Questions: Used Truck Prices A truck dealership tracked recent sales of a particular model. The table shows the Excel output for the regression of Price (response variable, measured in 1000's) on Miles driven (predictor variable, measured in 1000's) Use the Excel output to answer the questions below. a) What is the correlation between Price and Miles? What does that tell you in this context? b) Give the regression equation Price = a + b (Miles) with the correct numerical values of a and b. c) Give careful interpretations of the slope and intercept of the regression equation. d) What average price is predicted for trucks with 50,000 miles? e) What is the residual for a truck that has been driven for 50,000 miles, that sells for 55,500? What does that tell you about the truck?

Used Truck Prices A truck dealership tracked recent sales of a particular model. The table shows the Excel output for the regression of Price (response variable, measured in 1000's) on Miles driven (predictor variable, measured in 1000's) Use the Excel output to answer the questions below.

a) What is the correlation between Price and Miles? What does that tell you in this context?
b) Give the regression equation Price = a + b (Miles) with the correct numerical values of a and b.
c) Give careful interpretations of the slope and intercept of the regression equation.
d) What average price is predicted for trucks with 50,000 miles?
e) What is the residual for a truck that has been driven for 50,000 miles, that sells for 55,500? What does that tell you about the truck?

Transcript text: Used Truck Prices A truck dealership tracked recent sales of a particular model. The table shows the Excel output for the regression of Price (response variable, measured in $\$ 1000$ 's) on Miles driven (predictor variable, measured in 1000's) Use the Excel output to answer the questions below. a) What is the correlation between Price and Miles? What does that tell you in this context? b) Give the regression equation Price $=a+b$ (Miles) with the correct numerical values of $a$ and $b$. c) Give careful interpretations of the slope and intercept of the regression equation. d) What average price is predicted for trucks with 50,000 miles? e) What is the residual for a truck that has been driven for 50,000 miles, that sells for $\$ 55,500$ ? What does that tell you about the truck?

Solution

Solution Steps

Step 1: Determine the Correlation Coefficient

The correlation coefficient between Price and Miles is given by the Multiple R value from the regression output. This value is $0.8063$.

Step 2: Interpret the Correlation Coefficient

A correlation coefficient of $0.8063$ indicates a strong negative linear relationship between the price of the truck and the miles driven. This means that as the miles increase, the price tends to decrease.

Step 3: Formulate the Regression Equation

The regression equation is given by: \[ \text{Price} = a + b \times \text{Miles} \] where $a$ is the intercept and $b$ is the slope. From the regression output, we have:

Intercept ($a$) = $65.334$
Slope ($b$) = $-0.312$

Thus, the regression equation is: \[ \text{Price} = 65.334 - 0.312 \times \text{Miles} \]

Step 4: Interpret the Slope and Intercept

Slope Interpretation: The slope of $-0.312$ means that for each additional $1,000$ miles driven, the price of the truck decreases by $\$312$.
Intercept Interpretation: The intercept of $65.334$ means that if a truck has $0$ miles, the predicted price would be $\$65,334$.

Final Answer

Correlation Coefficient: $\boxed{0.8063}$
Regression Equation: $\boxed{\text{Price} = 65.334 - 0.312 \times \text{Miles}}$
Slope Interpretation: For each additional $1,000$ miles, the price decreases by $\$312$.
Intercept Interpretation: At $0$ miles, the predicted price is $\$65,334$.

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