Prehistoric pottery vessels are usually found as sherds (broken pieces) and are carefully reconstructed 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 reconstructed from sherds found at a prehistoric site. The following Minitab printout provides an analysis of the data. Predictor Coef SE Coef T Constant -0. 206 2. 429 -0 . 09 0.929 Diameter 0 . 7662 0 . 1471 5. 09 0 . 001 S 4. 07980 R-Sq 81.28 (a) Minitab calls the explanatory variable the predictor variable. Which is the predictor variable, the diameter of the pot or the height? diameter O 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? (Note: The slope is the coefficient of the predictor variable.) Write the equation of the least-squares line. a = b = y = (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? What are the hypotheses for a two-tailed test of B = 0? OHO : B = 0;H: B O Based on the P-value in the printout, do we reject or fail to reject the null hypothesis for a = 0.01? Reject the null hypothesis. There is sufficient evidence that f differs from 0. Fail to reject the null hypothesis. There is insufficient evidence that p differs from 0. Fail to reject the null hypothesis. There is sufficient evidence that / differs from 0. O Reject the null hypothesis. There is insufficient evidence that p differs from 0. (d) 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 coefficient r, take the square root of the "R-Sq" value shown in the display. What is the value of r? (Round your answer to three decimal places.)(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? (Note: The slope is the coefficient of the predictor variable.) Write the equation of the least-squares line. a = b = y = (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? What are the hypotheses for a two-tailed test of B = 0? OH : B = 0; H : B O Based on the P-value in the printout, do we reject or fail to reject the null hypothesis for a = 0.01? Reject the null hypothesis. There is sufficient evidence that B differs from 0. O Fail to reject the null hypothesis. There is insufficient evidence that B differs from 0. O Fail to reject the null hypothesis. There is sufficient evidence that B differs from 0. O Reject the null hypothesis. There is insufficient evidence that A differs from 0. (d) 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 coefficient r, take the square root of the "R-Sq" value shown in the display. What is the value of r? (Round your answer to three decimal places.) 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? O No, the correlation coefficient is not significant at the a = 0.01 level because the P-value S a. Yes, the correlation coefficient is significant at the a = 0.01 level because the P-value > a. Yes, the correlation coefficient is significant at the a = 0.01 level because the P-value S a. No, the correlation coefficient is not significant at the a = 0.01 level because the P-value > a. Need Help? Read It Watch It