The following scatter plot of 4 different samples shows the correlation between weight and height in the samples. All 4 samples have the same coefficient of correlation of 0.6 taken together, what will be the net correlation coefficient?
Correct Answer: 0.6
Description: Ans. c. 0.6 (Ref: Park 23/e p852)Coefficient of correlation is given by the slope of the graph, since the slope of all four populations are same I.e. 0.6, overall correlation coefficient will remain as 0.6.Correlation Coefficient (r)The quantity r, called the linear correlation coefficient, measures the strength and the direction of a linear relationship between two variables.The linear correlation coefficient is sometimes referred to as the Pearson product moment correlation coefficient in honor of its developer Karl Pearson. Formula of Correlation Coefficient (r)n([?]xy) - ([?]x) ([?]y)r=--------------------------------------- Advantage:It does not depend on the units of X & YCan be used to compare any two variables regardless of their units.How to calculate?An essential first step in calculating a correlation coefficient is to plot the observations in a "scattergram" or "scatter plot" to visually evaluate the data for a potential relationship or the presence of outlying values.It is frequently possible to visualize a smooth curve through the data and thereby identify the type of relationship present.Independent variable is plotted on X-axis, dependent variable is plotted on Y-axis.Range of values:Pearson's Correlation Coefficient (r) has a value of between -1 and +1.Interpretation-1+1* Strong negative correlation* Strong positive correlation Positive correlationNo correlationNegative correlation* If x & y have a strong positive linear correlation, r is close to + 1Q.* An r value of exactly +1 indicates a perfect positive fitQ.* Positive values indicate a relationship between x and y variables such that as values for x increases, values for y also increase.* If there is no linear correlation or a weak linear correlation, r is close to 0Q.* A value near zero means that there is a random, nonlinear relationship between the two variables.* If x & y have a strong negative linear correlation, r is close to -1Q.* An r value of exactly -1 indicates a perfect negative fitQ.* Negative values indicate a relationship between x and y such that as values for x increase, values for y decrease.
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