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BiVariate Data edited version of ccollins @ www.lemars.k12.ia.us When two pieces of data are collected Data can be organized as a SCATTERPLOT – if data is numbers Or in a TWO WAY TABLE – if data is categories Scatter Plot A scatter plot is a graph of a collection of ordered pairs (x,y). The graph looks like a group of dots, but some of the graphs move in a general direction. Positive Association If the x-coordinates and the y-coordinates both increase, then it is POSITIVE ASSOCIATION This means that both values are going up and a line of best fit can be drawn Line of best fit shows the general direction that a group of points seems to be heading Positive Association If you look at the age of a child and the child’s height, you will find that as the child gets older, the child gets taller. Because both are going up, it is positive correlation. Negative Association If the y-coordinates decrease while the x-coordinates increase then it is NEGATIVE ASSOCIATION. This means the two are related as opposites and a line of best fit can be drawn. Negative Association If you look at the age of your family’s car and its value, you will find as the car gets older, the car is worth less. This is negative association. No Association If there seems to be no pattern, and the points looked scattered, then it is no association. This means the two are not related. No Association If you look at the size shoe a baseball player wears, and their batting average, you will find that the shoe size does not make the player better or worse, then are not related. Scatterplots Which scatterplots below show a linear trend? a) c) Negative Association e) Positive Association b) d) f) Constant Association Scatterplots cluster – points are near each other – not necessarily any other correlation cluster outlier outlier – when a point is not near the line of best fit non-linear association the pattern of the points is predictable, but not a line linear association a line of best fit can be drawn and predictions can be made non-linear linear Objective - To plot data points in the coordinate plane and interpret scatter plots. y Sport Utility Vehicles (SUVs) Sales in U.S. 1991 1992 1993 1994 1995 1996 1997 1998 1999 0.9 1.1 1.4 1.6 1.7 2.1 2.4 2.7 3.2 Vehicle Sales (Millions) Year Sales (in Millions) 5 4 3 2 1 1991 1993 1995 1997 1999 1992 1994 1996 1998 2000 Year x Scatterplot - a coordinate graph of data points. y Trend appears linear. Year SUV Sales Positive association. Predict the sales in 2001. Vehicle Sales (Millions) Trend is increasing. 5 4 3 2 1 1991 1993 1995 1997 1999 1992 1994 1996 1998 2000 Year x If bivariate data is about categories -not numbers- it is displayed in a Two Way Frequency Table similar information to a venn diagram 21 22 70 30 100 Although all the information is not given, using reason we can complete the table A Relative Frequency Table Shows the percent in each category – Frequency can be compared to rows or columns you have to read carefully!!! 21 22 70 30 100 The relative frequency of cell phone owners who own a mp3 player is… you are comparing to mp3 cell phone 57 TOTAL mp3 70 = .81 21 22 70 30 100 what is the relative frequency mp3 no mp3 total cell phone /70 /30 /100 no cell /70 /30 /100 total cell phone no cell total mp3 57/70 13/70 70/70 no mp3 21/30 9/30 30/30 total 78/100 22/100 100/100 cell phone no cell total mp3 .81 .19 1.00 no mp3 .70 .30 1.00 total .78 .22 1.00