Question

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 = 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 -0.230 2.429 -0.09 0.929 Diameter 0.8040 0.1551 5.33 0.005 S = 4.15380 R-Sq = 89.6%

(a) The standard error Se of the linear regression model is given in the printout as "S." What is the value of Se?

(b) The standard error of the coefficient of the predictor variable is found under "SE Coef." Recall that the standard error for b is Se/√Σx2 – (1/n)(Σx)2. From the Minitab display, what is the value of the standard error for the slope b?

(c) The formula for the margin of error E for a c% confidence interval for the slope β can be written as E = tc(SE Coef). The Minitab display is based on n = 13 data pairs. Find the critical value tc for a 95% confidence interval in the relevant table. Then find a 95% confidence interval for the population slope β. (Use 3 decimal places.) tc lower limit upper limit

Answer 1

predictor	Coef	SE Coef	T	P
Constant	-0.230	2.429	-0.09	0.929
Diameter	0.8040	0.1551	5.33	0.005

S = 4.15380 R-Sq = 89.6%

(a) The standard error Se of the linear regression model is given in the printout as "S." What is the value of Se?

S= Se = 4.15380 .........from the output

Answer:- 4.15380

b)

The standard error of the coefficient of the predictor variable is found under "SE Coef."

"SE Coef." for Diameter = 0.1551

Answer:- 0.1551

c)

n = 13 , tc = tn-1 , alpha/2 = ?

1- alpha = 0.95 ; alpha = 0.05 , alpha /2 = 0.025

tc = t12,0.025 = 2.179

The margin of error = tc * (SE Coef)  = 2.179 * 0.1551 = 0.3379

The 95 % confidence interval for B is

( b +- margin of error)

b = 0.8040

( 0.8040 +- 0.3379 )

( 0.8040 - 0.3379 ; 0.8040 + 0.3379)

( 0.4661 , 1.1419) ~ ( 0.466 , 1.142)

0.466< B <  1.142

tc = 2.179

Upper limit = 1.142

Lower limit = 0.466