Unit 2 Scatterplots

scatterplot

represents relationship between two quantitative variables

x-axis = explanatory variable

y-axis = response variable

explanatory variable

independent variable on x-axis

predicts response variable

input variable

response variable

dependent variable

is predicted by the explanatory variable

output variable

DOFS + context

Direction

Outliers

Form

Strength

Direction (DOFS + context)

increasing/positive - y-increasing as x-increases

decreasing/negative - y-decreasing as x-increases

constant/no direction - y-stays the same as x-increases

Outliers (DOFS + context)

dots outside of the pattern in the x-direction or y-direction

dots away from the majority of the dots in the x-direction or y-direction

If not outliers, say: "no unusual features"

Form (DOFS + context)

linear - dots follow a linear pattern

non-linear - dots do not follow a linear pattern (maybe quadratic, exponential, or logarithmic)

Strength (DOFS + context)

strong - dots are close to one another and/or clearly adhering to the pattern/form

weak - dots are not close to one another and/or not clearly adhering to the pattern/form

Context (DOFS + context)

Say: "The relationship between [explanatory variable] and [response variable]"

Template for DOFS + context

The relationship between [explanatory variable] and [response variable] has a [strength] [direction] [form] pattern with [outliers].

r represents the

correlation coefficient

If given r without a scatterplot, we describe the relationship between two quantitative variables

using Direction and Strength + context.

If given r with a scatterplot, we describe the relationship between two quantitative variables

using DOFS + context.

r is between

-1 and 1

If r is positive,

the direction is increasing/positive.

If r is negative,

the direction is decreasing/negative.

If r is between 0 and 0.3,

the strength is very weak.

If r is between 0.3 and 0.5,

the strength is moderately weak.

If r is between 0.5 and 0.7,

the strength is moderately strong.

If r is between 0.7 and 1,

the strength is very strong.

If r = 0,

there is no correlation between the explanatory and response variables.

If r = 1,

there is perfect correlation between the explanatory and response variables.

Just because two quantitative variables are correlated does not mean

that one variable causes the outcome of the other.

To find the value of r on our calculators,

press STAT > CALC > 8:LinReg(a+bx).

To create a scatter plot on our calculators,

enter the explanatory variable's data in L1

enter the respond variable's data in L2

press 2ND Y=, turn plot 1 on, and press ZOOM > 9:ZoomStat