A multiple regression is run with three explanatory variables, X1, X2, and X3. The p-values of their three regression coefficients turn out to be 0.07, 0.02, and 0.35, respectively, the R-square value for the regression is 0.73, and the standard error of estimate is 27.49. Which of the following will definitely be true if the regression is run again without X3? a. The standard error of estimate will be less than 27.49. b. The p-values of X1 and X2 will both be less 0.05. c. The R-square value will be larger than 0.73. d. None of these choices are guaranteed to be true.
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 multiple regression is run with three explanatory variables, X1, X2, and X3. The p-values of their three regression coefficients turn out to be 0.07, 0.02, and 0.35, respectively, the R-square value for the regression is 0.73, and the standard error of estimate is 27.49. Which of the following will definitely be true if the regression is run again without X3?
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