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 Constant Diameter S = 3.91620 Coef SE Coef 2.429 0.1686 I 5.33 P 0.929 0.019 R-Sq = 70.7% (a) The standard error S. 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 S₂/Ex² - (1/n)(Ex)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 ß can be written as E = t_(SE Coef). The Minitab display is based on n = 7 data pairs. Find the critical value to for a 95% confidence interval in the relevant table. Then find a 95% confidence interval for the population slope B. (Use 3 decimal places.) to lower limit upper limit
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 Constant Diameter S = 3.91620 Coef SE Coef 2.429 0.1686 I 5.33 P 0.929 0.019 R-Sq = 70.7% (a) The standard error S. 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 S₂/Ex² - (1/n)(Ex)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 ß can be written as E = t_(SE Coef). The Minitab display is based on n = 7 data pairs. Find the critical value to for a 95% confidence interval in the relevant table. Then find a 95% confidence interval for the population slope B. (Use 3 decimal places.) to lower limit upper limit
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 18PFA
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Transcribed Image Text: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
Constant
Diameter
S = 3.91620
Coef
-0.185
0.7959
lower limit
upper limit
R-Sq= 70.75
SE Coef
2.429
0.1686
T
5.33
P
0.929
0.019
(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 S₂/Ex² - (1/n)(Ex)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 ß can be written as E = t_(SE
Coef). The Minitab display is based on n = 7 data pairs. Find the critical value to for a 95% confidence interval in the
relevant table. Then find a 95% confidence interval for the population slope B. (Use 3 decimal places.)
to
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