Module 11 Math 075

Bivariate Data Proceed similarly as univariate distributions … What is univariate data? Which graphical models do we typically use with univariate numerical data? Still graph the data. Still analyze numerical summary/descriptive statistics (what is this?)

What do you see? Think-pair-share

... What do you see?

... What do you see?

Bivariate Data Like we were saying... proceed similarly as univariate distributions With bivariate data, we still graph (use visual model(s) to describe data; scatter plot; Least Squares Regression Line (LSRL) With bivariate data, we still look at overall patterns and deviations from those patterns (DOFS: Direction, Outlier(s), Form, Strength). How did we look for patterns in univariate numeric data? What did we use?

Bivariate Distributions Explanatory variable, x, ‘factor,’ may help predict or explain changes in response variable; explanatory variable is usually on horizontal axis Response variable, y, measures an outcome of a study, usually on vertical axis

Bivariate Data Distributions For example ... Alcohol (explanatory) and body temperature (response). Generally, the more alcohol consumed, the higher the body temperature. Still use caution with ‘cause.’ Sometimes we don’t have variables that are clearly explanatory and response. Sometimes there could be two ‘explanatory’ variables, such as ACT scores and SAT scores, or activity level and physical fitness.

Response and explanatory 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. What is the response and explanatory variables?

Response and explanatory Tim is just interested in a relationship so there is no clear explanatory or response variable. Kelly is treating a student’s height as the explanatory variable and the student’s weight as the response variable.

Response and explanatory Julie asks “Can I predict a state’s mean SAT math score if I know its mean SAT Critical Reading score?” Jim wants to know how the mean SAT math score and Critical Reading scores this years in the 50 states are related to each other.

Response and explanatory Julie is treating the mean SAT Critical Reading scores as the explanatory variable and the mean SAT Math scores as the response variable. Jim is simply interested in exploring a relationship between the two variables. For him, there is no clear explanatory or response variable.

Response and explanatory How does drinking beer affect the level of alcohol in people’s blood. The legal limit for driving in all states is 0.08%. In a study, adult volunteers drank different numbers of beer. Thirty minutes later, a police officer measured their blood alcohol levels.

Response and explanatory The explanatory variable is the number of cans of beers and the response variable is the blood alcohol level.

Response and explanatory The National Student Loan Survey provides data for the amount of debt of recent college graduates, their current income, and how stressed they feel about college debt. A sociologist looks at the data with the goal of using the amount of debt and income to explain the stress caused by college debt.

Response and explanatory Explanatory: The amount of debt and income Response: Stress caused by college debt.

Your Turn Discuss with a partner for 1 minute; come up with a situation where we have two variables that are related, but neither are clearly explanatory nor response. Discuss with your partner for 1 minute; come up with a situation where we have two variables that are related and there is clearly an explanatory and response variable.

Graphical models… Main graphical representations used to display bivariate data (two quantitative variables) is scatterplot and least squares regression line (LSRL).

Scatterplots * Scatterplots show relationship between two quantitative variables measured on the same individuals or objects. * Each individual/object in data appears as a point (x, y) on the scatterplot. * Plot explanatory variable (if there is one) on horizontal axis. If no distinction between explanatory and response, either can be plotted on horizontal axis. * Label both axes. Scale both axes with uniform intervals (but scales don’t have to match); and doesn’t have to start with zero; not considered misleading with scatterplots.

Creating & Interpreting Scatterplots Let’s collect some data: your age in years and the number of states you have visited in your lifetime. Input into Stat Crunch & create scatter plot; which is our explanatory and which is our response variable? Let’s do some predicting... to the best of our ability...

Interpreting Scatterplots Look for overall patterns (DOFS) including: direction: up or down, + or – association? outliers/deviations: individual value(s) falls outside overall pattern; no outlier rule for bi-variate data – unlike uni-variate data form: linear? curved? clusters? gaps? strength: how closely do the points follow a clear form? Strong, weak, moderate?

Measuring Linear Association Scatterplots (bi-variate data) show direction, outliers/ deviation(s), form, strength of relationship between two quantitative variables Linear relationships are important; common, simple pattern; linear relationships are our focus in this course Linear relationship is strong if points are close to a straight line; weak if scattered about Other relationships (quadratic, logarithmic, etc.)

Linear relationships

Non-linear relationships

Let’s go back to previous scatterplots... With a partner, look at one of the previous scatterplots (your choice) and analyze through DOFS (direction, outlier(s), form, strength) Three minutes... Then report out in groups that choose the same scatterplots) Be ready to make predictions based on the scatterplot

Creating & Interpreting Scatterplots Go to my website, download the COC Math 075 Survey Data. Copy & paste columns (‘Height’ And ‘Weight’) Is data messy? Does it need to be ‘fixed?’ ... Hint, scan for ordered pairs (this is bivariate data); each and every point must be an ordered pair. Graph it; do we need to evaluate any points (any possible inaccuracies?) Person 131 & 61; what should we do?

Creating & Interpreting Scatterplots ‘Height’ & ‘Weight’ Create a scatter plot of the data. Analyze (DOFS) Let’s do some predictions... It is difficult to do predictions sometimes? We will get back to this with a ‘better’ model... Person 131 & 61; what should we do???