Slide 1Practice ProblemsAdditional Reading and ExamplesTest 3Slide 5Describing RelationshipsMotivating ExampleMotivating ExampleMotivating ExampleMotivating ExampleMotivating ExampleExample 26Correlation CoefficientExample 26TI-83/84 CalculatorSlide 16Anscombe Data – Page 111Slide 18Slide 19Data Set 1Data Set 2Data Set 3Data Set 4Clicker2C. Regression LineRegression LineRegression LineRegression LineEquation of a LineEquation of a LineSlide 31Prediction EquationResidualMethod of Least SquaresLeast Squares EstimatesExample 27Example 27Example 27Example 27Example 27Example 27Example 27Example 27TI-83/84 CalculatorPredictionExtrapolationExtrapolationExample 28Example 28Example 28Example 28Example 28Example 28Example 28Slide 55STAT 210Lecture 15Describing Relationships Between VariablesSeptember 29, 2016Practice ProblemsPages 130 through 137Relevant problems: V.3 (c), V.4 (c), V.7 (b), V.9 (d), and V.10 (c) Recommended problems: V.3 (c), V.7 (b), V.9 (d), and V.10 (c)Additional Reading and ExamplesRead pages 120 and 121Test 3Thursday, October 6Questions for the first 10 minutes, then test – papers due promptly at the end of class!Chapter 5 (pages 99 – 129)Combination of multiple choice questions and written/short answer questions and problems.Formulas provided; Bring a calculator!Practice Tests and Formula Sheet on Blackboard.ClickerDescribing RelationshipsTo describe the relationship between two variables we must describe the direction, form, and strengthof the relationship.A scatterplot and the correlation coefficient are twostatistical tools that can be used to help describe therelationship.Motivating ExampleWatching television also often means watching or dealing with commercials, and of interest is to describe the relationship between the number of hours of television watched per day and the number of commercials watched.If the goal is to use number of hours of television watched to predict number of commercials watched, identify the independent and dependent variables.Motivating ExampleWatching television also often means watching or dealing with commercials, and of interest is to describe the relationship between the number of hours of television watched per day and the number of commercials watched.Independent variable = X = number of hours of televisionDependent variable = Y = number of commercials watchedMotivating ExampleThe scatterplot on the next slide depicts the relationship for a random sample of 23 people. From the scatterplot:(a). Completely describe the relationship between the number of hours of television and the number of commercials watched each day; and(b). Take an educated guess as to what value you think the correlation coefficient r is equal to.Motivating Example0 2 4 6 8 10 12051015202530354045Hours of TelevisionN u m b e r o f C o m m e rc ia lsMotivating Example(a). Completely describe the relationship between the number of hours of television and the number of commercials watched each day; andThere is a fairly strong, positive, linear relationship.(b). Take an educated guess as to what value you think the correlation coefficient r is equal to.Any guess between 0.60 and 0.98 (indicating a fairly strong, positive relationship) would be acceptable. The actual value of the correlation coefficient is r = .9227 (this exact value can only be computed if you are given the actual data).Example 26x y x2 y2 xy 6 15 36 225 9020 31 400 961 620 0 10 0 100 014 16 196 256 22425 28 625 784 70016 20 256 400 32028 40 784 1600 112018 25 324 625 45010 12 100 144 120 8 15 64 225 120145 212 2785 5320 3764S x S y S x2 S y2 S xyCorrelation CoefficientSxx = S x2 - ( S x )2 nSyy = S y2 - ( S y )2 nSxy = S xy - ( S x )(S y ) nr = Sxy Sxx * SyyExample 26Sxx = 682.5 Syy = 825.6 Sxy = 690 Sxy 690r = = = .9192 Sxx Syy (682.5)(825.6)This confirms the strong, positive, linear relationship between number of ads run and number of cars sold.TI-83/84 Calculator1. First, turn on diagnostics. Hit 2ND and 0, bringing up the Catalog. Scroll down to DiagnosticOn and hit Enter twice. You only need to do this the first time.2. Enter the data into two lists, say L1 and L2.3. Hit STAT, then CALC, and choose option 8:LinReg(a+bx)4. Enter the list containing the X data (say L1), then comma (,), then the list containing the Y data (say L2). Hit Enter and r = is the correlation coefficient.ClickerAnscombe Data – Page 111As directed in class, compute the correlation coefficient for the set of data you are assigned. Determine the value to two decimal places.You can and are encouraged to work together.Data Set 1 x y Data Set 2 x yData Set 3 x yData Set 4 x y10 8.04 8 6.95 13 7.58 9 8.8111 8.33 14 9.96 6 7.24 4 4.26 12 10.84 7 4.82 5 5.68 10 9.14 8 8.1413 8.74 9 8.77 11 9.26 14 8.10 6 6.13 4 3.10 12 9.13 7 7.26 5 4.74 10 7.46 8 6.77 13 12.74 9 7.11 11 7.81 14 8.84 6 6.08 4 5.39 12 8.15 7 6.42 5 5.73 8 6.58 8 5.76 8 7.71 8 8.84 8 8.47 8 7.04 8 5.25 19 12.50 8 5.56 8 7.91 8 6.89X Y X2Y2XY10 8.04 100 64.6416 80.48 6.95 64 48.3025 55.613 7.58 169 57.4564 98.549 8.81 81 77.6161 79.2911 8.33 121 69.3889 91.6314 9.96 196 99.2016 139.446 7.24 36 52.4176 43.444 4.26 16 18.1476 17.0412 10.84 144 117.5056 130.087 4.82 49 23.2324 33.745 5.68 25 32.2624 28.499 82.51 1001 660.1727 797.6Data Set 1Data Set 12 4 6 8 10 12 14 16024681012Anscombe data set1xyData Set 22 4 6 8 10 12 14 16012345678910Anscombe Data set 2xyData Set 32 4 6 8 10 12 14 1602468101214Anscombe Dataset 3xyData Set 46 8 10 12 14 16 18 2002468101214Anscombe Dataset4xyClicker2C. Regression LineNow our goal is to determine the equation of the line that best models (explains) the relationship between X and Y. This is referred to as the regression line.Regression Line Y . . . . . . . . . . . . .
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