Using the data below which represents the rate of return of a certain company stock for 11? months, compared with the rate of return of a certain index of 500 stocks. Both are in percent. Treating the rate of return of the index as the explanatory? variable, x how do I determine the estimates of 0β0 and β1? Assuming the residuals are normally? distributed, how would I test whether a linear relation exists between the rate of return of the? index, x, and the rate of return for the company? stock, y, at the α=0.10 level of significance stating the null and alternative hypotheses and showing the P-value for the hypothesis test? If I'm assuming the residuals are normally? distributed, how do I then construct a? 90% confidence interval for the slope of the true? least-squares regression line and then determine the mean rate of return for the company stock if the rate of return of the index is 3.15%?
Month Rates of return of the index, x Rates of the return of the company stock, y
APR-07 4.23 3.38
MAY-07 3.25 5.09
JUN-07 -1.78 0.54
JULY-07 -3.20 2.88
AUG-07 1.29 2.69
SEP-07 3.58 7.41
OCT-07 1.48 -4.83
NOV-07 -4.40 -2.38
DEC-07 -0.86 2.37
JAN-08 -6.12 -4.27
FEB-08 -3.48 -3.77