Question

• Given the following data where city MPG is the response variable and weight is the explanatory variable, explain why a regression line would be appropriate to analyze the relationship between these variables:

Model	City MPG	Weight
Mazda MX-5 Miata	25	2365
Mercedes/Benz SLK	22	3020
Mitsubishi Eclipse	23	3235
Pontiac Firebird	18	3545
Porsche Boxster	19	2905
Saturn SC	27	2420

• Construct the regression line for this data.
• Interpret the meaning of the y-intercept and the slope within this scenario.
• What would you predict the city MPG to be for a car that weighs 3000 pounds?
• If a car that weighs 3000 pounds actually gets 32 MPG, would this be unusual? Calculate the residual and talk about what that value represents

Answer 1

Using Minitab software, we get the following output :

The regression line is :

Interpretation of y intercept : When weight = 0 pound, the predicted value of city MPG is 39.68 MPG

Interpretation of slope : For a unit increase in weight, the predicted value of City MPG will decrease by 0.00595 MPG.

The predicted value of city MPG to be for a car that weighs 3000 pounds

= 39.68 - (0.00595*3000)

= 21.83

If a car that weighs 3000 pounds actually gets 32 MPG, residual = actual - predicted = 32 - 21.83 = 10.17

Since residual is quite high, so we can say that this would be unusual.