Regression equation of y on x

To find the regression equation of y on x, we need to follow the following steps:

1. Calculate the mean of x and y
2. Calculate the deviations of x and y from their respective means
3. Calculate the product of the deviations of x and y
4. Calculate the sum of the product of deviations of x and y
5. Calculate the square of deviations of x
6. Calculate the sum of square of deviations of x
7. Calculate the regression coefficient, b
8. Calculate the intercept, a
9. Write the regression equation

Explanation of steps

1. Calculate the mean of x and y
Find the mean of x and y by adding all values and dividing by the number of values:

mean of x = (x1 + x2 + x3 + ... + xn) / n
mean of y = (y1 + y2 + y3 + ... + yn) / n

2. Calculate the deviations of x and y from their respective means
Subtract each value of x and y from their respective means:

deviation of x = x - mean of x
deviation of y = y - mean of y

3. Calculate the product of the deviations of x and y
Multiply each deviation of x with its corresponding deviation of y:

product of deviations = (deviation of x1 * deviation of y1) + (deviation of x2 * deviation of y2) + ... + (deviation of xn * deviation of yn)

4. Calculate the sum of the product of deviations of x and y
Add up all the products of deviations of x and y:

sum of product of deviations = (deviation of x1 * deviation of y1) + (deviation of x2 * deviation of y2) + ... + (deviation of xn * deviation of yn)

5. Calculate the square of deviations of x
Square each deviation of x:

square of deviation of x = (deviation of x1)^2 + (deviation of x2)^2 + ... + (deviation of xn)^2

6. Calculate the sum of square of deviations of x
Add up all the squares of deviations of x:

sum of square of deviations of x = (deviation of x1)^2 + (deviation of x2)^2 + ... + (deviation of xn)^2

7. Calculate the regression coefficient, b
Calculate the regression coefficient, b, using the following formula:

b = sum of product of deviations / sum of square of deviations of x

8. Calculate the intercept, a
Calculate the intercept, a, using the following formula:

a = mean of y - (b * mean of x)

9. Write the regression equation
Write the regression equation using the values of a and b:

y = a + b*x

Conclusion

In conclusion, the regression equation of y on x can be found by following the above steps. The regression equation can be used to predict the value of y for any given value of x. It is important to note that the regression equation only provides a linear relationship between x and y and may not be accurate for all situations.