Question

Heidi collected data on the mileage (in thousands of kilometers) and the value (in thousands of dollars) of 11 cars of the same make and model. The data showed a strong negative linear relationship. Based on the least-squares regression analysis output, which of the following is an appropriate least-squares equation for this model?

a. Value = 39.575 - 0.246 * Mileage
b. Value = 39.575 + 0.246 * Mileage
c. Value = -0.246 * Mileage + 39.575
d. Value = -0.246 * Mileage - 39.575

Answer 1

The appropriate least-squares equation for this model is Value = 39.575 - 0.246 * Mileage (option a). The slope of the line represents the change in the dependent variable (value) for every one-unit increase in the independent variable (mileage). The y-intercept of the line represents the value of the car when the mileage is zero.

Step-by-step explanation:

The appropriate least-squares equation for this model is Value = 39.575 - 0.246 * Mileage (option a).

In a linear regression analysis, the least-squares equation represents the line that best fits the data points. The slope of the line represents the change in the dependent variable (value) for every one-unit increase in the independent variable (mileage). In this case, the slope is -0.246, indicating that for every one-unit increase in mileage, the value of the car decreases by 0.246 thousand dollars.

The y-intercept of the line represents the value of the car when the mileage is zero. In this case, the y-intercept is 39.575 thousand dollars, indicating the estimated value of the car when it has no mileage.