Date DJIA S&P 500 Day 1 35405.24 4536.54 Day 2 35629.33 4579.38 Day 3 35111.16 4467.44 Day 4 35089.74 4510.53 Day 5 35091.13 4493.87 Day 6 35462.78 4511.54 Day 7 35768.06 4577.18 Day 8 35241.59 4514.08 Day 9 34738.06 4408.64 Day 10 34566.17 4411.67 Day 11 34988.84 4461.07 Day 12 34934.27 4485.01 Day 13 34312.03 4390.26 Day 14 34079.18 4358.87 Day 15 33596.61 4314.76 Day 16 33131.76 4235.50 Day 17 33223.83 4278.70 Day 18 34058.75 4394.65 Day 19 33892.60 4363.94 Day 20 33294.95 4316.26 Day 21 33891.35 4396.54 Day 22 33794.66 4353.49 Day 23 33614.80 4318.87 Day 24 32817.38 4211.09 Day 25 32632.64 4180.70 Day 26 33286.25 4287.88 Day 27 33174.07 4249.52 Day 28 32944.19 4194.31 Day 29 32945.24 4183.11 Day 30 33544.34 4252.45 Day 31 34063.10 4367.86 Day 32 34480.76 4421.67 Day 33 34754.93 4473.12 Day 34 34552.99 4471.18 Day 35 34807.46 4521.61 Day 36 34358.50 4466.24 Day 37 34707.94 4510.16 Day 38 34861.24 4553.06 Day 39 34955.89 4585.52 Day 40 35294.19 4641.60 Day 41 35228.81 4592.45 Day 42 34678.35 4540.41 Day 43 34818.27 4555.86 Day 44 34921.88 4572.64 Day 45 34641.18 4515.12 Day 46 34496.51 4491.15 Day 47 34583.57 4490.21 Day 48 34721.12 4498.28 Day 49 34308.08 4402.53 Day 50 34220.36 4387.45 Day 51 34564.59 4436.59 Day 52 34451.23 4382.59 Day 53 34411.69 4401.69 Day 54 34911.20 4452.21 Day 55 35160.79 4469.45 Day 56 34792.76 4383.66 Day 57 33811.40 4281.78 Day 58 34049.46 4286.12 Day 59 33240.18 4165.20 Day 60 33301.93 4193.96 Day 61 33916.39 4297.50 Day 62 32977.21 4121.93 Day 63 33061.50 4165.38 Day 64 33128.79 4185.48 Day 65 34061.06 4290.17 Day 66 32997.97 4156.87 Day 67 32899.37 4133.34 Day 68 32245.70 4001.24 Day 69 32160.74 4011.05 Day 70 31834.11 3945.18 Day 71 31730.30 3920.08 Day 72 32196.66 4033.89 Day 73 32223.42 4018.01 Day 74 32654.59 4098.85 Day 75 31490.07 3913.68 Day 76 31253.13 3890.79 Day 77 31261.90 3911.36 Day 78 31880.24 3983.75 Day 79 31928.62 3951.48 Day 80 32120.28 3968.73 Day 81 32637.19 4047.84 Day 82 33212.96 4168.24 Day 83 32990.12 4142.15 Day 84 32813.23 4091.23 Day 85 33248.28 4186.82 Day 86 32899.70 4098.54 Day 87 32915.78 4111.43 Day 88 33180.14 4170.68 Day 89 32910.90 4105.77 Day 90 32272.79 4027.82 Day 91 31392.79 3890.86 Day 92 30516.74 3739.63 Day 93 30364.83 3725.48 Day 94 30668.53 3779.99 Day 95 29927.07 3656.77 Day 96 29888.78 3664.84 Day 97 30530.25 3774.79 Day 98 30483.13 3749.89 Day 99 30677.36 3785.73 Day 100 31500.68 3901.74 Day 101 31438.26 3910.11 Day 102 30946.99 3811.55 Day 103 31029.31 3828.83 Day 104 30775.43 3795.38 Day 105 31097.26 3835.33 Day 106 30967.82 3821.39 Day 107 31037.68 3855.08 Day 108 31384.55 3892.62 Day 109 31338.15 3909.38 Day 110 31173.84 3844.43 Day 111 30981.33 3808.80 Day 112 30772.79 3811.78 Day 113 30630.17 3780.38 Day 114 31288.26 3873.16 Day 115 31072.61 3820.85 Day 116 31827.05 3926.69 Day 117 31874.84 3969.90 Day 118 32036.90 4008.95 Day 119 31899.29 3951.63 Day 120 31990.04 3956.84 Day 121 31761.54 3931.05 Day 122 32197.59 4033.61 Day 123 32529.63 4062.43 Day 124 32845.13 4140.29 Day 125 32798.40 4128.63 Day 126 32396.17 4101.19 Day 127 32812.50 4145.17 Day 128 32726.82 4161.94 Day 129 32803.47 4135.19 Day 130 32832.54 4150.06 Day 131 32774.41 4112.47 Day 132 33309.51 4200.24 Day 133 33336.67 4197.27 Day 134 33761.05 4290.15 Day 135 33912.44 4287.14 Day 136 34152.01 4295.20 Day 137 33980.32 4264.04 Day 138 33999.04 4273.74 Day 139 33706.74 4238.48 Day 140 33063.61 4147.99 Day 141 32909.59 4138.73 Day 142 32969.23 4130.77 Day 143 33291.78 4189.12 Day 144 32283.40 4067.66 The Dow Jones Industrial Average (DJIA) and the Standard & Poor's 500 (S&P 500) indexes are used as measures of overall movement in the stock market. The DJIA is based on the price movements of 30 large companies; the S&P 500 is an index composed of 500 stocks. Some say the S&P 500 is a better measure of stock market performance because it is broader based. Suppose the closing price for the DJIA and the S&P 500 for 144 days in a certain year are as provided in the file closingprices4.xlsx. (b) Develop an estimated linear regression equation showing how S&P 500 (y) is related to DJIA (x). What is the estimated linear regression model? (Round your numerical values to four decimal places.) ŷ =        (c) What is the 95% confidence interval for the parameter ?1? (Round your answers to three decimal places.)  to  Based on this interval, what conclusion can you make about the hypotheses that the parameter ?1 is equal to zero? (Make your conclusion regardless of any validity concerns.) Because this interval     include zero, we     the hypothesis that ?1 = 0. (d) What is the 95% confidence interval for the parameter ?0? (Round your answers to three decimal places.)  to  Based on this interval, what conclusion can you make about the hypotheses that the parameter ?0 is equal to zero? (Make your conclusion regardless of any validity concerns.) Because this interval     include zero, we     the hypothesis that ?0 = 0. (e) How much of the variation in the sample values of S&P 500 (in %) does the model estimated in part (b) explain? (Round your answer to two decimal places.)  % (f) Suppose that the closing price for the DJIA is 38,900. Estimate the closing price for the S&P 500 using the linear regression model you estimated in part (b). (Round your answer to the nearest integer.)