Sample Covariance Calculator

How to Use the Sample Covariance Calculator

This guide provides detailed instructions on how to use the Sample Covariance Calculator to compute the sample covariance and correlation coefficient of two sets of values. Follow these steps carefully to ensure accurate results.

Step 1: Enter X Values

• Locate the X Value Input Field: Begin by finding the input field labeled ‘X Value’.
• Enter Each X Value: Carefully input each of your X values into the field. Ensure that each value is a number between -1,000,000 and 1,000,000. The input should be made in increments of 0.01 for precision.
• Repeat as Needed: Continue entering each X value until all values have been input into the system.

Step 2: Enter Y Values

• Locate the Y Value Input Field: Next, find where to input your Y values using the input field labeled ‘Y Value’.
• Enter Each Y Value: Just like with the X values, enter each Y value number which should be within the permissible range of -1,000,000 to 1,000,000, and maintain the step increment of 0.01.
• Complete Y Values Input: Make sure all your Y values required for the calculation are entered.

Step 3: Calculate Mean of X and Y Values

• Review Mean Calculation for X: To find the mean of the X values, the calculator will sum all X entries and divide by the total number of X values input. The resulting mean value will be displayed as ‘Mean of X Values’ rounded to four decimal places.
• Review Mean Calculation for Y: Similarly, the mean for the Y values will be calculated by summing all Y entries and dividing by their count. Look for the ‘Mean of Y Values’ result rounded to the fourth decimal place.

Step 4: Compute Sample Covariance

• Understanding the Calculation: The sample covariance is computed using the formula:
  (Σ((X – Mean X) * (Y – Mean Y))) / (N – 1), where N is the number of pairs of data.
• View the Covariance Result: Once calculated, this result will be displayed in the ‘Sample Covariance’ field with four decimal precision.

Step 5: Calculate the Correlation Coefficient

• Correlation Coefficient Formula: The correlation coefficient uses the formula:
  Covariance / (Sqrt(Σ((X – Mean X)²) / (N – 1)) * Sqrt(Σ((Y – Mean Y)²) / (N – 1))).
• Interpret the Result: The ‘Correlation Coefficient’ provides insight into the strength of the relationship between the X and Y datasets and is also rounded to four decimal digits.

Your calculations are complete when all fields show values without error messages. Use these results to analyze the relationship between your X and Y datasets effectively.