Part (a) (2.5 points) Consider the following statement: “The covariance is a bet
ID: 3247828 • Letter: P
Question
Part (a) (2.5 points)
Consider the following statement: “The covariance is a better way to measure the strength and the direction of a relationship between two variables than the correlation coefficient.” Please indicate whether you agree or disagree and justify your answer.
Part (b) (2. 5 points)
Consider the following statement: “The coefficient of determination is a better way to measure the strength and the direction of a relationship between two variables than the correlation coefficient.” Please indicate whether you agree or disagree and justify your answer.
Explanation / Answer
Ans:
a)“The covariance is a better way to measure the strength and the direction of a relationship between two variables than the correlation coefficient.”
Disagree
Covariance indicates how two variables are related. A positive covariance means the variables are positively related, while a negative covariance means the variables are inversely related.
Correlation is another way to determine how two variables are related. In addition to telling you whether variables are positively or inversely related, correlation also tells you the degree to which the variables tend to move together.
As stated above, covariance measures variables that have different units of measurement. Using covariance, you could determine whether units were increasing or decreasing, but it was impossible to measure the degree to which the variables moved together because covariance does not use one standard unit of measurement. To measure the degree to which variables move together, you must use correlation.
b)“The coefficient of determination is a better way to measure the strength and the direction of a relationship between two variables than the correlation coefficient.”
Disagree
Cofficient of correlation(r) determines the strength and direction of association dependent and independent variables.
The coefficient of determination(r2) is a measure of the variation of the dependent variable that is explained by the regression line and the independent variable.