In regression analysis, which of the following correlation coefficients represents the strongest relationship between the independent and dependent variables?
Answer(s): C
Because the range of values is between-1 and 1.-89 suggests a very strong inverse relationship between the independent and dependent variables. A value of --1 signifies a perfect inverse relationship, and a value of 1 signifies a perfect direct relationship.
The following data on variables x and y was collected from June to October.The correlation coefficient between variables x and y is nearest to:
Answer(s): B
The simplest way to solve this problem is to use a scatter diagram:The data points appear to form a straight line with a negative slope. Thus,-1 is the best estimate of the coefficient of correlation.
The correlation coefficient that indicates the weakest linear association between two variables is:
The correlation coefficient can vary from -1 to +1. A--1 relationship indicates a perfect inverse correlation, and a +1 relationship indicates a perfect direct correlation. A zero correlation coefficient indicates no linear association between the variables. Thus, the correlation coefficient that is nearest to zero would indicate the weakest linear association. Of the options given in the question, the correlation coefficient that is nearest to zero is -0.11.
Correlation is a term frequently used in conjunction with regression analysis and is measured by the value of the coefficient of correlation, r. The best explanation of the value r is that it:
Answer(s): D
The coefficient of correlation (r) measures the strength of the linear relationship between the dependent and independent variables. The magnitude of r is independent of the scales of measurement of x and y. The coefficient has a range of-1 to +1. A value of zero indicates no linear relationship between the x and y variables. A value of+1 indicates a perfectly direct relationship, and a value of --1 indicates a perfectly inverse relationship.
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