The Consumer Reports New Car Buying Guide contains lots of information for a large number of new car models. Some of the data for 110 of these cars has been extracted. This project will focus on the relationships among several of these variables including:
Weight = Weight of the car (in pounds)
CityMPG = EPA's estimated miles per gallon for city driving
FuelCap = Size of the gas tank (in gallons)
QtrMile = Time (in seconds) to go 1/4 mile from a standing start
Acc060 = Time (in seconds) to accelerate from zero to 60 mph
PageNum = Page number on which the car appears in the buying guide
Tasks:
- Initial guesses (BEFORE looking at the data)
Consider the relationship you would expect to see between each the following pairs of variables for the car data. Place the letter for each pair on the chart below to indicate your guess as to the direction (negative, neutral, or positive) and strength of the association between the two variables. Note: You may have more than one letter at about the same spot.
(a) Weight vs. City MPG (d) Weight vs. QtrMile Time
(b) Weight vs. Fuel Capacity (e) Acceleration 060 vs. QtrMile Time
(c) Page Number vs. Fuel Capacity (f) City MPG vs. QtrMile Time
Strong
Moderate
Weak
No
Weak
Moderate
Strong
Negative
Negative
Negative
Association
Positive
Positive
Positive
2 Associations from scatterplots
Use matrix of scatter plot to examine the various pairs of car variables listed above.
Revise your estimates on the direction and strength of each association in the chart below.
How did you do with your initial guesses?
Strong
Moderate
Weak
No
Weak
Moderate
Strong
Negative
Negative
Negative
Association
Positive
Positive
Positive
- Compute correlations for each pair
The correlation coefficient, denoted by r, is a measure of the strength of the linear association between two variables. Use technology (or values supplied by your instructor) to find the correlation for each of the six pairs of variables, (a) – (f), and record the results in the table (two decimal places is fine).
correlation
correlation
(a) Weight vs. CityMPG
(d) Weight vs. QtrMile
(b) Weight vs. FuelCapacity
(e) Acc060 vs. QtrMile
(c) PageNum vs. Fuel Capacity
(f) CityMPG vs. QtrMile
4 Properties of correlation
Based on your observations of the scatterplots and computed correlations, write down at least three properties that would appear to be true about a sample correlation and its interpretation.
(1)
(2)
(3)
Sample Solution