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##### 9.1 - Correlation

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**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**Example: Graph & Determine the correlation**• X 2.4 1.6 2 2.6 1.4 1.6 2 2.2 • Y 225 184 220 240 180 184 186 215 • X= advertising expenses in 1000’s • Y= sales in 1000’s**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**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**Finding correlation coefficient with calculator**• Clear data • STAT 4:ClrList 2nd 1 , 2nd 2 enter • Enter data • STAT 1:edit L1 for x’s L2 for y’s enter after each • Turn on diagnostics • 2nd 0 scroll down to DIAGNOSTIC ON enter • Turn Stat plotter on • 2nd 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)**Example: Graph & Determine the correlation coefficient with**TI-83 • X 2.4 1.6 2 2.6 1.4 1.6 2 2.2 • Y 225 184 220 240 180 184 186 215 • X= advertising expenses in 1000’s • Y= sales in 1000’s**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 3rd 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