Correlation Coefficient and Standard Deviation

This video tutorial explains how to calculate the correlation coefficient using two methods: the covariance method and an alternative formula. It provides a detailed step-by-step guide on calculating the correlation coefficient, including the computation of sample standard deviation. The tutorial also verifies the results using both methods to ensure accuracy.

What is the correlation coefficient used to measure?

• The sum of two variables

• The difference between two variables

• The average of two variables

• The strength and direction of a linear relationship between two variables

Which formula is used to calculate the correlation coefficient using covariance?

• Difference of X and Y divided by their variances

• Covariance of X and Y divided by the product of their standard deviations

• Sum of X and Y divided by their means

• Product of X and Y divided by their standard deviations

How do you calculate the sample mean of a variable?

• Product of all values divided by the number of values

• Sum of all values divided by the number of values

• Sum of all values divided by their standard deviation

• Difference of all values divided by the number of values

What is the next step after calculating the covariance of X and Y?

• Calculate the sample standard deviation

• Calculate the difference of X and Y

• Calculate the sum of X and Y

• Calculate the product of X and Y

What is the formula for the sample standard deviation of a variable?

• Square root of the sum of deviations from the mean divided by n

• Sum of deviations from the mean divided by n

• Product of deviations from the mean divided by n-1

• Square root of the sum of squared deviations from the mean divided by n-1

How is the correlation coefficient calculated using the first formula?

• Sum of X and Y divided by their means

• Difference of X and Y divided by their variances

• Sample covariance divided by the product of sample standard deviations

• Product of X and Y divided by their standard deviations

What is the purpose of verifying the correlation coefficient with an alternative formula?

• To determine the variance of X and Y

• To calculate the mean of X and Y

• To find a different correlation coefficient

• To ensure accuracy of the calculated correlation coefficient

What is the alternative formula for calculating the correlation coefficient?

• Product of X and Y divided by their standard deviations

• n times the sum of XY minus the product of the sums of X and Y, divided by the square root of the product of n times the sum of squares minus the square of the sums

• Sum of X and Y divided by their means

• Difference of X and Y divided by their variances

What is the result of the correlation coefficient calculation using both formulas?

• The second formula gives a higher result

• The results are different

• The results are the same

• The first formula gives a higher result

Why is it important to use both formulas to calculate the correlation coefficient?

• To find the average of X and Y

• To confirm the accuracy of the result

• To calculate the sum of X and Y

• To determine the variance of X and Y