STAT 200
Chapter 2
Looking at Data  Relationships
The following are the advertised horsepower ratings and expected gas mileage for 14 vehicles.
Vehicle
Horsepower (hp)
Gas mileage (mpg)
Origin of the car
1
170
22
European
2
205
20
American
3
190
15
American
4
125
31
American
5
310
10
American
6
285
13
American
7
127
29
Asian
8
140
25
Asian
9
215
21
Asian
10
210
23
American
11
170
18
Asian
12
140
23
American
13
194
21
Asian
14
115
29
European
What type of variables are the horsepower and gas mileage variables?
Question of interest: Do vehicles with higher horsepower tend to be less fuel efficient? In
this chapter, we will be examining the relationship between two quantitative variables.
Scatterplots
(Section 2.1)
•
help visualize possible relationship between two quantitative
(but not categorical) vari
ables
•
a plot of pairs of observations on the
x

y
plane,
e.g.,
x
i
= horsepower of vehicle
i
,
y
i
= gas mileage of vehicle
i
•
the meanmean point (
x,
y
) provides the center of the cloud of data points:
e.g.,
x
= 185
.
4
hp
,
y
= 21
.
4
mpg
1
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Here is the scatterplot of the horsepower and gas mileage for the 14 vehicles.
The horsepower readings are plotted on the horizontal (
x
) axis, and the gas mileage data
are plotted on the vertical (
y
) axis. Each vehicle is represented by a point in the plot.
Roles for variables
Which of the two variables to plot on the xaxis and which on the yaxis?
•
explanatory variable to be plotted on the xaxis
•
response variable to be plotted on the yaxis
The explanatory variable is believed to have some influence on the value of the response
variable.
However, it is not always apparent which is the explanatory variable and which is the re
sponse variable, e.g., relationship between height and weight of toddlers.
In such a case,
either variable can go on the xaxis.
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 Spring '08
 KARIM
 Least Squares, Linear Regression, Regression Analysis, Errors and residuals in statistics

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