1. 9.1 - Correlation Correlation = relationship between 2 variables (x,y): x= independent or explanatory variable y= dependent or response variable Types of correlations (make scatter plot to determine) – Negative Linear As x↑, y ↓ – Positive Linear As x ↑, y ↑ – Non-linear Quadratic, exponential etc. – No correlation No relationship can be determined

2. Example: Graph & Determine the correlation X2.41.622.61.41.62 2.2 Y225184220240180184186215 X= advertising expenses in 1000’s Y= sales in 1000’s

3. Correlation Coefficient, r Correlation Coefficient, r = a measure of the strength and direction of a LINEAR relationship between 2 variables – Negative r = negative correlation (x↑, y↓) Between -1 and 0 inclusive -1 strong relationship & 0 is weak relationship – Positive r = positive correlation (x↑, y↑) Between 0 and 1 inclusive 1 is strong relationship & 0 is weak relationship

4. Examples: Determine if each would be a weak or strong relationship and if it is positive, negative or no correlation. 1. r=-.95 2. r=.001 3. r=.98 4. r= -.3 5. r= 1.35

5. Finding correlation coefficient with calculator Clear data – STAT 4:ClrList 2 nd 1, 2 nd 2 enter Enter data – STAT 1:edit L1 for x’s L2 for y’s enter after each Turn on diagnostics – 2 nd 0 scroll down to DIAGNOSTIC ON enter Turn Stat plotter on – 2 nd y= 1:plot on ON Type: scatter Graph data – ZOOM 9:ZoomStat Find linear equation and correlation coefficient – STAT → CALC 4:LinReg enter – r = correlation coefficient (pos. or neg., strong or weak)

6. Example: Graph & Determine the correlation coefficient with TI-83 X2.41.622.61.41.62 2.2 Y225184220240180184186215 X= advertising expenses in 1000’s Y= sales in 1000’s

7. Correlation & Causation Cause = Why? Effect = What? Types of Relationships Direct cause & effect relationship. – Size of gas tank, cost to fill up on that day Reverse cause & effect relationship. – The more people who was the car, the less time it takes Relationship caused by 3 rd or many other “lurking” variables. – Damage caused by fire, # firefighters fighting it, “lurking” is size of fire – Height and weight (age, gender, etc) Relationship caused by coincidence – lurking variables. – The more pairs of shoes owned, the more books you read