Chapter 14, Problem 1RP

For a linear equation y = b₀ + b₁x, identify the

1.                                            a.      independent variable.
2.                                            b.      dependent variable
3.                                             c.      slope.
4.                                            d.      y-intercept.

To determine

To identify: The independent variable for a linear equation $y=b_0+b_{1}x$.

Answer to Problem 1RP

The independent variable for a linear equation $y=b_0+b_{1}x$ is x.

Explanation of Solution

Given info:

The linear equation is $y=b_0+b_{1}x$.

Justification:

In case of regression equation the independent variable is that variable whose variation is independent of other variables.

In the regression equation the predictor variable x is an independent variable.

To determine

To identify: The dependent variable for a linear equation $y=b_0+b_{1}x$.

Answer to Problem 1RP

The dependent variable for a linear equation $y=b_0+b_{1}x$ is y.

Explanation of Solution

Justification:

In case of regression equation the dependent variable is that response variable which responds to the independent variable.

In the regression equation the response variable y is an dependent variable.

To determine

To identify: The slope for a linear equation $y=b_0+b_{1}x$.

Answer to Problem 1RP

The slope for a linear equation $y=b_0+b_{1}x$ is $b_1$.

Explanation of Solution

Justification:

In case of regression equation the slope measure the change of dependent variable due to the unit change of independent variable.

In the regression equation, the slope is $b_1$.

To determine

To identify: The y­-intercept for a linear equation $y=b_0+b_{1}x$.

Answer to Problem 1RP

The y-intercept for a linear equation $y=b_0+b_{1}x$ is $b_0$.

Explanation of Solution

Justification:

In case of regression equation the y-intercept implies that the y-value where the line intersect the y-axis.

In the regression equation, the y-intercept is $b_0$.