Use the better fitting regression model from (8) to predict mpg when hp is 100. Round the predicted mpg value to one decimal place. Interpret the results. y= 0.0682x+30.099 

To predict the miles per gallon (mpg) when horsepower (hp) is 100 using the linear regression model provided, we can substitute \( x = 100 \) into the equation:

\[
y = 0.0682x + 30.099
\]

### Step 1: Substitute \( x = 100 \)

\[
y = 0.0682(100) + 30.099
\]

\[
y = 6.82 + 30.099
\]

\[
y = 36.919
\]

### Step 2: Round to One Decimal Place

The predicted mpg is approximately:

\[
y = 36.9
\]

### Interpretation of the Result

This prediction suggests that when the horsepower of a car is 100, the expected fuel efficiency (mpg) is approximately 36.9. According to the regression model, as horsepower increases, mpg also tends to increase by a small amount (0.0682 mpg per additional horsepower), suggesting a positive correlation between horsepower and mpg in this dataset.

Would you like more details on how this regression model could be interpreted or applied further?

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Here are some related questions to deepen your understanding:

1. How would the interpretation change if the slope was negative?
2. What does the intercept of 30.099 represent in the context of this model?
3. How reliable is this prediction outside the range of observed data?
4. How might increasing horsepower beyond 100 affect mpg, assuming the model holds?
5. How could this model be validated to ensure its accuracy?

**Tip:** Always check the range of data used to create a regression model. Predicting far outside this range can lead to inaccurate results.

Use the better fitting regression model from (8) to predict mpg when hp is 100. Round the predicted mpg value to one decimal place. Interpret the results. y= 0.0682x+30.099

Explore how to predict the miles per gallon (mpg) of a vehicle with a horsepower (hp) of 100 using a linear regression model. This problem demonstrates the use of a linear regression formula, y = 0.0682x + 30.099, to estimate fuel efficiency based on horsepower, and provides insights into interpreting regression results. Suitable for Grades 11-12.

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