Libardo PachecoJackson ParkeAshlee FrancomQuinton Wood

Project 3

Part I. Use the data to make a scatter plot that compares city mileage on the x-axis with

highway mileage on the y-axis. Explain if this looks like a linear relationship. It does Look like a linear relationship, because as the Highway mileage goes up so does the City mileage. It doesn’t seem to be curving like an exponential growth graph would do.

1. Draw a line from the point showing the least mileage to the point showing the

greatest mileage, and identify the coordinates of these points. (27, 37) and (12, 18)Does this line look

like it’s a “good fit” to generalize the rate of change between city mileage and

highway mileage? Yes Describe the probable relationship. As Highway mpg increase so do City mpg.

2. Find the rate of change (slope) for the line in Part I.1. Interpret this rate of

change using the proper units. Slope=19/15 From the slope we see that for every 19 Highway mpg the City mpg goes up 15.

3. Find the equation of the linear function that gives the highway mileage as a

function of the city mileage. f(HighwayMPG)=19/15x+2.8

4. What highway mileage does the function predict for a car that gets 21 mpg in city

driving? 29.4 HighwayMPG Compare this to the Mercedes-Benz C-Class C250 Coupe and the

Subaru Forester 2.5 X Limited SUV. Our prediction is only 2 HighwayMPG higher than the Subaru and 2 Highway MPG lower than the Mercedes. What are the percent differences between

the predicted values and the actual values? Our prediction was 95% of the actual value of 31 HighwayMPG for the Mercedes and 109% of the 27 HighwayMPG of the Subaru. Explain the differences. One factor that we are not considering is that the Subaru is about 200 lbs. lighter than the Mercedes and that is probably making a difference. Overall our prediction is pretty accurate with a small margin of error.

5. What city mileage does the function predict for a car that gets 21 mpg in highway

driving? 14.37 CityMPG Compare this to the Acura MDX. 14.37CityMPG vs. 16 CityMPG for the Acura What is the percent difference between the predicted value and the actual value? The predicted value is 90% of the actual value. Explain the difference. The difference is explained by the margin of error. We are not taking into account the different weight of the cars or other gas saving features of the car.

6. Explain the constant term (y-intercept) of the function using proper units.

Y=19/15X+2.8 or CityMPG=19/15(HighwayMPG)+2.8

That tells us that if there was a car that got 0 CityMPG it would get 2.8 HighwayMPG.

Part II. Use the data to make a scatter plot that compares car’s weight on the x-axis with

highway mileage on the y-axis. Explain if this looks like a linear relationship. It does look like a linear relationship, even though there are some outliers.

1. Draw the best line you can that makes a “good fit” to generalize the rate of

change between car’s weight and highway mileage?

2. Find the rate of change (slope) for the line in Part II.1. Using points (3153, 31) and (6050, 18) we get a slope of -13/2897 Interpret this rate of change using the proper units. We lose 13 HighwayMPG for every 2897 lbs. that we gain.

3. Find the equation of the linear function that gives the highway mileage as a

function of the car’s weight. Y=-13/2897X+45.14

4. What highway mileage does the function predict for a car weighing 4000 lb? 27.19 HighwayMPG

Compare this to similar cars in the table. The Cadillac CTS Base Coupe weighs 3898 lbs. and gets 27 HighwayMPG. And the AstonMartin DB9 Coupe weighs 3968 and gets 20 HighwayMPG. What are the percent differences between the predicted values and the actual values? The predicted value of 27.65 HMPG for the Cadillac CTS was only 2.41% more than the actual value of 27HMPG. The predicted value of 27.33 HMPG for the Aston Martin is 36.65% more than the actual value of 20 HMPG. Explain the differences. The difference must be the margin of error. The Aston Martin is known for making fast, high performance cars and probably sacrifices a lot of gas savings to get the most performance out of its car.

5. What weight does the function predict for a car that gets 21 mpg in highway

driving? 5379.5 lbs. Compare this to similar cars in the table and explain the difference. The Acura ZDX weighs 5534 lbs and gets 23 HMPG. The Audi Q7 3.0 Premium SUV weighs 5291 lbs. and gets 22 HMPG. Those cars are very close in both HighwayMPG and the predicted weight. The difference is not much and probably falls into the margin of error.

6. Explain the constant term (y-intercept) of the function using proper units. (0lbs., 45.14 HMPG) is the Y intercept. A car weighing 0 lbs would get 45.14 HMPG. Y=-13/2897X=45.14 That line is going down. For every 2897lbs that a car increases, it loses 13 HMPG.

Below is just a reference page showing a lot of the work done to get the answers.