United Technologies versus the S&P 500 United Technologies is a conglomerate that

Chapter 14, Problem 17

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United Technologies versus the S&P 500 United Technologies is a conglomerate that includes companies such as Otis Elevators and Carrier Heating and Cooling. The ticker symbol of the company is UTX. The following data represent the rate of return of UTX stock for 11 months, compared with the rate of return of the Standard and Poors Index of 500 stocks. Both are in percent. Month Rate of Return of S&P 500, x Rate of Return in United Technologies, y Apr-10 1.48 1.82 May-10 -8.20 -9.57 Jun-10 -5.39 -3.67 Jul-10 6.88 9.53 Aug-10 -4.74 -7.72 Sept-10 8.76 9.24 Oct-10 3.69 4.97 Nov-10 -0.23 1.24 Dec-10 6.53 4.59 Jan-11 2.26 3.27 Feb-11 3.20 3.28 Source: TD Ameritrade (a) Treating the rate of return of the S&P 500 as the explanatory variable, x, determine the estimates of b0 and b1. (b) Assuming the residuals are normally distributed, test whether a linear relation exists between the rate of return of the S&P 500, x, and the rate of return for United Technologies stock, y, at the a = 0.1 level of significance. (c) Assuming the residuals are normally distributed, construct a 90% confidence interval for the slope of the true leastsquares regression line. (d) What is the mean rate of return for United Technologies stock if the rate of return of the S&P 500 is 3.25%?