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	P
Constant	-0.197	2.429	-0.09	0.929
Diameter	0.7581	0.1471	4.47	0.006
S = 4.07980 R-Sq = 83.3%

(b) For the least-squares line = 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 =

= + x

(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?

(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.)