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The regression coefficients are zero if A)r=1 B)r=2 C)r=0 D)r=-1?
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The regression coefficients are zero if A)r=1 B)r=2 C)r=0 D)r=-1?
Explanation:
Regression coefficients represent the relationship between the independent variable(s) and the dependent variable in a regression model. When the regression coefficients are zero, it indicates that there is no relationship between the independent variable(s) and the dependent variable.
Reasons why regression coefficients are zero:
- Case A: r=1
When the correlation coefficient (r) between the independent variable(s) and the dependent variable is 1, it indicates a perfect positive linear relationship. In this case, the regression coefficients will not be zero because there is a strong relationship between the variables.
- Case B: r=2
The correlation coefficient (r) ranges from -1 to 1, so a value of 2 is not possible. Therefore, this option is not valid.
- Case C: r=0
When the correlation coefficient (r) between the independent variable(s) and the dependent variable is 0, it indicates no linear relationship between the variables. In this scenario, the regression coefficients will be zero because there is no association between the variables.
- Case D: r=-1
When the correlation coefficient (r) is -1, it indicates a perfect negative linear relationship. In this case, the regression coefficients will not be zero because there is a strong negative relationship between the variables.
Therefore, the correct answer is Option C: r=0, where the regression coefficients are zero due to the absence of a linear relationship between the independent variable(s) and the dependent variable.
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The regression coefficients are zero if A)r=1 B)r=2 C)r=0 D)r=-1?
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The regression coefficients are zero if A)r=1 B)r=2 C)r=0 D)r=-1? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The regression coefficients are zero if A)r=1 B)r=2 C)r=0 D)r=-1? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The regression coefficients are zero if A)r=1 B)r=2 C)r=0 D)r=-1?.
The regression coefficients are zero if A)r=1 B)r=2 C)r=0 D)r=-1? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The regression coefficients are zero if A)r=1 B)r=2 C)r=0 D)r=-1? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The regression coefficients are zero if A)r=1 B)r=2 C)r=0 D)r=-1?.
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