Which of the following statements is true about the geometric mean of two regression coefficient?

Choose the correct code for the following statements being correct or incorrectStatement I: The geometric mean of the two regression coefficients of X and Y variables gives the value of the coefficient of correlation.Statement II: If the population distribution is not normal  and a sampling distribution of mean is prepared by taking small sized samples, the sampling distribution of mean is not normal.

1. Both the statements I and II are correct

2. Both the statements I and II are incorrect

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   • Choose the correct code for the following statements being correct or incorrectStatement I: The geometric mean of the two regression coefficients of X and Y variables gives the value of the coefficient of correlation.Statement II: If the population distribution is not normal  and a sampling distribution of mean is prepared by taking small sized samples, the sampling distribution of mean is not normal.
   • Answer (Detailed Solution Below)
   • Which of the following statements is true about the geometric mean of two regression coefficients?
   • What is the geometric mean of the two regression coefficients?
   • Is the geometric mean of two regression coefficient Mcq?
   • What is the correlation coefficient is the geometric mean between the regression coefficient?

3. Statement I is correct, but II is incorrect

4. Statement II is correct, but I is incorrect.

Answer (Detailed Solution Below)

Option 1 : Both the statements I and II are correct

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Statement I: The geometric mean of the two regression coefficients of X and Y variables gives the value of the coefficient of correlation.

Explanation:

1. The regression coefficient is a statistical measure of the average functional relationship between two or more variables.
2. In regression analysis, one variable is considered as dependent and the other(s) as an independent.
3. Thus, it measures the degree of dependence of one variable on the other(s). 
4. The geometric mean between the two regression coefficients is equal to the coefficient of correlation, r = 
   
   .

Thus, the statement I is correct.

Statement II: If the population distribution is not normal and the sampling distribution of mean is prepared by taking small-sized samples, the sampling distribution of mean is not normal.

Explanation: 

1. The central limit theorem (CLT) states that the distribution of sample means approximates a normal distribution as the sample size gets larger.
2. Thus, if the sampling distribution of mean is prepared by taking small-sized samples, the distribution will not be normal.

​Thus, statement II is also correct.

Therefore, option I is the correct answer.

Which of the following statements is true about the geometric mean of two regression coefficients?

What is the geometric mean of the two regression coefficients?

Is the geometric mean of two regression coefficient Mcq?

What is the correlation coefficient is the geometric mean between the regression coefficient?