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

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 76E

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