The diameter, height, and volume of 31 black cherry trees in allegheny national forest are recorded: diameter height volume8.3 70 10.38.6 65 10.38.8 63 10.210.5 72 16.410.7 81 18.810.8 83 19.711 66 15.611 75 18.211.1 80 22.611.2 75 19.911.3 79 24.211.4 76 2111.4 76 21.411.7 69 21.312 75 19.112.9 74 22.212.9 85 33.813.3 86 27.413.7 71 25.713.8 64 24.914 78 34.514.2 80 31.714.5 74 36.316 72 38.316.3 77 42.617.3 81 55.417.5 82 55.717.9 80 58.318 80 51.518 80 5120.6 87 77colnamecountdescriptionc1diameter 31diameter of tree in inches (measured at 4.5 feet above ground)c2height31height of treec3volume31volume of tree in cubic feetusing minitab to answer the following questions: a) fit the least squares regression line to predict volume from diameter using minitab. b) test the significance for the slope coefficient in the above fitted line. c) do a scatter plot of the volume and the diameter with the regression line plotted on the same graph. d) what percentage of the total variation of volume is explained by the diameter? e) find a 95% confidence interval for the mean volume when the diameter = 10.f) find a 95% prediction interval for the volume when the diameter = 10.g) calculate the correlation coefficients between volume and the diameter using minitab. test the hypothesis that the variables are uncorrelated for this pair of variables. best answer