1. Linear Regression

2. Scatterplot: Regression Line: Correlation: A line that describes how a response variable y changes as an explanatory variable x changes. Used to predict the values of y for a given value of x. r-value Measures the strength and direction of the linear relationship between two quantitative variables Always between -1 and 1. Shows the relationship between two quantitative variables measured on the same graph. Each point is an (x,y) coordinate Form: y = a + bx *be sure to label x- & y –axis and 2 points!

3. Interpretations Slope: Correlation: direction, strength, linearxy There is a direction, strength, linear of association between x and y Direction: Direction: positive or negative Strength: Strength: Strong, Moderate, or Weak Linear: Linear: *if scatterplot appears to be linear, it is linear Form: y = a + bx a = y-intercept b = slope unitx increase/decreaseby For each unit increase in x, there is an approximate increase/decrease of b in y.

4. Example 1: The following data are advertised horsepower and expected gas mileage for several 2007 vehicles a) Create a scatterplot of these data b) Find the regression line and correlation. c) Interpret the slope and correlation. VehicleHorsepowerHighway Gas Mileage (MPG) Audi A420032 BMW 32823030 Buick LaCrosse20030 Chevy Cobalt14832 Chevy Trailblazer29122 Ford Expedition30020 GMC Yukon29521 Honda Civic14040 Honda Accord16634 Hyundai Elantra13838 Lexus IS 35030628 Lincoln Navigator30018 Mazda Tribute21225 Toyota Camry15834 VW Beetle15030

5. Calculator Screens—Create Scatterplot 1)Enter data into L1 and L2 2)Create Scatterplot using L1 and L2 3)Zoom – 9: ZoomStat

6. Calculator Screens–Regression Line 1)STAT -- CALC 2)8: LinReg (a+ bx) XList: L1 Ylist: L2 3) Calculate

7. Example 1: a) Create a scatterplot of these data b) Find the regression line and correlation. y = 47.55 -.086x r = -.87 Slope: For each unit increase in horsepower, there is an approximate decrease of.086 miles per gallon in Highway Gas Mileage. Correlation: There is a strong, negative linear relationship between horsepower and gas mileage.

8. Example 2: The data for 11 stand mixers is given below. a)Create a scatterplot of the data. b)Find the regression line and correlation. c)Interpret slope and correlation. d)Find the price for a mixer that weighs 20 pounds. y= -20.71 + 12.53x r =.74 Slope: For each 1-pound increase in weight, there is an approximate increase of $12.53 in price. Correlation: There is a positive, moderate linear relationship between weight and price. y = -20.71 + 12.53(20) = $229.89Approximately $229.89 Weight (pounds)Price (dollars) 23 180 28250 19 300 17 150 25 300 26 370 21400 32350 16200 17150 830