A box office analyst seeks to predict opening weekend box office gross for movies. Toward this goal, the analyst plans to use online trailer views as a predictor. For each of the 66 movies, the number of online trailer views from the release of the trailer through the Saturday before a movie opens and the opening weekend box office gross (in millions of dollars) are collected and stored in the accompanying table. The least-squares regression equation for these data isYi=−0.914+1.408Xi and the standard error of the estimate is SYX=19.887. Assume that the straight-line model is appropriate and there are no serious violations the assumptions of the least-squares regression model. Compute the test statistic. Online TrailerViews (millions)60.6949.18210.5509.36881.46232.87523.6745.7192.55342.76710.44128.7077.17859.1086.70012.32212.3410.2961.0953.4425.2516.36129.1131.7631.2029.92650.9385.77531.3388.92813.28859.24382.236Opening WeekendBox Office Gross($millions)29.6336.4834.85426.972107.04161.95715.5568.53110.93239.76716.90611.8724.141146.42116.0506.6683.8717.9970.5360.8372.4224.182102.3021.06310.07611.55646.4410.56519.0316.20512.50240.300174.751Online TrailerViews (millions)3.76535.5860.10041.5374.9896.6300.9422.25811.3278.96615.17713.71431.23152.61216.2356.88411.6982.82723.07512.6060.82627.5367.2733.3234.2673.7907.59712.9127.0675.0207.73916.7957.643Opening WeekendBox Office Gross($millions)4.13761.02516.17288.4124.69033.3773.7051.51318.47012.2024.35730.43653.00346.60713.0033.77618.2233.47113.60240.0111.38520.1303.4041.20710.9518.34411.61413.5015.1061.98522.80013.6892.080

The least-squares regression equation for these data is, Yi=−0.914+1.408Xi online trailer views(millions)(Xi) Opening Weekend Box office gross ($millions)(YI) Yi=-0.914+1.408Xi (Y-Y^i) (Y-Y^i)2 (Xi-X¯)2=(Xi-17.26943939)2 60.694 29.633 84.543152 -54.910152 3015.124793 1885.692464 9.182 6.483 12.014256 -5.531256 30.59479294 65.40667595 10.55 4.854 13.9404 -9.0864 82.56266496 45.15086577 9.368 26.972 12.276144 14.695856 215.9681836 62.4327445 81.462 107.041 113.784496 -6.743496 45.4747383 4120.684837 32.875 61.957 45.374 16.583 274.995889 243.5335218 23.674 15.556 32.418992 -16.862992 284.3604992 41.01839656 5.719 8.531 7.138352 1.392648 1.939468452 133.4126502 2.553 10.932 2.680624 8.251376 68.08520589 216.5735884 42.767 39.767 59.301936 -19.534936 381.6137245 650.1255969 10.441 16.906 13.786928 3.119072 9.728610141 46.62758456 28.707 11.872 39.505456 -27.633456 763.6078905 130.8177926 7.178 4.141 9.192624 -5.051624 25.51890504 101.837149 59.108 146.421 82.310064 64.110936 4110.212115 1750.465154 6.7 16.05 8.5196 7.5304 56.70692416 111.7130491 12.322 6.668 16.435376 -9.767376 95.40163393 24.47715656 12.341 3.871 16.462128 -12.591128 158.5365043 24.28951486 0.296 7.997 -0.497232 8.494232 72.15197727 288.0976449 1.095 0.536 0.62776 -0.09176 0.008419898 261.6124897 3.442 0.837 3.932336 -3.095336 9.581104953 191.1980802 5.251 2.422 6.479408 -4.057408 16.46255968 144.4428855 