Predictor variables in equation R2 R? Cp ed 0.211 0.195 88.9 tjobs sci 0.351 0.337 65.1 0.288 0.274 75.8 rd 0.635 0.628 16.4 ed, tjobs ed, sci ed, rd tjobs, sci tjobs, rd sci, rd 0.369 0.342 63.9 0.338 0.310 69.2 0.686 0.673 9.7 0.492 0.470 42.9 0.728 0.717 2.5 0.649 0.634 16.1 ed, tjobs, sci ed, tjobs, rd ed, sci, rd tjobs, sci, rd 0.492 0.459 44.9 0.734 0.716 3.6 0.687 0.666 11.6 0.735 0.718 3.3 ed, tjobs, sci, rd 0.737 0.714 5.0
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.
Patent Production. Where we considered relating the number of patents per 1000 workers and four predictor variables: workforce education score, high-tech jobs, percentage of scientists and engineers in the workforce, and investment in research and development. The table below contains the values of R2, R2 a, and Cp for regression equations that contain each predictor variable, each
pair of predictor variables, each triple of predictor variables, and all four predictor variables. Use this table to do the following.
a. Use the maximum-R2 criterion to obtain a regression equation.
b. Use the adjusted-R2 criterion to obtain a regression equation.
c. Use the Mallows’ Cp criterion to obtain a regression equation.
d. Are the regression equations that you obtained in parts (a), (b), and (c) the same?
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