Which of the following statements is true concerning a correlation coefficient?

Which of the following statements are true?a. The correlation coefficient is dependent on the choice of both origin and scale observations.b. The correlation coefficient is dependent on the units of measurements.c. The coefficient of correlation is the square root of the coefficient of determination.d. The zero value of the correlation coefficient cannot estimate the value of the dependent variable. (adsbygoogle = window.adsbygoogle || []).push({});

1. a and b are true
2. a, b and c are true
3. c and d are true
4. Only d is true.

Answer (Detailed Solution Below)

Option 3 : c and d are true

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Correlation coefficient:

• The correlation coefficient is a statistical measure of the strength of the relationship between the relative movements of two variables.
• The values range between -1.0 and 1.0. A calculated number is greater than 1.0 or less than -1.0 means that there was an error in the correlation measurement.
• A correlation of -1.0 shows a perfect negative correlation, while a correlation of 1.0 shows a perfect positive correlation.
• A correlation of 0.0 shows no linear relationship between the movements of the two variables.
• The coefficient of correlation is the square root of the coefficient of determination.
• The zero value of the correlation coefficient cannot estimate the value of a dependent variable.
• A value of exactly 1.0 means there is a perfect positive relationship between the two variables.
• For a positive increase in one variable, there is also a positive increase in the second variable.
• A value of -1.0 means there is a perfect negative relationship between the two variables.
• Pearson's correlation coefficient,

Therefore, c and d are true.

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