Name:
Assigned TF and Section time:
Statistics 100 Quiz 2
Wednesday 23 February 2011
This quiz has five questions and is worth 25 points; four of the questions are on the second
page.
The scatterplot below shows the relationship between driver age (in years) and the maximum
distance at which a highway sign is legible (in feet). The summary statistics for the variables
age
and
distance
are given below the plot.
300
400
500
600
Distance
20
40
60
80
Age
Variable  Obs
Mean
Std. Dev.
+
age 
30
51.0
21.78
distance 
30
423.3
81.72
correlation age distance = 0.80
1. What is the equation of the least squares regression line for these data?
From the table above we have
s
y
= 81
.
72
, s
x
= 21
.
78, and the correlation
r
=

0
.
80. Thus,
we can find the slope by substituting these values in:
b
1
=
r
·
s
y
s
x
= (

0
.
80)
×
81
.
72
21
.
78
=

3
.
002
Also from the table, ¯
y
= 423
.
3
,
¯
x
= 51 and so the
y
–intercept is given by:
b
0
= ¯
y

b
1
¯
x
= 423
.
3

(

3
.
002)(51) = 576
.
402
So the equation of the least squares regression line is given by:
y
= 576
.
402

3
.
002
x
.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 Grandal
 Statistics, Least Squares, Linear Regression, Regression Analysis, regression line, maximum legibility distance

Click to edit the document details