Critical Thinking: Using Information from a Computer Display to Test for Significance Refer to the Minitab printout regarding prehistoric pottery.

(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 yˆ 5a 1bx, 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 leastsquares line.

(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 5 0? Based on the P-value in the printout, do we reject or fail to reject the null hypothesis for a 5 0.01?

(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 sample 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? 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?

use the following information. Prehistoric pottery vessels are usually found as sherds (broken pieces) and are carefully reconstructed if enough sherds can be found. Information taken from Mimbres Mogollon Archaeology by A. I. Woosley and A. J. McIntyre (University of New Mexico Press)
provides data relating x 5body diameter in centimeters and y 5height 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 P Constant -0.223 2.429 -0.09 0.929 Diameter 0.7848 0.1471 5.33 0.001 S = 4.07980 R-Sq = 80.3%AppendixLO1