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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.

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. Correct Answer c and d are true

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,

[ alt="correlation coefficient formula" src="https://www.gstatic.com/education/formulas2/355397047/en/correlation_coefficient_formula.svg" style="width: 200px; height: 49px;">

[ alt="correlation coefficient formula correlation coefficient formula var 1" class="ZFAGbf" data-atf="1" role="img" src="https://www.gstatic.com/education/formulas2/355397047/en/correlation_coefficient_formula_correlation_coefficient_formula_var_1.svg" style="color: rgb(32, 33, 36); display: inline-block;"> = correlation coefficient
[ alt="correlation coefficient formula correlation coefficient formula var 2" class="ZFAGbf" data-atf="1" role="img" src="https://www.gstatic.com/education/formulas2/355397047/en/correlation_coefficient_formula_correlation_coefficient_formula_var_2.svg" style="color: rgb(32, 33, 36); display: inline-block;"> = values of the x-variable in a sample
[ alt="correlation coefficient formula correlation coefficient formula var 3" class="ZFAGbf" data-atf="1" role="img" src="https://www.gstatic.com/education/formulas2/355397047/en/correlation_coefficient_formula_correlation_coefficient_formula_var_3.svg" style="color: rgb(32, 33, 36); display: inline-block;"> = mean of the values of the x-variable
[ alt="correlation coefficient formula correlation coefficient formula var 4" class="ZFAGbf" data-atf="1" role="img" src="https://www.gstatic.com/education/formulas2/355397047/en/correlation_coefficient_formula_correlation_coefficient_formula_var_4.svg" style="color: rgb(32, 33, 36); display: inline-block;"> = values of the y-variable in a sample
[ alt="correlation coefficient formula correlation coefficient formula var 5" class="ZFAGbf" data-atf="1" role="img" src="https://www.gstatic.com/education/formulas2/355397047/en/correlation_coefficient_formula_correlation_coefficient_formula_var_5.svg" style="color: rgb(32, 33, 36); display: inline-block;"> = mean of the values of the y-variable

[ alt="F1 Lalita V Anil 15.02.21 D8" src="//storage.googleapis.com/tb-img/production/21/02/F1_Lalita%20V_Anil_15.02.21_D8.png" style="width: 414px; height: 155px;">

Therefore, c and d are true.

Related Questions

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1. The coefficient of rank correlation has the same limits as the Karl Pearson's coefficient of correlation.
2. The coefficient of correlation is independent of the change of origin but not of scale.
3. The covariance between $$X$$ and $$Y$$ is defined as $$\frac{{\sum {xy} }}{n}$$ where, $$x = \left( {X - \overline X } \right),y = \left( {Y - \overline Y } \right)$$      and $$n = $$ no. of paired observations.
4. $${b_{xy}}$$ is called regression coefficient of $$X$$ variable on $$Y$$ variable.
5. If $${b_{xy}}$$ is 0.4 and $${b_{yx}}$$ is 1.6, coefficient of determination would be 0.8.
Select the correct answer:
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