Chapter 3:
Correlation
Transformation
Investigation
Find the Correlation
Height in
Feet
Weight in
pounds
5.5
6.0
5.25
150
180 138
6.25 5.75 6.0
5.75 5.5 5.75
191
168
172
R = 0.97
181
148 172
Find the Correlation
Height in
Feet
Weight in
pounds
5.5
6.0
150
Height in
Inches
Weight in
pounds
5.25
6.25 5.75 6.0
5.75 5.5 5.75
180 138
191
172
181
168
148 172
66
72
75
69
72
69
66
150
180 138
191
172
181
168
148 172
63
R = 0.97
69
Find the Correlation…The person measuring height was
off by 2 inches. Each person is actually 2 inches shorter
than reported previously.
Height in
Inches
Weight in
pounds
66
72
150
Height in
Inches
Weight in
pounds
63
75
69
72
69
66
180 138
191
172
181
168
148 172
64
70
73
67
70
67
64
150
180 138
191
172
181
168
148 172
61
R = 0.97
69
67
Find the Correlation…The scale was incorrect; each
person is actually 5 pounds heavier than previously
reported.
Height in
Inches
Weight in
pounds
66
72
150
Height in
Inches
Weight in
pounds
63
75
69
72
69
66
180 138
191
172
181
168
148 172
66
72
75
69
72
69
66
155
185 143
196
177
186
173
153 177
63
R = 0.97
69
69
Find the Correlation…The scale was incorrect; each
person is actually 5 pounds heavier than previously
reported.
Height in
Inches
Weight in
pounds
66
72
150
Height in
Inches
Weight in
pounds
63
75
69
72
69
66
180 138
191
172
181
168
148 172
66
72
75
69
72
69
66
155
185 143
196
177
186
173
153 177
63
R = 0.97
69
69
Why?!
• Since r is calculated using standardized values
(z-scores), the correlation value will not
change if the units of measure are changed
(feet to inches, etc.)
• Adding a constant to either x or y or both will
not change the correlation because neither
the standard deviation nor distance from the
mean will be impacted.