Analyzing Data using the Graphing Calculators

Graphing

Describing Relationships: Correlation

Correlation (r2 ) measures the strength of the relationship

Value

-1 1

Strong Correlation

Exam score

Quality of B

reakfast

r2 = + 0.8

Best Fit line

Medium Correlation

Weight

Shoe S

ize

r2 = + 0.4

Best Fit line

Weak Correlation

Weight

Shoe S

ize

r2 = - 0.2

Best Fit line

55504540353025201510

60

50

40

30

20

Input

Out

put

55504540353025201510

95

85

75

65

55

Input

Out

put

302010

55

45

35

Input

Out

put

Line of Best Fit: y = ax + b

Mathematically describes a linear relationship between data

• Slope (a)• Y-Intercept (b)

55504540353025201510

60

50

40

30

20

Input

Out

put

Slope of the best fit line: y = ax + b

Positive

Y-intercept (b): Where the line crosses X=0

Y=ax+b

Crickets As Thermometers

Is there a relationship between the number of times a cricket will chirp and the temperature outside?

Graphing Data: Table (x,y)

Temp. °FChirps per

minute77 13664 8481 14855 6073 13258 65

Y is

the

out

put

or d

epen

dent

var

iabl

e

X axis input or independent variable

1. What is the line of best fit equation?

2. What is the correlation?

Can you Can-Can?

Is there a relationship between the circumference (distance around) and the diameter (the distance across) of various cylinder objects?

Data table: coordinate pairs (x,y)

Object Diameter (cm) Circumference (cm)Orange Juice Can 3 10Coffee Can (small) 5 16Tomato Juice Can 10.8 32.5Coffee Can (large) 13 40Rolled Oats Container 10 32.3Soup Can 6.8 21Candle 4.5 18

Y is

the

out

put

or d

epen

dent

var

iabl

e

X axis input or independent variable

1. What is the line of best fit equation?

2. What is the correlation?

How much weight will I lose?

Is there a relationship between the circumference (distance around) and the diameter (the distance across) of various cylinder objects?

Data tableWeeks Attended

ProgramTotal Weight Loss

12 194 188 84 1612 26

7 125 129 2914 31

Y is

the

out

put

or d

epen

dent

var

iabl

e

X axis input or independent variable

1. What is the line of best fit equation?

2. What is the correlation?

Height vs. Shoe SizeY

is t

he o

utpu

t or

dep

ende

nt v

aria

ble

X axis input or independent variable

Data tableName Height (in) Shoe Size

Proof of Causality?