6.361 4.182 8.042288 -3.860288 14.90182344 118.99405 29.113 102.302 40.077104 62.224896 3871.937682 140.2699278 1.763 1.063 1.568304 -0.505304 0.255332132 240.4496627 1.202 10.076 0.778416 9.297584 86.44506824 258.1626087 9.926 11.556 13.061808 -1.505808 2.267457733 53.92610213 50.938 46.441 70.806704 -24.365704 593.6875314 1133.571973 5.775 0.565 7.2172 -6.6522 44.25176484 132.122137 31.338 19.031 43.209904 -24.178904 584.6193986 197.9243975 8.928 6.205 11.656624 -5.451624 29.72020424 69.57961116 13.288 12.502 17.795504 -5.293504 28.0211846 15.85185965 59.243 40.3 82.500144 -42.200144 1780.852154 1761.77979 82.236 174.751 114.874288 59.876712 3585.22064 4220.653997 3.765 4.137 4.38712 -0.25012 0.062560014 182.3698833 35.586 61.025 49.191088 11.833912 140.0414732 335.4963924 0.1 16.172 -0.7732 16.9452 287.139803 294.7896491 41.537 88.412 57.570096 30.841904 951.2230423 588.9144978 4.989 4.69 6.110512 -1.420512 2.017854342 150.8091917 6.63 33.377 8.42104 24.95596 622.7999395 113.1976706 0.942 3.705 0.412336 3.292664 10.84163622 266.5852772 2.258 1.513 2.265264 -0.752264 0.565901126 225.3433127 11.327 18.47 15.034416 3.435584 11.80323742 35.31258595 8.966 12.202 11.710128 0.491872 0.241938064 68.94710577 15.177 4.357 20.455216 -16.098216 259.1525584 4.378302617 13.714 30.436 18.395312 12.040688 144.9781675 12.64114928 31.231 53.003 43.059248 9.943752 98.87820384 194.9251746 52.612 46.607 73.163696 -26.556696 705.2581024 1249.09659 16.235 13.003 21.94488 -8.94188 79.95721793 1.07006486 6.884 3.776 8.778672 -5.002672 25.02672714 107.8573514 11.698 18.223 15.556784 2.666216 7.108707759 31.04093692 2.827 3.471 3.066416 0.404584 0.163688213 208.5840556 23.075 13.602 31.5756 -17.9736 323.050297 33.70453395 12.606 40.011 16.835248 23.175752 537.1154808 21.74766698 0.826 1.385 0.249008 1.135992 1.290477824 270.3866991 27.536 20.13 37.856688 -17.726688 314.2354674 105.4022667 7.273 3.404 9.326384 -5.922384 35.07463224 99.92880056 3.323 1.207 3.764784 -2.557784 6.542258991 194.5031718 4.267 10.951 5.093936 5.857064 34.3051987 169.0634302 3.79 8.344 4.42232 3.92168 15.37957402 181.6952864 7.597 11.614 9.782576 1.831424 3.354113868 93.55608383 12.912 13.501 17.266096 -3.765096 14.17594789 18.98727807 7.067 5.106 9.036336 -3.930336 15.44754107 104.0897696 5.02 1.985 6.15416 -4.16916 17.38189511 150.0487655 7.739 22.8 9.982512 12.817488 164.2879986 90.82927504 16.795 13.689 22.73336 -9.04436 81.80044781 0.225092739 7.643 2.08 9.847344 -7.767344 60.33163281 92.66833541 SUM:1139.783 1544.809 1544.490464 0.318536 25311.85057 24581.09161 From the above table, ∑i=166(Xi-X¯)2=24581.09161 ∑i=166(Y-Y^i)2=25311.85057 The standard error of β1 is, se(β1)=1n-2×∑i=166(Y-Y^i)2∑i=166(Xi-X¯)2 =166-2×25311.8505724581.09161=0.016089508=0.126844 From the given regression line, the slope coefficient is, β^1=1.408. The null hypothesis is,Ho:β1=0 The alternative hypothesis is, H1:β1≠0 The test statistic is, t=β^1-β1se(β1) =1.408-00.126844 =11.100( rounded to three decimals)