Balloon Activity Thoughts Did you discover a relationship between the circumference of the balloons and the time it took for them to descend? What were the variables? Which variable do you think influenced the other? Do you think that there is a correlation between the two variables?

CHAPTER 4 Scatterplots and Correlation “ Face Book users get worse grades in College!!” “ “The more you use Face Book the worse your grades are!!!”

/?ID= N&TAG=RELATED;PHOTOVIDEO Does anybody know someone that gambles online???

Relationships Between 2 Variables If you want to look for relationships between two variables, you need to measure both variables on the same individuals. Often we must examine other variables as well as the relationship between 2 variables can be strongly influenced by other variables in the background.

Cont. In these relationships, usually the two variables play different roles: one explains or influences the other, the other is the results of the first explanatory variable = may explain or influence changes in the variable being measured  always plotted on the x-axis of scatterplots response variable = measures an outcome of a study  dependent on the explanatory variable  always plotted on the y-axis of scatterplots

Does Correlation imply Causation?? It is possible there is no explanatory-response distinction (so on the graph, the axes would not matter). This is the case when all you do is observe both values to see if any relationship exists and do not have a plan to use the data to explain or cause each other. “Cell Phones disrupt teens sleep”

Correlation “DOES NOT IMPLY” Causation In many studies, causation is actually the main objective, although this is not always the case.  Causation = to show the explanatory variable causes changes in the response variable.

Example 4.1 Beer and blood alcohol:  How does drinking beer affect the level of alcohol in our blood?  The legal limit for driving in all states is 0.08%. Student volunteers at the Ohio State University drank different numbers of cans of beer. Thirty minutes later, a police officer measured their blood alcohol content. Number of beers consumed is the explanatory variable, and percent of alcohol in the blood is the response variable

Example 4.2 A college student aid officer looks at the findings of the National Student Loan Survey. She notes data on the amount of debt of recent graduates, their current income, an how stressful they feel about college debt. She isn’t interested in predictions but is simply trying to understand the situation of recent college graduates. The distinction between explanatory and response variables does not apply. A sociologist looks at the same data with an eye to using amount of debt and income, along with other variables, to explain the stress caused by college debt. Now the amount of debt and income are explanatory variables and stress level is the response variable.

Scatterplots Scatterplots= the best way to look at relationships between two quantitative variables  Look for overall patterns and deviations from them  Explanatory = x-axis; Response = y-axis; Both evenly scaled and labeled

Example 4.3 (Some people use SAT scores to ranks schools. Lets look at why that is not proper.)

Scatterplots on TI-83 To Construct on the TI-83: (look at data set on page 113 #39 for example) Explanatory variable in L1, Response variable in L2 StatPlots, first graph choice, L1 and L2, ZoomStat (#9)

Problem 4.39 Merlins Breeding. Often the percent of an animal species in the wild that survive to breed again is lower following a successful breeding season. This is part of nature’s self-regulation to keep population size stable. Below is the number of breeding pairs in an isolated area and the percent of males who returned the next breeding season. Lets look at the graph. Breeding pairs Percent Return

HW

LESSON 2 Interpreting Scatterplots

When looking at scatterplots, you need to examine the overall pattern and look for any striking deviations.

Overall Pattern: mention direction, form, and strength Direction = what type of association do the points have Positive association = rises left to right Negative association = falls left to right Form = is the plot linear (roughly), non-linear, curved, etc **can also mention clusters here

Cont… Strength = how closely the points follow a clear form **strong, moderately strong, weak, moderately weak

OUTLIERS = INDIVIDUAL VALUES THAT FALLS OUTSIDE THE OVERALL PATTERN OF THE RELATIONSHIP Clusters Gaps Striking Deviations

Direction: Negative Association Form : Linear Strength: Moderately Strong

Categorical Variables SCATTERPLOTS SHOW RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES ONLY  IF YOU WANT TO INCLUDE A CATEGORICAL VARIABLE ON YOUR PLOT, USE DIFFERENT COLORS OR SYMBOLS FOR DIFFERENT CATEGORIES (THIS ADDS A THIRD VARIABLE TO YOUR PLOT)

Class Work PAGE 98, #7 DO IT TODAY!!(DUE TODAY)

Warm up Weight (pounds) Variability in braking distance (feet) Make a scatter plot. 2. Describe the direction, form, and strength

LINEAR RELATIONS IN SCATTERPLOTS ARE MOST IMPORTANT AND MOST COMMON. THEY ARE CONSIDERED: STRONG IF THE POINTS LIE CLOSE TO A STRAIGHT LINE WEAK IF THE POINTS ARE WIDELY SCATTERED STRENGTH IS NOT ALWAYS EASY TO SEE OR BEST TO JUDGE BY EYE SO WE NEED A NUMERICAL MEASURE ALONG WITH OUR GRAPHS TO PROPERLY NOTE THE STRENGTH, WHICH IS CORRELATION Correlation

Correlation = measures direction and strength of a linear relationship between 2 quantitative variables Symbol: r Formula: ***We will be using the TI-83 NO UNITS ON r !!!

Facts about Correlation 1. Explanatory and response don’t matter. Correlation will be the same answer no matter which is x (L1) and which is y (L2). 2. r is just a number, it has no units. If you change the units of the values of x and y (i.e. inches to centimeters), r will still be the same value. Positive r = positive association Negative r = negative association

Facts continued… 4.  r near 0 is very weak  strength increases as r moves away from 0 in either direction  r close to –1 or 1 means almost perfect straight line (r = –1 or 1 would be a perfect straight line)  In general, some basic guidelines to follow:  0.0 – 0.24 weak  0.25 – 0.49 moderately weak  0.5 – 0.74 moderately strong  0.75 – 0.99 strong

Cautions with Correlation Correlation requires both variables to be quantitative. You can’t plug categorical variable values into the formula for r. Correlation does not describe curved relationships between variables no matter how strong they are. LINEAR ONLY! Correlation is not resistant. r is strongly affected by outliers. Correlation is not a complete summary of two-variable data. You need to give the means and standard deviations of both x and y along with the r value and your graph.

TI-83/84 Instructions BEFORE YOU BEGIN: Hit 2 nd 0 (Catalog). Scroll down to DiagnosticOn. Hit Enter twice (should say Done). (You can’t find r on the calculator without this done. Once it is done, it should always be there unless memory is reset or batteries die.) TO FIND THE CORRELATION r: Always make the scatterplot first and check for linearity and outliers. Hit STAT, choose CALC. Choose 8:LinReg(a+bx). Enter L1,L2. Hit Enter. The results screen gives you a=, b=, r 2 =, and r=. Give answer to r with given sign and 3 decimal places rounded properly.

Examples Age Hours slept Sketch a scatter plot 2.Describe direction, form, and strength 3.Find correlation

Homework: 4.(12,13,15-20,24)

Problem Data on dating. A student wonders if tall women tend to date taller men than do short women. The following table gives the height of women and the men they are dating. Make a scatter plot. Find the correlation r. Do the data show that taller women tend to date taller men Women (x) Men (y)

Warm-up Find correlation. Age Hours slept