Answer true or false to each of the following statements and explain your answers. a. If the F-test for the utility of a multiple linear regression equation rejects the null hypothesis, then each of the predictor variables in the regression equation is useful in predicting the response variable. b. The t-test for the utility of a particular predictor variable in a multiple linear regression equation can be affected by the other predictor variables in the equation.
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.
Answer true or false to each of the following statements and explain your answers.
a. If the F-test for the utility of a multiple linear regression equation rejects the null hypothesis, then each of the predictor variables in the regression equation is useful in predicting the response variable.
b. The t-test for the utility of a particular predictor variable in a multiple linear regression equation can be affected by the other predictor variables in the equation.
a.
Hypotheses for testing the utility of multiple regression equation:
The null and alternative hypotheses to test the significance of a regression equation is,
H0:β1=β2=...=βk=0.
H1: at least one of the βi's is non-zero (i=1,2,...,k).
If the F-test for the utility of a multiple linear regression rejects the null hypothesis, then automatically, the alternative hypothesis is accepted. Now, the alternative hypothesis can be accepted when at least one of the βi's is non-zero. This condition does not require for all βi's to be non-zero. Having only one non-zero βi is sufficient to reject the null hypothesis. This means that the null hypothesis is rejected, if there is only one useful predictor variable in the regression equation.
Thus, the statement “If the F-test for the utility of a multiple linear regression equation rejects the null hypothesis, then each of the predictor variables in the regression equation is useful in predicting the response variable.” is False.
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