Notation Using the weights (lb) and highway fuel consumption amounts (mi/gal) of the 48 cars listed in Data Set 35 “Car Data” of Appendix B, we get this regression equation:
y^ = 58.9 - 0.00749x, where x represents weight.
c. What is the predictor variable?

Verified step by step guidance

1. Step 1: Understand the regression equation provided: y^ = 58.9 - 0.00749x. In this equation, y^ represents the predicted value of the dependent variable, and x represents the independent variable (predictor variable).
2. Step 2: Recall that the predictor variable is the variable used to predict or explain changes in the dependent variable. It is the input variable in the regression equation.
3. Step 3: Identify the role of x in the equation. Here, x is multiplied by the coefficient -0.00749, indicating that it is the variable used to predict y^.
4. Step 4: Note that the problem states x represents weight. Therefore, weight is the predictor variable in this regression equation.
5. Step 5: Conclude that the predictor variable is the independent variable, which in this case is the weight of the cars (measured in pounds).

Key Concepts

Predictor Variable

In regression analysis, the predictor variable, also known as the independent variable, is the variable that is used to predict the value of another variable. In the given regression equation, 'x' represents the weight of the cars, which is used to predict the highway fuel consumption (y). Understanding the role of the predictor variable is essential for interpreting the relationship between the variables in the model.

Regression Equation

A regression equation is a mathematical representation that describes the relationship between a dependent variable and one or more independent variables. The equation provided, y^ = 58.9 - 0.00749x, indicates how changes in the predictor variable (weight) affect the predicted value of the dependent variable (fuel consumption). This equation allows for predictions and insights into the nature of the relationship between the variables.

Dependent Variable

The dependent variable, also known as the response variable, is the outcome that is being predicted or explained in a regression analysis. In this context, 'y' represents the highway fuel consumption of the cars, which depends on the weight of the cars (the predictor variable). Understanding the dependent variable is crucial for interpreting the results of the regression and assessing the impact of the predictor.