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	-0.227	2.429	-0.09	0.929
Diameter	0.7770	0.1470	5.33	0.001
S = 4.09980	R-Sq = 79.1%

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


(b) The standard error of the coefficient of the predictor variable is found under "SE Coef." Recall that the standard error for b is S_e/√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 = t_c(SE Coef). The Minitab display is based on n = 16 data pairs. Find the critical value t_c 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

a) The value of S according to the table is

b)The standard error for the slope according to the minitab output is

C) Now to find the confidence interval

We need to have the critical table value first

Here n=16

And the table value would be checked via t distribution table with n-1=15 degrees of freedom and one sided rejection proability of 0.025 as both sides would then combine to be 0.05 which is 95%.

So the table value is

So E would be

  

The estimated value for beta according to table is

So

  

Thank you !!