Regression Line and Arithmetic Mean

Regression analysis is a statistical method used to determine the relationship between a dependent variable and one or more independent variables. It is used to predict the value of the dependent variable based on the value of the independent variable(s).

The regression line is a line of best fit that is used to model the relationship between the dependent and independent variables. It is used to predict the value of the dependent variable based on the value of the independent variable.

The arithmetic mean is a measure of central tendency that is calculated by adding all the values in a set of data and dividing by the number of values.

Calculating the Arithmetic Mean of Y

In this question, we are given that the regression line y on x is 3x + 4 and the arithmetic mean of x is -1. We need to find the arithmetic mean of y.

To calculate the arithmetic mean of y, we need to know the values of y for each value of x. We can use the regression line to calculate the value of y for any given value of x.

Let's assume that we have a set of values for x. We can use the regression line to calculate the corresponding values of y. For example, if x = 0, then y = 4. If x = 1, then y = 7. If x = -1, then y = 1.

Once we have the values of y for each value of x, we can calculate the arithmetic mean of y by adding all the values of y and dividing by the number of values. For example, if we have the following values of y:

y = {4, 7, 1}

Then the arithmetic mean of y is:

(4 + 7 + 1) / 3 = 4

Therefore, the arithmetic mean of y is 4.

Conclusion

In conclusion, we can calculate the arithmetic mean of y by using the regression line to calculate the values of y for each value of x and then calculating the arithmetic mean of those values. In this question, we were given the regression line y on x and the arithmetic mean of x, and we used those values to calculate the arithmetic mean of y.