Which of the following statements is/are correct in respect of regress...
Regression coefficients measures the degree of linear relationship between two variables and does not give the value by which one variable changes for a unit change in the other variable.
option (a) is correct.
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Which of the following statements is/are correct in respect of regress...
Regression Coefficients
Regression coefficients are statistical measures that quantify the relationship between two variables in a regression model. They provide valuable information about the strength and direction of the relationship between the independent variable(s) and the dependent variable.
Statement 1: It measures the degree of linear relationship between two variables.
This statement is correct. The regression coefficient, also known as the slope coefficient or beta coefficient, measures the degree of the linear relationship between the independent variable and the dependent variable. It indicates the change in the dependent variable for a unit change in the independent variable. The magnitude of the coefficient represents the strength of the relationship, with larger coefficients indicating a stronger relationship.
Statement 2: It gives the value by which one variable changes for a unit change in the other variable.
This statement is also correct. The regression coefficient quantifies the change in the dependent variable for a unit change in the independent variable. For example, if the regression coefficient is 0.5, it means that for every one unit increase in the independent variable, the dependent variable is expected to increase by 0.5 units. Similarly, if the coefficient is -0.2, it indicates that for every one unit increase in the independent variable, the dependent variable is expected to decrease by 0.2 units.
Therefore, both Statement 1 and Statement 2 are correct.
Conclusion
Regression coefficients are important statistical measures that provide valuable information about the relationship between variables in a regression model. They measure the degree of the linear relationship between two variables and quantify the change in one variable for a unit change in the other variable. Understanding regression coefficients is crucial in interpreting regression models and making informed decisions based on the relationships they represent.