The variables are x=SP500 market monthly log return and y = monthly return of Merck 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(-0.062669, -0.165514, 0.117081, -0.098828, 0.129259, 0.027767, 0.070758, 0.077571, -0.013032, -0.022631, 0.157752, 0.01936, 0.043661, -0.034447, 0.02299, -0.063771, -0.039316, 0.048148, -0.014649, 0.020381, 0.056224, -0.013762, -0.051921, 0.055139, -0.083019, -0.018317, 0.024927, 0.085363, 0.022041, -0.029711, -0.033271, -0.030647, -0.000342, 0.053617, 0.035673, 0.064812, 0.015134, -0.002603, 0.016942, 0.021688, -0.043275, 0.116327, 0.056151, -0.025544, 0.05593, 0.011572, -0.029547, -0.069338)

For the questions below, use 3 decimal places.
Part a)
The slope of the least square regression line is
${\hat \beta}_1$=

Part b)
The lag 1 serial correlation of the residuals is: .

Part c)
The Durbin-Watson statistic applied to the residuals of the least squares line is: .

Part d)
Based on the P-value of the Durbin-Watson test for serial correlation of the residuals, the conclusion with a significance level of 0.05 is (choose one of the following).


A. There is significant negative correlation
B. Not enough information to decide on the strength of serial correlation
C. The serial correlation is not significantly different from 0
D. There is significant positive correlation

Hint: