Pre-historic pottery vessels are usually found as sherds (broken pieces) and are carefully re-constructed if enough sherds can be found. An archaeological study provides data relating x = body diameter in centimeters and y = height in centimeters of prehistoric vessels re-constructed from sherds found at a pre-historic site. The following Minitab printout provides an analysis of the data. Predictor Coef SE Coef T PConstant -0.251 2.429 -0.09 0.929Diameter 0.7581 0.1471 3.74 0.005S = 4.07980 R-Sq = 70.0%A) Minitab calls the explanatory variable the predictor variable. Which is the predictor variable, the diameter of the pot or the height?B) For the least-squares line y = a + bx, what is the value of the constant a? What is the value of the slope b?C) The P-value for a two-tailed test corresponding to each coefficient is listed under P. The t value corresponding to the coefficient is listed under T. What is the P-value of the slope?D) What are the hypotheses for a two-tailed test of β = 0?1. H0: β < 0; H1: β = 0H0: β ≠ 0; H1: β = 0 2. H0: β = 0; H1: β < 0H0: β = 0; H1: β > 03. H0: β = 0; H1: β ≠ 0E) Based on the P-value in the printout, do we reject or fail to reject the null hypothesis for α = 0.01?1. Reject the null hypothesis. There is sufficient evidence that β differs from 02. Fail to reject the null hypothesis. There is insufficient evidence that β differs from 0. 3. Fail to reject the null hypothesis. There is sufficient evidence that β differs from 0.4.Reject the null hypothesis. There is insufficient evidence that β differs from 0.F) Recall that the t value and resulting P-value of the slope b equal the t value and resulting P-value of the corresponding correlation coefficient r. To find the value of the sample correlation coefficientr, take the square root of the "R-Sq" value shown in the display. What is the value of r?G) Consider a two-tailed test for r. Based on the P-value shown in the Minitab display, is the correlation coefficient significant at the 1% level of significance?1. No, the correlation coefficient is not significant at the α = 0.01 level because the P-value ≤ α.2. Yes, the correlation coefficient is significant at the α = 0.01 level because the P-value > α. 3. Yes, the correlation coefficient is significant at the α = 0.01 level because the P-value ≤ α.4. No, the correlation coefficient is not significant at the α = 0.01 level because the P-value > α.