DESCRIBING RELATIONSHIPS 3.1 Scatterplots

Questions To Ask What individuals do the data describe? What are the variables? How are they measured? Are all of the variables quantitative or is at least one a categorical variable?

Explanatory vs. Response Domain / Range Independent/ Dependent x / y Input / Output Cause / Effect Outcome Predicts changes in the outcome

Example p. 144 – Explanatory or Response? Linking SAT Math and Critical Reading Scores 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 and Critical Reading scores this year in the 50 states related to each other. For each student, identify the explanatory variable and the response variable if possible. Julie – treating the mean SAT Critical reading score as the explanatory variable and the mean SAT Math score as the response variable. Jim – just interested in exploring the relationship between the two variables. No clear explanatory and response variables.

Be careful with “cause”. Just because two variables have a relationship, does not mean one causes the other!!!!

Scatterplots Shows the relationship between two quantitative variables measured on the same individuals. One variable on the horizontal axis, the other on the vertical. (eXplanatory variable goes on the x-axis) Each individual is represented by a point on the plot.

How to make a Scatterplot 1. Decide which variable should go on each axis. 2. Label and scale your axes. 3. Plot individual data values.

Example p. 148 – The Endangered Manatee The identified point represents the year In 1996, there were 732,000 powerboat registrations in Florida. That year, 60 manatees were killed by boats.

Describing Scatterplots - FODS F – O – D – S – Form – One big group? Any clusters? Linear? Curved? Outliers – Any points that deviate significantly from the overall pattern. Direction – positively associated (+ slope) negatively associated (- slope) Strength – how closely do the points follow the overall pattern?

Example p. 148 – The Endangered Manatee Form – Overall linear pattern Outliers – No clear outliers Direction – Positive association Strength – Fairly strong

Example p. 149 Form – Roughly linear with two clusters Outliers – No clear outliers Direction – Positive association Strength – Fairly strong

Adding Categorical Variables To add categorical variables, use different types of marks (●, ○, □, +) for your points.

Using the Calculator – TI Series – p. 146 TeamAverage Points Per Game Wins Alabama Arkansas Auburn25.78 Florida25.57 Georgia Kentucky15.85 Louisiana State Mississippi16.12 Mississippi State25.37 South Carolina Tennessee20.35 Vanderbilt26.76 STAT  Edit Enter data. x-variable in L1 y-variable in L2

Using the Calculator – TI Series – p. 146 STAT  Edit Enter data. x-variable in L1 y-variable in L2 2 nd  STAT PLOT Select Scatterplot x-list: L1 y-list: L2

Using the Calculator – TI Series – p. 146 Zoom 9 to graph TRACE allows you to jump from one point to another.

Using the Calculator – HP Prime – p. 146 Apps Select Statistics 2 Var

Using the Calculator – HP Prime – p. 146 TeamAverage Points Per Game Wins Alabama Arkansas Auburn25.78 Florida25.57 Georgia Kentucky15.85 Louisiana State Mississippi16.12 Mississippi State25.37 South Carolina Tennessee20.35 Vanderbilt26.76 Enter data x-variable in C1 y-variable in C2

Using the Calculator – HP Prime – p. 146 Press Plot Press Menu, make sure there is a dot next to trace, press Menu again. This allows you to jump from point to point. Press Symb First box is x-variable (C1), Second box is y-variable (C2) Make sure it says linear

HW Due: Block Day p. 159 # 1, 5, 7, 11, 27, 28