Unit 4 (2-Variable Quantitative): Scatter Plots Standards: SDP 1.0 and 1.2 Objective: Determine the correlation of a scatter plot.

Unit 4 (2-Variable Unit 4 (2-Variable Quantitative):Quantitative):Scatter PlotsScatter Plots

Standards: SDP 1.0 and 1.2Objective: Determine the correlation of

a scatter plot

Scatter PlotScatter Plot

• A scatter plot is a graph of a collection of ordered pairs (x,y).

• The graph looks like a bunch of dots, but some of the graphs are a general shape or move in a general direction.

Scatter Plots

• Summarizes the relationship between two quantitative variables.

• Horizontal axis represents one variable and vertical axis represents second variable.

• Plot one point for each pair of measurements.

Positive CorrelationPositive Correlation

• If the x-coordinates and the y-coordinates both increase, then it is POSITIVE CORRELATION.

• This means that both are going up, and they are related.

Positive CorrelationPositive Correlation

• If you look at the age of a child and the child’s height, you will find that as the child gets older, the child gets taller. Because both are going up, it is positive correlation.

Age 1 2 3 4 5 6 7 8

Height “

25 31 34 36 40 41 47 55

Negative CorrelationNegative Correlation

• If the x-coordinates and the y-coordinates have one increasing and one decreasing, then it is NEGATIVE CORRELATION.

• This means that 1 is going up and 1 is going down, making a downhill graph. This means the two are related as opposites.

Negative CorrelationNegative Correlation

• If you look at the age of your family’s car and its value, you will find as the car gets older, the car is worth less. This is negative correlation.

Age of car

1 2 3 4 5

Value

$30,000 $27,000

$23,500

$18,700

$15,350

No CorrelationNo Correlation

• If there seems to be no pattern, and the points looked scattered, then it is no correlation.

• This means the two are not related.

No CorrelationNo Correlation

• If you look at the size shoe a baseball player wears, and their batting average, you will find that the shoe size does not make the player better or worse, then are not related.

A number, r, from -1 to 1 that measures how well a line fits a set of data points. -1 – strong negative correlation -0.5 – weak negative corr. 0 – no correlation0.5 – weak positive corr.1 – strong positive corr.

Correlation Coefficient

Strength

Put the correlation coefficients in order from weakest to strongest

Ex 1: 0.87, -0.81, 0.43, 0.07, -0.98

Ex 2: 0.32, -0.65, 0.63, -0.42, 0.04

0.07, 0.43, -0.81, 0.87, & -0.98

0.04, 0.32, -0.42, 0.63, & -0.65

Match the Correlation Coefficient to the graph

GraphCorrelation Coefficients

-1

-0.5

0

0.5

1

Match the Correlation Coefficient to the graph

GraphCorrelation Coefficients

-1

-0.5

0

0.5

1

Match the Correlation Coefficient to the graph

GraphCorrelation Coefficients

-1

-0.5

0

0.5

1

A. The number of hours you work vs. The amount of money in your bank account

B. The number of hours workers receive safety training vs. The number of accidents on the job.

C. The number of students at Hillgrove vs. The number of dogs in Atlanta

Positive, Negative, or No Correlation?

Some Types of RegressionLinear Regression (straight line form)

Quadratic Regression (parabolic form)

Cubic Regression (cubic form)

ScatterplotsWhich scatterplots below show a linear trend?

a) c) e)

b) d) f)

NegativeCorrelation

PositiveCorrelation

ConstantCorrelation

Best Fit Line By Hand• The table shows the number of people y who attended

each of the first seven football games x of the season. Approximate the best-fitting line for the data.

•

• Steps:• 1) Draw a scatter plot.• 2) Sketch the best-fitting line.• 3) Choose 2 data points on the• best-fit line and solve for• the slope.• 4) Use one of the points and the slope• to solve for b in y = mx + b.

x 1 2 3 4 5 6 7

y 722 763 772 826 815 857 897

Year

Sport Utility Vehicles(SUVs) Sales in U.S.

