# VCU STAT 210 - Lecture15(2) (1) (55 pages)

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## Lecture15(2) (1)

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- Pages:
- 55
- School:
- Virginia Commonwealth University
- Course:
- Stat 210 - Basic Practice of Statistics

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STAT 210 Lecture 15 Describing Relationships Between Variables September 29 2016 Practice Problems Pages 130 through 137 Relevant 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 Examples Read pages 120 and 121 Test 3 Thursday October 6 Questions 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 Clicker Describing Relationships To describe the relationship between two variables we must describe the direction form and strength of the relationship A scatterplot and the correlation coefficient are two statistical tools that can be used to help describe the relationship Motivating Example Watching 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 Example Watching 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 television Dependent variable Y number of commercials watched Motivating Example The 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 N u m b e r o f C o m m e rc ia ls Motivating Example 45 40 35 30 25 20 15 10 5 0 0 2 4 6 Hours of Television 8 10 12 Motivating Example a Completely describe the relationship between the number of hours of television and the number of commercials watched each day and There 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 26 x y 6 20 0 14 25 16 28 18 10 8 15 31 10 16 28 20 40 25 12 15 145 Sx x2 36 400 0 196 625 256 784 324 100 64 212 Sy y2 225 961 100 256 784 400 1600 625 144 225 2785 S x2 xy 90 620 0 224 700 320 1120 450 120 120 5320 S y2 3764 S xy Correlation Coefficient Sxx S x2 S x 2 n Syy S y2 S y 2 n Sxy S xy S x S y n r Sxy Example 26 Sxx 682 5 Syy 825 6 Sxy r Sxy 690 690 Sxx Syy 9192 682 5 825 6 This confirms the strong positive linear relationship between number of ads run and number of cars sold TI 83 84 Calculator 1 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 Clicker Anscombe Data Page 111 As 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 y Data Set 3 x y Data Set 4 x y 10 8 13 9 11 14 6 4 12 7 5 10 8 13 9 11 14 6 4 12 7 5 10 8 13 9 11 14 6 4 12 7 5 8 8 8 8 8 8 8 19 8 8 8 8 04 6 95 7 58 8 81 8 33 9 96 7 24 4 26 10 84 4 82 5 68 9 14 8 14 8 74 8 77 9 26 8 10 6 13 3 10 9 13 7 26 4 74 7 46 6 77 12 74 7 11 7 81 8 84 6 08 5 39 8 15 6 42 5 73 6 58 5 76 7 71 8 84 8 47 7 04 5 25 12 50 5 56 7 91 6 89 Data Set 1 X Y X2 Y2 XY 10 8 04 100 64 6416 80 4 8 6 95 64 48 3025 55 6 13 7 58 169 57 4564 98 54 9 8 81 81 77 6161 79 29 11 8 33 121 69 3889 91 63 14 9 96 196 99 2016 139 44 6 7 24 36 52 4176 43 44 4 4 26 16 18 1476 17 04 12 10 84 144 117 5056 130 08 7 4 82 49 23 2324 33 74 5 5 68 25 32 2624 28 4 99 82 51 1001 660 1727 797 6 Data Set 1 y Anscombe data set1 12 10 8 6 4 2 0 2 4 6 8 10 x 12 14 16 Data Set 2 Anscombe Data set 2 10 9 8 7 y 6 5 4 3 2 1 0 2 4 6 8 10 x 12 14 16 Data Set 3 Anscombe Dataset 3 14 12 y 10 8 6 4 2 0 2 4 6 8 10 x 12 14 16 Data Set 4 Anscombe Dataset4 14 12 y 10 8 6 4 2 0 6 8 10 12 14 x 16 18 20 Clicker2 C Regression Line Now 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 X Regression Line Y X Regression Line Y X Equation of a Line Y intercept slope X The intercept is the predicted value of Y when x 0 Hence when x 0 the predicted y is the intercept value The slope is the amount that Y changes increases or decreases when X is increased by one unit Hence if x increases by 1 unit the predicted y increases or decreases by slope units Equation of a Line Y intercept slope X where the intercept is the predicted value of Y when X 0 and the slope is the amount that Y changes increases or decreases when X …

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