Statistic for the Day:
Number of People Who Have
Barreled Over Niagara Falls and
Survived: 9
Source: http://www.straightdope.com/columns/030718.html
Assignment: Read Chapter 10
These slides were created by Tom Hettmansperger and in some cases
modified by David Hunter
Results for Exam #1
40
20
0
Frequency
60
80
Histogram of exam1
15
20
25
30
35
40
45
50
exam1
Mean = 39.7
Median = 42
Arby’s
serving
1
2
3
4
5
6
7
8
9
10
11
12
13
14
reg roast beef
beef and cheddar
junior roast beef
super roast beef
giant roast beef
chicken breast fillet
grilled chicken deluxe
French dip
Italian sub
roast beef sub
turkey sub
light roast beef deluxe
light roast turkey deluxe
light roast chicken deluxe
5.5oz
6.9
3.1
9.0
8.5
7.2
8.1
6.9
10.1
10.8
9.7
6.4
6.8
6.8
calories
383
508
233
552
544
445
430
467
660
672
533
294
260
276
Research Question: At Arby’s are calories related to
the size of the sandwich?
Observational study
•Response = calories
•Explanatory variable = small or large sandwich
Small sandwich means less than 7 oz (n = 7)
Large sandwich means more than 7 oz (n = 7)
Arby's Sandwiches
700
calories
600
500
400
300
200
small
large
small = less than 7 oz
large = greater than 7 oz
700
calories
600
500
400
300
200
Small
Large
There seems to be a difference.
(Is it statistically significant?)
We can refine the explanatory variable and get more
information about the relationship between calories
and serving (sandwich) size:
Rather than split it into small and large,
keep the numerical values of the explanatory variable.
Arby's
700
calories
600
500
400
300
200
3
4
5
6
7
serving
size
8
9
10
11
Arby's
calories = -10.2 + 60.5x(serving)
Correlation = .83
700
calories
600
500
400
300
200
3
4
5
6
7
8
9
10
11
serving
S = 78.5202
R-Sq = 72.2 %
R-Sq(adj) = 69.8 %
Best fitting line through the data: called the REGRESSION LINE
Strength of relationship: measured by CORRELATON
calories = -10 + 60x(serving size in oz)
------------------------------------------------For example if you have a 6 oz sandwich
on the average you expect to get about:
-10 + 60x6 = -10 + 360 = 350 calories
-------------------------------------------------For a 10 oz sandwich:
-10 + 60x10 = -10 +600 = 590
calories = -10 + 60x(serving size in oz)
• -10 is called the intercept
• 60 is called the slope
• For every extra oz of serving
you get an increase of 60 calories
Weight
Question: What is the relationship between weight
and ideal weight (Stat 100.2 Spring 04)?
200
150
100
Ideal Weight
250
Men and Women Combined
100
150
200
Weight
250
200
150
100
Ideal Weight
250
Men and Women Combined
100
150
200
250
Weight
Red line: Weight = Ideal Weight
250
Men and Women Combined
Correlation = .867
150
200
S=15.17
100
Ideal Weight
R-squared = .752
100
150
200
250
Weight
Yellow “regression” line:
Ideal weight = 25.6 + 0.78 Weight
140
160
180
200
Ideal Weight
220
240
Men Only
150
200
Weight
250
200
180
160
140
Ideal Weight
220
240
Men Only
150
200
250
Weight
Red line: Weight = Ideal Weight
Men Only
240
Correlation = .850
160
180
200
S=12.36
140
Ideal Weight
220
R-squared = .723
150
200
250
Weight
Yellow “regression” line:
Ideal weight = 66.2 + 0.61 Weight
140
130
120
110
100
Ideal Weight
150
160
Women Only
100
120
140
Weight
160
180
200
140
130
120
110
100
Ideal Weight
150
160
Women Only
100
120
140
160
180
Weight
Red line: Weight = Ideal Weight
200
160
Correlation = .827
150
R-squared = .684
110
120
130
140
S=8.14
100
Ideal Weight
Women Only
100
120
140
160
180
Weight
Yellow regression line:
Ideal weight = 53.7 + 0.52 Weight
200
Spring 2004
Mean
Wt.
Median
Comb.
152
Ideal
Wt.
145
Diff. Wt.
Diff.
145
Ideal
Wt.
140
7
Men
174
172
2
165
170
-5
Women 136
124
12
135
120
15
5
Fall 2001 Mean
Wt.
Spring 2004 Mean
Comb.
146
Ideal
Wt.
138
Diff. Wt.
Diff.
152
Ideal
Wt.
145
8
Men
174
171
3
174
172
2
Women 132
122
10
136
124
12
7