Sales (in Millions)

19911992

199319941995

1996

19971998

1999

0.91.1

1.41.61.7

2.1

2.42.7

3.2

1991 1993 1995 1997 1999 1992 1994 1996 1998 2000

x

y

Year

Veh

icle

Sal

es (

Mil

lion

s)

5

4

3

2

1

Objective - To plot data points in the coordinate plane and interpret scatter

plots.

1991 1993 1995 1997 1999 1992 1994 1996 1998 2000

x

y

Year

Veh

icle

Sal

es (

Mil

lion

s)

5

4

3

2

1

Trend is increasing.

Scatterplot - a coordinate graph of data points.

Trend appears linear.

Positive correlation.

Year SUV Sales

Predict the sales in 2001.

Plot the data on the graph such that homework timeis on the y-axis and TV time is on the x-axis..

StudentTime SpentWatching TV

Time Spenton Homework

Sam

Jon

Lara

Darren

Megan

Pia

Crystal

30 min.

45 min.

120 min.

240 min.

90 min.

150 min.

180 min.

180 min.

150 min.

90 min.

30 min.

90 min.

90 min.

90 min.

Plot the data on the graph such that homework timeis on the y-axis and TV time is on the x-axis.

TV Homework

30 min.

45 min.

120 min.

240 min.

90 min.

150 min.

180 min.

180 min.

150 min.

90 min.

30 min.

120 min.

120 min.

90 min.

Time Watching TV

Tim

e on

Hom

ewor

k

30 90 150 210 60 120 180 240

240

210

180

150

120

90

60

30

Describe the relationship between time spent onhomework and time spent watching TV.

Time Watching TV

Tim

e on

Hom

ewor

k

30 90 150 210 60 120 180 240

240

210

180

150

120

90

60

30

Trend is decreasing.

Trend appears linear.

Negative correlation.

Time on TV Time on HW

Best Fit Line Using A TI-30x Calculator

1) Press [2nd], then [Stat]

2) Select 2-VAR

3) Press [Data]

4) X1 = first data point’s x

Y1 = first data point’s y

5) Keep pressing down arrow to go to new points

6) Press [STATVAR]

7) a = slope, b = y-intercept

Best Fit Line UsingA TI-84 Graphing Calculator

• See Handout

Example 1: Consumer Debt

The table shows the total outstanding consumer debt (excluding home mortgages) in billions of dollars in selected years. (Data is from the Federal Reserve Bulletin.)

Let x = 0 correspond to 1985.

a) Using a graphing calculator, draw the scatterplot. Interpret the plot:

1. Form

2. Strength

3. Direction

Year 1985 1990 1995 2000 2003

Consumer Debt 585 789 1096 1693 1987

Example 1: Consumer Debt (cont)

b) Find the regression equation appropriate for this data set. Round values to two decimal places.

c) Find and interpret the slope of the regression equation in the context of the scenario.

Year 1985 1990 1995 2000 2003

Consumer Debt 585 789 1096 1693 1987

79.859 463.35y x

Example 1: Consumer Debt (cont)

d) Find the approximate consumer debt in 1998.

e) Find the approximate consumer debt in 2008.

1501.52 billion

2300.11 billion

Example 1: Consumer Debt (cont)

f) Using the regression equation, predict the year when consumer debt will reach 2,500 billion dollars.

25.5 years or

2010 and a 1/2 year

Example 2: Health

The table below shows the number of deaths per 100,000 people from heart disease in selected years. (Data is from the U.S. National Center for Health Statistics.)

Let x = 0 correspond to 1960.a) Using a graphing calculator, draw the scatterplot. Interpret the plot:

1. Form

2. Strength

3. Direction

Year 1960 1970 1980 1990 2000 2002

Deaths 559 483 412 322 258 240

Example 2: Health (cont)

b) Find the regression equation appropriate for this data set. Round values to two decimal places.

c) Find and interpret the slope of the regression equation in the context of the scenario.

7.616 559.25y x

Example 2: Health (cont)

d) Find an approximation for the number of deaths due to heart disease in 1995.

e) Predict the number of deaths from heart disease in 2008.

635

194