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 = centimeters of prehistoric vessels reconstructed from sherds found at a prehistoric site. The following Minitab printout provides an analysis of the data. body diameter in centimeters and y = height in %3D Predictor Coef SE Coef т Constant -0.197 2.429 -0.09 0.929 Diameter 0.8013 0.1443 5.33 0.021 S = 4.28610 R-Sq = 74.2%
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
(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 = 12 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 β. (Use 3 decimal places.)
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