examining relationships

DESCRIBING RELATIONSHIPS3.1 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

OutcomePredicts changes in

the outcome

Example p. 144 – Explanatory or Response?Linking SAT Math and Critical Reading ScoresJulie 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 Scatterplot1. 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 1996. 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 ManateeForm – Overall linear pattern

Outliers – No clear outliers

Direction – Positive association

Strength – Fairly strong

Example p. 149Form – 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. 146Team Average Points

Per GameWins

Alabama 34.8 12Arkansas 36.8 11Auburn 25.7 8Florida 25.5 7Georgia 32.0 10Kentucky 15.8 5Louisiana State 35.7 13Mississippi 16.1 2Mississippi State 25.3 7South Carolina 30.1 11Tennessee 20.3 5Vanderbilt 26.7 6

• 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

• 2nd 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. 146Team Average

Points Per Game

Wins

Alabama 34.8 12

Arkansas 36.8 11

Auburn 25.7 8

Florida 25.5 7

Georgia 32.0 10

Kentucky 15.8 5

Louisiana State 35.7 13

Mississippi 16.1 2

Mississippi State 25.3 7

South Carolina 30.1 11Tennessee 20.3 5

Vanderbilt 26.7 6

• 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