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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.