Scatterplots and Correlations

ScatterplotsDescribing relationship on bivariate data

Scatterplots and Correlation

Explanatory variablesA researcher wants to know if taking increasing amounts of ginkgo

biloba will result in increased capacities of memory ability for different students. He administers it to the students in doses of 250 milligrams, 500 milligrams, and 1000 milligrams. What is the explanatory variable in this study?

a) Amount of ginkgo biloba given to each student.

b) Change in memory ability.

c) Size of the student’s brain.

d) Whether the student takes the ginkgo biloba.

Explanatory variables (answer)A researcher wants to know if taking increasing amounts of ginkgo

biloba will result in increased capacities of memory ability for different students. He administers it to the students in doses of 250 milligrams, 500 milligrams, and 1000 milligrams. What is the explanatory variable in this study?

a) Amount of ginkgo biloba given to each student.b) Change in memory ability.

c) Size of the student’s brain.

d) Whether the student takes the ginkgo biloba.

Numeric bivariate dataThe first step in analyzing numeric bivariate data is to

a) Measure strength of linear relationship.

b) Create a scatterplot.

c) Model linear relationship with regression line.

Numeric bivariate data (answer)The first step in analyzing numeric bivariate data is to

a) Measure strength of linear relationship.

b) Create a scatterplot.c) Model linear relationship with regression line.

ScatterplotsLook at the following scatterplot. Choose which description BEST fits

the plot.

Direction: positive, form: linear, strength: strong Direction: negative, form: linear, strength: strong a) Direction: positive, form: non-linear, strength: weak Direction: negative, form: non-linear, strength: weak a) No relationship

Scatterplots (answer)Look at the following scatterplot. Choose which description BEST fits

the plot.

Direction: positive, form: linear, strength: strong Direction: negative, form: linear, strength: strong a) Direction: positive, form: non-linear, strength: weak Direction: negative, form: non-linear, strength: weak a) No relationship

ScatterplotsLook at the following scatterplot. Choose which description BEST fits

the plot.

Direction: positive, form: non-linear, strength: strong Direction: negative, form: linear, strength: strong a) Direction: positive, form: linear, strength: weak Direction: positive, form: non-linear, strength: weak a) No relationship

Scatterplots (answer)Look at the following scatterplot. Choose which description BEST fits

the plot.

Direction: positive, form: non-linear, strength: strong Direction: negative, form: linear, strength: strong a) Direction: positive, form: linear, strength: weak Direction: positive, form: non-linear, strength: weak a) No relationship

ScatterplotsLook at the following scatterplot. Choose which description BEST fits

the plot.

Direction: positive, form: non-linear, strength: strong Direction: negative, form: linear, strength: strong a) Direction: positive, form: linear, strength: weak Direction: positive, form: non-linear, strength: weak a) No relationship

Scatterplots (answer)Look at the following scatterplot. Choose which description BEST fits

the plot.

Direction: positive, form: non-linear, strength: strong Direction: negative, form: linear, strength: strong a) Direction: positive, form: linear, strength: weak Direction: positive, form: non-linear, strength: weak a) No relationship

ScatterplotsWhich of the following scatterplots displays the stronger linear

relationship?

a) Plot A

b) Plot B Same for both

Scatterplots (answer)Which of the following scatterplots displays the stronger linear

relationship?

a) Plot A

b) Plot B Same for both

ScatterplotsLook at the following scatterplot. Which variable is categorical?

a) Height

b) Weight Gender

Scatterplots (answer)Look at the following scatterplot. Which variable is categorical?

a) Height

b) Weight Gender

tips for drawing scatterplots1. SCALE THE HORIZONTAL AND VERTICAL

AXES. INTERVAL MUST BE UNIFORM

(DISTANCE OF THE TICK MARKS). IF THE

SCALE DOES NOT BEGIN AT ZERO,

INDICATE A BREAK ON YOUR PLOT.

2. LABEL BOTH AXES

3. IF YOU ARE GIVEN A GRID, TRY TO ADOPT

A SCALE SO THAT YOUR PLOT USES THE

WHOLE GRID. DON’T COMPRESS THE PLOT

INTO ONE CORNER OF THE GRID.

“r” ranges from −1 to +1

“r” quantifies the strength and direction of a linear relationship between two quantitative variables.

Strength: How closely the points follow a straight line.

Direction is positive when individuals with higher x values tend to have higher values of y.

Categorical Variables in Scatterplots

TO ADD CATEGORICAL VARIABLE TO A SCATTERPLOT, USE A DIFFERENT COLOR

OR SYMBOL FOR EACH CATEGORY.