Which of the following statements concerning the linear correlation coefficient are true? I: If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables. II: If the slope of the regression line is negative, then the linear correlation coefficient is negative. III: The value of the linear correlation coefficient always lies betweenminus1 and 1. IV: A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of minus0.82.
Accepted Solution
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Answer:I: If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables. II: If the slope of the regression line is negative, then the linear correlation coefficient is negative. III: The value of the linear correlation coefficient always lies between minus 1 and 1. Step-by-step explanation:A correlation coefficient is a measure of how closely the variables are related. This coefficient ranges from -1 to 1, with -1 being a perfect fit for a decreasing data set and 1 being a perfect fit for an increasing data set.If the data set has a negative correlation coefficient, the data is decreasing; this means that the slope of the regression line will be negative.The closer the correlation coefficient is to -1 or 1, the better the fit; this means that a correlation coefficient of -0.82 will be stronger than one of 0.62.