Regression Equations

The two regression equations given are:

- 3x + y = 13
- 2x + 5y = 20

Regression Equation of y on x

The regression equation of y on x is the equation that expresses the dependent variable y in terms of the independent variable x. In other words, it is the equation that allows us to predict the value of y for a given value of x.

To determine which of the two regression equations is the equation of y on x, we need to rearrange each equation so that y is isolated on one side of the equation.

For the first equation, we can isolate y as follows:

- 3x + y = 13
- y = 13 - 3x

For the second equation, we can isolate y as follows:

- 2x + 5y = 20
- 5y = 20 - 2x
- y = (20 - 2x) / 5

Comparing the Equations

Now that we have both equations in the form y = mx + b, we can compare them to determine which one is the regression equation of y on x.

- The first equation is y = 13 - 3x, which means that the slope of the line is -3 (the coefficient of x). This equation expresses y in terms of x, so it could represent the regression equation of y on x.
- The second equation is y = (20 - 2x) / 5, which means that the slope of the line is -2/5 (the coefficient of x). This equation also expresses y in terms of x, so it could also represent the regression equation of y on x.

Conclusion

Both equations could be the regression equation of y on x, as they both express y in terms of x. However, without more information about the data and the context of the problem, we cannot determine which equation is the more appropriate regression equation.