Exploring Relationships Between Numerical Variables

Exploring Relationships Between Numerical VariablesScatterplots

Seating Chart

Try this …

• The first step in analyzing data it to make a ______.

• What is the slope of the following line?

graph

-1

Vocabulary

• A __________ helps us decide if there is a relationship between two numerical variables.

• The __________ variable is plotted on the x-axis.

• The ________ variable (the one we are most interested in) is plotted on the y-axis.

scatterplot

explanatory

explanatory

resp

onse

response

Golf• The goal of golf is to putt at or under

___.

• Every round starts off at the_______.

• The golfer must decide:• Hit ____(use a driver & hit off a

tee)• Hit ______(fairway has short grass)

• Very difficult to be accurate when hitting __.

Does the average driving distance affect accuracy?

par

tee box

long straight

far

Making a Scatterplot (by hand)① Decide which variable is the explanatory variable and label

the x-axis. Label the y-axis with the response variable.② Scale each axis individually.③ Draw a dot to represent each athlete.

Average Driving Distance

Driv

ing

Accu

racy

245 250 255 260 265 270 275

0.64

0.68

0.72

0.76

0.80

0.84

0.88

Making a Scatterplot (TI-84)

① Enter L1 (explanatory variable / x-axis) Enter L2 (response variable / y-axis)

② Turn the Scatterplot on

Making a Scatterplot (TI-84)

③ Look at the scatterplot

④ Check out the scale

Association: direction

There exists a relationship between the two variables.

Negative Positive

Association: no direction

If there is no relationship between the two variables, we say there is __ association. no

Mean Driving Accuracy

Mean Putting Average

Good DriversBad Putters

Bad DriversBad Putters

Bad DriversGood Putters

Good DriversGood Putters

Association: form

• Linear

• Non-Linear

Association: strength

• Very Strong • Strong

• Moderate • Weak

Sum it Up

• The _________ is a graph that displays the relationship between two numerical variables.

• In a scatterplot, the __________ variable is plotted on the horizontal axis and the ________ variable is plotted on the vertical axis.

• We can describe the __________ of two variables:• direction (________ or _______ )• form ( _____ or_________ )• strength (_____ to ____ )

scatterplot

explanatoryresponse

association positive negative

linear non-linearstrong weak