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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. Coef SE Coef Predictor T P Constant -0.242 2.429 -0.09 0.929 Diameter 0.7905 0.1471 5.57 0.001 S = R-Sq = 86.18 4.07980 (a) Minitab calls the explanatory variable the predictor variable. Which is the predictor variable, the diameter of the pot o the height? diameter O height (b) For the least-squares line ŷ = a + bx, what is the value of the constant a? What is the value of the slope b? (Note: Th slope is the coefficient of the predictor variable.) Write the equation of the least-squares line. a = -0.242 b = 0.7905 ý = -0.242 + 0.7905 (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? 0.001 What are the hypotheses for a two-tailed test of ß = 0? OHo: B< 0; H,: ß = 0 O Ho: B = 0; H,: ß # 0 Hoi ß = 0; H: ß < 0 O Ho: B+ 0; H,: B = 0 Ho: B = 0; Hq: ß > 0 Based on the P-value in the printout, do we reject or fail to reject the null hypothesis for a = 0.01? O Reject the null hypothesis. There is sufficient evidence that B differs from 0. Fail to reject the null hypothesis. There is insufficient evidence that ß differs from 0. O Fail to reject the null hypothesis. There is sufficient evidence that ß differs from 0. Reject the null hypothesis. There is insufficient evidence that ß 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

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. Coef SE Coef Predictor T P Constant -0.242 2.429 -0.09 0.929 Diameter 0.7905 0.1471 5.57 0.001 S = R-Sq = 86.18 4.07980 (a) Minitab calls the explanatory variable the predictor variable. Which is the predictor variable, the diameter of the pot o the height? diameter O height (b) For the least-squares line ŷ = a + bx, what is the value of the constant a? What is the value of the slope b? (Note: Th slope is the coefficient of the predictor variable.) Write the equation of the least-squares line. a = -0.242 b = 0.7905 ý = -0.242 + 0.7905 (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? 0.001 What are the hypotheses for a two-tailed test of ß = 0? OHo: B< 0; H,: ß = 0 O Ho: B = 0; H,: ß # 0 Hoi ß = 0; H: ß < 0 O Ho: B+ 0; H,: B = 0 Ho: B = 0; Hq: ß > 0 Based on the P-value in the printout, do we reject or fail to reject the null hypothesis for a = 0.01? O Reject the null hypothesis. There is sufficient evidence that B differs from 0. Fail to reject the null hypothesis. There is insufficient evidence that ß differs from 0. O Fail to reject the null hypothesis. There is sufficient evidence that ß differs from 0. Reject the null hypothesis. There is insufficient evidence that ß 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

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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. SE Coef Predictor Coef T P Constant -0.242 2.429 -0.09 0.929 Diameter 0.7905 0.1471 5.57 0.001 S = 4.07980 R-Sq = 86.1% (a) Minitab calls the explanatory variable the predictor variable. Which is the predictor variable, the diameter of the pot or the height? O diameter O height (b) For the least-squares line ý = 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 = -0.242 b =0.7905 ý = -0.242 +0.7905 (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? 0.001 What are the hypotheses for a two-tailed test of ß = 0? Ho: ß < 0; H,: ß = 0 O Ho: B = 0; H,: Bß# 0 O Hoi ß = 0; H,: ß < 0 O Ho: B# 0; H,: ß = 0 O Hoi ß = 0; H,: ß > 0 Based on the P-value in the printout, do we reject or fail to reject the null hypothesis for a = 0.01? O Reject the null hypothesis. There is sufficient evidence that ß differs from 0. O Fail to reject the null hypothesis. There is insufficient evidence that ß differs from 0. O Fail to reject the null hypothesis. There is sufficient evidence that ß differs from 0. O Reject the null hypothesis. There is insufficient evidence that ß 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. O Yes, the correlation coefficient is significant at the a = 0.01 level because the P-value > a. O Yes, the correlation coefficient is significant at the a = 0.01 level because the P-value s a. O No, the correlation coefficient is not significant at the a = 0.01 level because the P-value > a.
Transcribed Image Text: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. SE Coef Predictor Coef T P Constant -0.242 2.429 -0.09 0.929 Diameter 0.7905 0.1471 5.57 0.001 S = 4.07980 R-Sq = 86.1% (a) Minitab calls the explanatory variable the predictor variable. Which is the predictor variable, the diameter of the pot or the height? O diameter O height (b) For the least-squares line ý = 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 = -0.242 b =0.7905 ý = -0.242 +0.7905 (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? 0.001 What are the hypotheses for a two-tailed test of ß = 0? Ho: ß < 0; H,: ß = 0 O Ho: B = 0; H,: Bß# 0 O Hoi ß = 0; H,: ß < 0 O Ho: B# 0; H,: ß = 0 O Hoi ß = 0; H,: ß > 0 Based on the P-value in the printout, do we reject or fail to reject the null hypothesis for a = 0.01? O Reject the null hypothesis. There is sufficient evidence that ß differs from 0. O Fail to reject the null hypothesis. There is insufficient evidence that ß differs from 0. O Fail to reject the null hypothesis. There is sufficient evidence that ß differs from 0. O Reject the null hypothesis. There is insufficient evidence that ß 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. O Yes, the correlation coefficient is significant at the a = 0.01 level because the P-value > a. O Yes, the correlation coefficient is significant at the a = 0.01 level because the P-value s a. O No, the correlation coefficient is not significant at the a = 0.01 level because the P-value > a.
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