Prehistoric pottery vessels are usually found as sherds (broken pieces) and are
ID: 3226088 • Letter: P
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 -0.257 2.429 -0.09 0.929
Diameter 0.7797 0.1659 5.33 0.023
S = 4.17540 R-Sq = 72.1%
(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/x2 – (1/n)(x)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 can be written as E = tc(SE Coef). The Minitab display is based on n = 9 data pairs. Find the critical value tc for a 90% confidence interval in the relevant table. Then find a 90% confidence interval for the population slope . (Use 3 decimal places.)
tc:
lower limit:
upper limit:
Explanation / Answer
Solution (a)
The standard error of the linear regression model (given in question) is = 4.17540
Solution (b)
The standard error for the slope b = 0.1659
Solution (c)
E = tc *(SE Coef)
The tc value is 2.3646 (using excel function T.INV.2T)
SE Coef (from the question) = 0.1659
So, E = 2.3646 * 0.1659= 0.3923
The confidence interval is given by + margin of error = 0.7797 + 0.3923 = (0.387, 1.172)
That is, lower limit: 0.387
upper limit: 1.172