Calculating the Coefficient of Correlation and Obtaining the Lines of Regression

Data:
Before we begin calculating the coefficient of correlation and obtaining the lines of regression, let's first understand the given data. Unfortunately, the data is not provided in the question. However, I will assume that we are given a set of paired data, with one variable being the independent variable (X) and the other being the dependent variable (Y).

Step 1: Calculate the Mean of X and Y
To calculate the coefficient of correlation, we need to find the mean of both X and Y. The mean of a set of numbers is obtained by summing all the numbers and dividing by the total count.

Step 2: Calculate Deviations from the Mean
Next, we need to calculate the deviations of each X value from the mean of X, and the deviations of each Y value from the mean of Y. Deviation is obtained by subtracting the mean from each individual value.

Step 3: Calculate the Product of Deviations
In this step, we multiply the deviations of X and Y for each pair of data points. This will give us the product of deviations for each pair.

Step 4: Calculate the Sum of the Product of Deviations
Now, we sum up all the products of deviations calculated in the previous step.

Step 5: Calculate the Sum of Squares of Deviations
We also need to calculate the sum of squares of deviations for both X and Y. This is done by squaring each deviation and summing up the squares.

Step 6: Calculate the Coefficient of Correlation
The coefficient of correlation (r) is calculated using the formula: r = (sum of products of deviations) / sqrt((sum of squares of deviations for X) * (sum of squares of deviations for Y))

Step 7: Interpret the Coefficient of Correlation
The coefficient of correlation ranges from -1 to 1, where -1 represents a perfect negative correlation, 0 represents no correlation, and 1 represents a perfect positive correlation. The sign (+/-) indicates the direction of the correlation.

Step 8: Obtain the Lines of Regression
To obtain the lines of regression, we need to calculate the regression coefficients (a and b). The equation for the regression line is given by: Y = a + bX, where X is the independent variable, Y is the dependent variable, a is the intercept, and b is the slope.

Step 9: Calculate the Regression Coefficients
The regression coefficient b can be calculated using the formula: b = (r * (standard deviation of Y)) / (standard deviation of X)
The regression coefficient a can be calculated using the formula: a = (mean of Y) - (b * (mean of X))

Step 10: Obtain the Lines of Regression
Using the calculated regression coefficients, we can now obtain the lines of regression. The line of regression for Y on X is given by: Y = a + bX, and the line of regression for X on Y is given by: X = (Y - a) / b

Conclusion:
By following the above steps, we can calculate the coefficient of correlation and