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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 P 2.429 0.1471 Predictor Constant Diameter Coef -0.230 0.7797 -0.09 3.72 0.929 0.007 S = 4.07980 R-Sq = 73.5% (a) Minitab calls the explanatory variable the predictor variable. Which is the predictor variable, the diameter of the pot or the height? height diameter (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.

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 P 2.429 0.1471 Predictor Constant Diameter Coef -0.230 0.7797 -0.09 3.72 0.929 0.007 S = 4.07980 R-Sq = 73.5% (a) Minitab calls the explanatory variable the predictor variable. Which is the predictor variable, the diameter of the pot or the height? height diameter (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.

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. T P -0.09 3.72 Predictor Constant a = Diameter b= Coef -0.230 0.7797 SE Coef 2.429 0.1471 S = 4.07980 R-Sq = 73.5% (a) Minitab calls the explanatory variable the predictor variable. Which is the predictor variable, the diameter of the pot or the height? height diameter 0.929 (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. 0.007 What are the hypotheses for a two-tailed test of 3 = 0? Ho: ß <0; H₁: B = 0 Ho: B = 0; H₁: B <0 B=0; HBO (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? Ho: B = 0; H₁: B = 0 Ho: B = 0; H₁: ß >0 Ho: Based on the P-value in the printout, do we reject or fail to reject the null hypothesis for x = 0.01? Reject the null hypothesis. There is sufficient evidence that 3 differs from 0. Fail to reject the null hypothesis. There is insufficient evidence that 3 differs from 0. Fail to reject the null hypothesis. There is sufficient evidence that differs from 0. Reject the null hypothesis. There is insufficient evidence that differs from 0. (d) Recall that the t value and resulting P-value of the slope bequal 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? No, the correlation coefficient is not significant at the x = 0.01 level because the P-values a the correlation coefficient is significant at the x = 0.01 level because the P-value> a. correlation coefficient is significant at the x = 0.01 level because the P-values a coefficient is not significant at the x = 0.01 level because the P-value > x. Yes, Yes, the No, the correlation
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. T P -0.09 3.72 Predictor Constant a = Diameter b= Coef -0.230 0.7797 SE Coef 2.429 0.1471 S = 4.07980 R-Sq = 73.5% (a) Minitab calls the explanatory variable the predictor variable. Which is the predictor variable, the diameter of the pot or the height? height diameter 0.929 (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. 0.007 What are the hypotheses for a two-tailed test of 3 = 0? Ho: ß <0; H₁: B = 0 Ho: B = 0; H₁: B <0 B=0; HBO (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? Ho: B = 0; H₁: B = 0 Ho: B = 0; H₁: ß >0 Ho: Based on the P-value in the printout, do we reject or fail to reject the null hypothesis for x = 0.01? Reject the null hypothesis. There is sufficient evidence that 3 differs from 0. Fail to reject the null hypothesis. There is insufficient evidence that 3 differs from 0. Fail to reject the null hypothesis. There is sufficient evidence that differs from 0. Reject the null hypothesis. There is insufficient evidence that differs from 0. (d) Recall that the t value and resulting P-value of the slope bequal 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? No, the correlation coefficient is not significant at the x = 0.01 level because the P-values a the correlation coefficient is significant at the x = 0.01 level because the P-value> a. correlation coefficient is significant at the x = 0.01 level because the P-values a coefficient is not significant at the x = 0.01 level because the P-value > x. Yes, Yes, the No, the correlation
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