Weight (pounds), x	Miles per Gallon, y

3723	18

3767	17

2739	25

3490	19

3242	22

2935	23

3764	16

2630	24

3400	18

3707	17A certain​ gas-powered car weighs 

35743574 

pounds and gets 

2020 

miles per gallon. Is the miles per gallon of this car above average or below average for cars of this​ weight?

The estimated average miles per gallon for cars of this weight is 

enter your response here 

miles per gallon. The miles per gallon of this car is 

▼
 
above

below
 
average for cars of this weight.

​(Round to three decimal places as​ needed.)

To answer whether the miles per gallon (MPG) of the car weighing 3574 pounds is above or below average, we can first use a linear regression to estimate the average MPG based on weight. The data provided for the weights (in pounds) and the corresponding MPG will allow us to calculate this relationship.

### Step 1: Organize the Data
We have the following pairs of values for weight (x) and miles per gallon (y):
\[
(3723, 18), (3767, 17), (2739, 25), (3490, 19), (3242, 22), (2935, 23), (3764, 16), (2630, 24), (3400, 18), (3707, 17)
\]

### Step 2: Perform Linear Regression
We will now fit a linear regression line using these data points. The regression line equation is generally in the form:
\[
y = mx + b
\]
where:
- \(m\) is the slope,
- \(b\) is the intercept.

We will calculate \(m\) and \(b\) to model the relationship between weight and miles per gallon, then use the weight 3574 pounds to estimate the MPG.

Let me compute the regression.The linear regression model gives us the equation:

\[
y = -0.00724x + 44.08074
\]

For a car weighing 3574 pounds, the estimated average miles per gallon (MPG) is:

\[
y = -0.00724(3574) + 44.08074 \approx 18.204
\]

Since the car's actual MPG is 20 miles per gallon, which is higher than the estimated average of 18.204 MPG, the car's MPG is **above average**.

### Final Answer:
- The estimated average miles per gallon for cars of this weight is **18.204 miles per gallon**.
- The miles per gallon of this car is **above average**.

Would you like more details on the process or clarification?

Here are 5 related questions to deepen your understanding:
1. How is the slope of the regression line interpreted in this context?
2. Can we use this regression line for predicting MPG for cars much heavier or lighter than the given range?
3. What would the MPG estimate be for a car weighing 4000 pounds?
4. How does the correlation between weight and MPG affect fuel efficiency predictions?
5. What assumptions do we make when using linear regression?

**Tip:** Always ensure your data follows a linear trend before applying linear regression to avoid misleading results.

A certain gas-powered car weighs 3574 pounds and gets 20 miles per gallon. Is the miles per gallon of this car above average or below average for cars of this weight? The estimated average miles per gallon for cars of this weight is ______ miles per gallon. The miles per gallon of this car is above or below average for cars of this weight. (Round to three decimal places as needed.)

Solve a linear regression problem to estimate the average miles per gallon for a gas-powered car weighing 3574 pounds. This problem includes key concepts in algebra and statistics, with a step-by-step guide to using the regression formula y = mx + b. The actual car's MPG is compared to the estimated average. Suitable for students in Grades 10-12.

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