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 Constant -0.221 2.429 -0.09 0.929 Diameter 0.8067 0.1524 5.33 0.001 S - 4.23750 R-Sq - 87.58 (a) The standard error S, of the linear regression model s given in printout as "S." What is the value of S? (b) The standard error of the coefficient of the predictor variable is found under "SE Coef." Recall that the standard error for b is SVEX - (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 B can be written as E = t(SE Coef). The Minitab display is based on n = 14 data pairs. Find the critical value t, for a 90% confidence interval in the relevant table. Then find a 90% confidence interval for the population slope B. (Use 3 decimal places.) t. 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 Coef SE Coef T Constant -0.221 2.429 -0.09 0.929 Diameter 0.8067 0.1524 5.33 0.001 S - 4.23750 R-Sq - 87.58 (a) The standard error S, of the linear regression model s given in printout as "S." What is the value of S? (b) The standard error of the coefficient of the predictor variable is found under "SE Coef." Recall that the standard error for b is SVEX - (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 B can be written as E = t(SE Coef). The Minitab display is based on n = 14 data pairs. Find the critical value t, for a 90% confidence interval in the relevant table. Then find a 90% confidence interval for the population slope B. (Use 3 decimal places.) t. lower limit upper limit
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 2ECP
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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
Coef
SE Coef
Constant
-0.221
2.429
-0.09
0.929
Diameter
0.8067
0.1524
5.33
0.001
S = 4.23750
R-Sq = 87.5%
(a) The standard error S. of the linear regression model is given in the printout as "S." What is the value ofS,?
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 SJVEX² - (1/n)(Ex). 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 B can be written as E = t (SE Coef). The Minitab display is based on n = 14 data pairs. Find the critical value
%3D
t, for a 90% confidence interval in the relevant table. Then find a 90% confidence interval for the population slope B. (Use 3 decimal places.)
lower limit
upper limit
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