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We are given a linear regression model to predict the gas mileage (y) based on car weight (x), with the regression equation of the form:

\[
y = b_0 + b_1 \cdot x
\]

From the table in the image, we have the following regression coefficients:

- Constant (intercept \( b_0 \)): 12.81
- Coefficient of weight (\( b_1 \)): 1.41

The car's weight is given as 3,000 pounds. Since the weight in the graph is measured in hundreds of pounds, this translates to \( x = 30 \).

Now, substituting \( x = 30 \) into the regression equation:

\[
y = 12.81 + (1.41 \cdot 30)
\]

Let's calculate the gas mileage.The predicted gas mileage for a car that weighs 3,000 pounds is approximately 55.11 miles per gallon. The closest answer choice is:

**C) 55**

Would you like any further details or have any questions?

Here are 5 related questions you might explore:
1. How do residuals affect the accuracy of a regression model?
2. What is the significance of the p-value in the regression output?
3. How would the prediction change if the weight was 3,500 pounds?
4. What is the role of the standard error of the coefficient in regression analysis?
5. How does multicollinearity impact regression results?

**Tip:** In regression analysis, a low p-value indicates that the predictor (in this case, weight) has a significant impact on the outcome variable (gas mileage).

Renly recorded the average car weight and gas mileage for top hybrid cars. The data was used to create a residual plot and regression output. Which of the following is closest to the actual gas mileage of a car that has an average weight of 3,000 pounds? Options: A) 51 B) 53 C) 55 D) 57 E) 59

Learn how to predict the gas mileage of a 3,000-pound car using linear regression. We calculate using the formula y = b0 + b1 * x, where the weight in hundreds of pounds translates to x = 30, and coefficients are provided. Closest predicted gas mileage is 55 miles per gallon.

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