How Faithful is the Old Faithful? The Practice of Statistics, 5 th Edition 1

Transcription

1 How Faithful is the Old Faithful? The Practice of Statistics, 5 th Edition 1

2 Who Has Been Eating My Cookies????????? Someone has been steeling the cookie I bought for your class A teacher from the highschool department? SCI stats team: help me identify the prime suspect in the case of the missing cookie The Practice of Statistics, 5 th Edition 2

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4 Activity: CSI Stats The Case of the Missing Cookies Collect Height and Hand Span of each member of your group in cm We are going to use the Hand Print span information to predict the prime s suspect height Record data on the table (hand span (cm) vs height cm) Make a graph with the class data on to a group white board. Example below: Describe what you see: What does the graph tell you about the relationship? Summarize your observations in a sentence or two.???which highschool teacher is believed to be the prime suspect? The Practice of Statistics, 5 th Edition 4

5 CHAPTER 3 Describing Relationships 3.1 Scatterplots and Correlation The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers

6 Scatterplots and Correlation Learning Objectives Define Explanatory and Response variables in situations where one variable helps to explain or influences the other Make a scatterplot to display the relationship between two quantitative variables. Describe the direction, form, and strength of a relationship displayed in a scatterplot and identify outliers in a scatterplot. Interpret the correlation. Understand the basic properties of correlation, including the influence of outliers on the correlation Use technology to calculate correlation. Explain why association does not imply causation. The Practice of Statistics, 5 th Edition 6

7 Explanatory and Response Variables Most statistical studies examine data on more than one variable. In many of these settings, the two variables play different roles. A response variable measures an outcome of a study. An explanatory variable may help explain or influence changes in a response variable. In the case of The Missing Cookie? The Practice of Statistics, 5 th Edition 7

8 Example1. : Weight and Height Tim wants to know if there is a relationship between height and weight. Kelly wants to know if she can predict a student s weight from his or her height. Information about height is easier to obtain than information about weight! Problem: For each student, identify the explanatory and response variables, if possible. Ex 2: Linking SAT Math and Critical Reading Scores The Practice of Statistics, 5 th Edition 8

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10 Scatterplots and How to Make them Scatterplot: Relationship between quantitative variables on the same individual Explanatory variable on the x-axis, and response on the y-axis Each individual data appears as a dot on the graph How to Make a Scatterplot 1. Decide which variable should go on each axis. Remember, the EXplanatory variable goes on the X-axis! 2. Label and scale your axes. 3. Plot individual data values. The Practice of Statistics, 5 th Edition 10

11 Track and Field Day Each member of a small statistics class ran a 40-yard sprint and then did a long jump (with a running start). The table below shows the sprint time (in seconds) and the long-jump distance (in inches) Sprint time (s) Long-jump distance (in) Problem: Make a scatterplot of the relationship between the sprint time and long-jump distance. Describe what you see. The Practice of Statistics, 5 th Edition 11

12 Describing Scatterplots To describe a scatterplot, follow the basic strategy of data analysis from Chapters 1 and 2. Look for patterns and important departures from those patterns. How to Examine a Scatterplot As in any graph of data, look for the overall pattern and for striking departures from that pattern. You can describe the overall pattern of a scatterplot by the direction, form, and strength of the relationship. An important kind of departure is an outlier, an individual value that falls outside the overall pattern of the relationship. DOFS!!!! The Practice of Statistics, 5 th Edition 12

13 Describing Scatterplots Two variables have a : positive association when above-average values of one tend to accompany above-average values of the other and when belowaverage values also tend to occur together. negative association when above-average values of one tend to accompany below-average values of the other. Strength Describe the scatterplot. Direction Form There is a moderately strong, negative, curved relationship between the percent of students in a state who take the SAT and the mean SAT math score. Further, there are two distinct clusters of states and two possible outliers that fall outside the overall pattern. The Practice of Statistics, 5 th Edition 13

14 Example: Describing a scatterplot Direction: In general, it appears that teams that score more points per game have more wins and teams that score fewer points per game have fewer wins. We say that there is a positive association between points per game and wins. Form: There seems to be a linear pattern in the graph (that is, the overall pattern follows a straight line). Strength: Because the points do not vary much from the linear pattern, the relationship is fairly strong. There do not appear to be any values that depart from the linear pattern, so there are no outliers. The Practice of Statistics, 5 th Edition 14

15 1. Describe the Track and Field Day Scatterplot 2. The Practice of Statistics, 5 th Edition 15

16 In Class-Work and Homework Hand back the Quiz Time Permitting: Religions and Babies Scatterplot that relates Income and Babies per Woman Calculator Activity Scatterplots on the calculator Homework: page 159 #1-13 ALL Quiz Next Class (please come see me if you have any questions!!!) The Practice of Statistics, 5 th Edition 16