data vectors for monthly market return and monthly stock return are x-c(-0.08955, -0.116457, 0.081953, 0.089772, 0.051721, 0.000196, 0.071522, 0.033009, 0.0351, -0.01996, 0.055779, 0.017615, -0.037675, 0.028115 0.057133, 0.014651, -0.085532, -0.055388, 0.066516, -0.048612, 0.083928, 0.036193, -0.002293, 0.063257, 0.022393, 0.031457,-0.001048, 0.028097, 0.013593, -0.018426, -0.021708, -0.058467, -0.074467, 0.102307, -0.005071, 0.008497, 0.04266, 0.039787, 0.030852, -0.007526, -0.064699, 0.038793, 0.012519, 0.019571, 0.023947,-0.019988, 0.002843, 0.007043) and y-c(-0.094831, -0.327553, 0.122848, 0.628447, -0.01477, -0.059504, 0.197838, 0.177291, 0.007631, 0.027493, 0.182835, -0.031815, -0.069106, 0.014097, 0.081 678. O. 111456,-0.145839, 0.000267, 0.1 17249,-0.1 12987, 0.052807,-0.008864, 0.041605,0.0071 02, 0.01488, 0.004349, 0.036686, 0.086333, 0.050099, 0.00546, -0.032588, -0.006479, -0.101895, 0.124084, -0.052417, -0.018101, 0.064759, 0.053416, 0.089713, 0.043379, -0.075531, 0.041759, -0.005326, 0.010095, -0.024979, -0.012179, -0.001281, 0.02781) For the questions below, use 3 decimal places Part a) The slope of the least square regression line is = 1.782577 Part b) The lag 1 serial correlation of the residuals is

Explanation / Answer

x=c(-0.08955, -0.116457, 0.081953, 0.089772, 0.051721, 0.000196, 0.071522, 0.033009, 0.0351, -0.01996, 0.055779, 0.017615, -0.037675, 0.028115, 0.057133, 0.014651, -0.085532, -0.055388, 0.066516, -0.048612, 0.083928, 0.036193, -0.002293, 0.063257, 0.022393, 0.031457, -0.001048, 0.028097, -0.013593, -0.018426, -0.021708, -0.058467, -0.074467, 0.102307, -0.005071, 0.008497, 0.04266, 0.039787, 0.030852, -0.007526, -0.064699, 0.038793, 0.012519, 0.019571, 0.023947, -0.019988, 0.002843, 0.007043)
y=c(-0.094831, -0.327553, 0.122848, 0.628447, -0.01477, -0.059504, 0.197838, 0.177291, 0.007631, 0.027493, 0.182835, -0.031815, -0.069106, 0.014097, 0.081678, 0.111456, -0.145839, 0.000267, 0.117249, -0.112987, 0.052807, -0.008864, 0.041605, -0.007102, 0.01488, 0.004349, 0.036686, 0.086333, 0.050099, 0.00546, -0.032588, -0.006479, -0.101895, 0.124084, -0.052417, -0.018101, 0.064759, 0.053416, 0.089713, 0.043379, -0.075531, 0.041759, -0.005326, 0.010095, -0.024979, -0.012179, -0.001281, 0.02781)
summary(lm(y~x))
Y=0.008312+1.782577*x
Y
e=resid(lm(y~x))
e
length(e)
e1=e[1:47]
e1
e2=e[2:48]
e2
cor(e1,e2)=-0.1245549

The lag 1, serial correlation of the residuals is=-0.1245549

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