Investigating Scatter Plots

• Scatter plots –

show correlations (relationships) between two different pieces of data.

dependent variable (y’s or range) are affected by the independent variable

independent variable (x’s or domain) cause the change in dependent variable

Investigating Scatter PlotsWeight Loss Over Time

0

50

100

150

200

250

0 2 4 6 8 10 12

Days worked out per month

Weig

ht

Weight

1 3 5 7 9 11 13 15 170

20000

40000

60000

80000

100000

How shirts affect salary

Shirts Owned

Sa

lary

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 540

50

60

70

80

90

100

Chart Title

Series1

Hours Studying

Tes

t Gra

des

Data is collected and plotted on a graph

A pattern may be generally linear, but not form a perfect straight line.

Investigating Scatter Plots

• Positive correlations occur when two variables or values move in the same direction.

As the number of hours that you study increases your overall class grade increases

Investigating Scatter Plots – Positive Correlation

Study Time Class Grade

0 55

0.5 61

1 67

1.5 73

2 81

2.5 89

3 91

3.5 93

4 95

4.5 97

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 540

50

60

70

80

90

100

How Study Time Affects Grades

Time in hours

Ove

rall

gra

de

Investigating Scatter Plots

• Negative Correlations occur when variables move in opposite directions

As the number of days per month that you exercise increases your actual weight decreases

Investigating Scatter Plots – Negative Correlation

Weight Loss Over Time

0

50

100

150

200

250

0 2 4 6 8 10 12

Days worked out per month

Weig

ht

Weight

Work out time Weight

0 200

0.5 205

1 190

1.5 195

2 180

2.5 190

3 170

3.5 177

4 160

4.5 170

5 150

5.5 168

6 140

6.5 150

7 130

7.5 170

8 120

8.5 130

9 110

9.5 115

10 100

10.5 120

11 90

11.5 90

12 80

Investigating Scatter Plots

• No correlation exists if there is no noticeable pattern in the data

There is no relationship between the number of shirts someone owns and their annual salary

Investigating Scatter Plots – No Correlation

How does your wardrobe affect your salary

0

20

40

60

80

0 10 20 30 40 50

Number of shirts owned

Sal

ary

number of shirts owned salary

1 1

2 0

3 50

4 30

5 25

6 17

7 2

8 40

9 8

10 25

11 12

12 7

13 19

14 55

15 71

16 9

Line of Best Fit

• A line of best fit is a line that best represents the trend of the data on a scatter plot.

• A line of best fit may also be called a trend line

An equation of this line can be used to make predictions

The slope of the line is the average increase or decrease in y for every x

The y intercept is the value of y when x =0 The line may pass through some of the points,

none of the points, or all of the points.

Use the data to create a scatter plot

SandwichTotal Fat (g)

(X)Total Calories

(y)

Hamburger 9 260

Cheeseburger 13 320

Quarter Pounder 21 420

Quarter Pounder with Cheese 30 530

Big Mac 31 560

Arch Sandwich Special 31 550

Arch Special with Bacon 34 590

Crispy Chicken 25 500

Fish Fillet 28 560

Grilled Chicken 20 440

Grilled Chicken Light 5 300

Scatter Plot of the Data

Fat Grams and Calories in Food

0

100

200

300

400

500

600

700

0 5 10 15 20 25 30 35 40

Total Fat Grams

To

tal C

alo

rie

s

Using Graph Calculator for scatter plots and line of best fit• Reset your calculator 2nd , + , 7, 1, 2

• See “STAT PLOT” above Y=

• 2nd , Y =, enter, enter ( this turns plotter on )

• STAT, Enter, L1 are x’s, L2 are y’s

• Enter in your data for fat and calories

Using Graph Calculator for scatter plots and line of best fit• See “STAT PLOT” above Y=

• 2nd , Y =, enter, enter ( this turns plotter on )

• STAT, Enter, L1 are x’s, L2 are y’s

• Enter in your data for fat and calories

• Press Graph, (why cant I see anything?)

Using Graph Calculator for scatter plots and line of best fit• 2nd , Y =, enter, enter ( this turns plotter on )

• STAT, Enter, L1 are x’s, L2 are y’s

• Enter in your data for fat and calories

• Press Graph, (why cant I see anything?)

• Window, adjust settings

Xmin = 0

Xmax = 35

Ymin = 0

Ymax = 600

• Graph

Using Graph Calculator for scatter plots and line of best fitWe can have the calculator find an equation for

line of best fit, using linear regression.

• STAT, CALC, #4,

• Store the equation using ALPHA TRACE

• Graph

Now that we have an equation that models the data’s behavior, we can make predictions.

How many calories would expect a food item to have if it had 35 grams of fat?

about 604

Y = 11.73x + 193C = 11.73f + 193

• The slope is the average increase in Calories for every gm of fat (slope is average change in y for every x)

• The y intercept is the number of calories when a food item has no fat (y intercept is the value of y when x equals 0)

Things to remember• positive correlation has X and Y values that

rise together.

• negative correlation has X values that rise as Y values decrease

• no correlation has no visible relationship

• line of best fit is the line that best shows the trend of the data

• An equation of the line of best fit is a model of the data’s behavior and can be used to make predictions

• Slope if average increase in y for every x

• Y intercept is value of y when x = 0