Scatterplotsand lines of best fit.

Warm Up

1. Draw a line with a positive slope. How can you tell when a line has a positive slope?

2. Draw a line with a negative slope. How can you tell when a line has a negative slope.

3. Describe, in words, how you would plot the points (2, -5) and (-3, 7).

Midterm Review

Today’s Objectives SWBAT identify and interpret

positive, negative, and no correlation and strong vs. weak correlations on a graph.

SWBAT draw scatterplots by hand and using the calculator.

SWBAT describe the relationship between an independent and dependent variable based on the scatter plot shown.

Scatter Plots A graph of plotted points that show the

relationship between two sets of data

They tell us if the two different variables are related, and if so, HOW they are related.

Where do we see scatterplots?

In the news. In science class. Where else can you think of?

If you can recognize positive and negative slope of a line…

then you can determine if a scatter plot is showing a positive or negative relationship between variables!

POSITIVE (the dots are going up)

NEGATIVE (the dots are going down)

Scatter plots also tell us if there is no relationship at all Which we call NO CORRELATION

Correlation

Correlation means relationship. When we say something has a

positive correlation, it has a positive relationship.

A negative correlation, means negative relationship.

No correlation means that there is no relationship between the two variables.

Take a vote: What type of correlation does the scatter plot show?

Take a Vote: What type of correlation does the scatter plot show?

Take a Vote: What type of correlation does the scatter plot show?

Strong vs. weak correlation

We can also describe correlations as:strong or weak

Take a Vote: What type of correlation does the scatter plot show? Strong or weak?

Take a Vote: What type of correlation does the scatter plot show? Strong or weak?

Take a Vote: What type of correlation does the scatter plot show? Strong or weak?

Take a Vote: Describe the correlation of the data sets shown in the scatterplots below using both types of descriptors:

Draw your own!

Draw three scatterplots using any combination of positive, negative, or no correlation AND strong or weak.

Hands Up, Pair Up

Walk around the room, high-fiving your classmates.

When I say “pair up,” the person that you are high-fiving becomes your partner.

Exchange scatterplots with your new partner. Describe the correlations of your partners’ scatterplots and check to see if you agree.

So what does the correlation tell us about the variables?

Again, correlation means RELATIONSHIP.

But correlation does not mean that one variable causes the other.

For example, there may be a relationship between age and weight, but being older does not necessarily cause you to weigh more.

Can you think of another example?

For example…What type of correlation do

we see here?So, that means that your

height as an adult depends on how tall you were when you were born.

Since they are positively correlated, this graph tells us that the taller you are at birth, the taller you will be when you are a fully grown adult.

Infant Birth Height

Heig

ht

as

an

Ad

ult

What does the scatter plot above tell us about the relationship between infant birth height and your height as an adult?

Describe the correlation. What does it tell us about average neighborhood income and crime rate?

Average Neighborhood Income

Cri

me

Rate

How about this?

What does the scatter plot above tell us about the relationship your English grade and the # of M&Ms you eat?

Number of M & Ms you eat

Your

Gra

de in E

ng

lish

Post it Note: Describe and interpret the correlation shown below:

Hours spent studying

Gra

de e

arn

ed

on

test •Is it positive,

negative, or no correlation?

•Strong or weak?

•What does this mean about the relationship between hours spent studying and grades?

Now let’s create scatterplots for specific sets of data

First, label your axes with the given variables.

Then label the axes in even increments so that your data will fit on the graph. What are even increments? How do you know if you have chosen

good increments? Then plot your points.

Example #1:

X Y

10 3

20 15

30 9

40 19

Example #2:

Week Average Temperatur

e

1 56

2 63

5 78

8 71

10 75

You Do!

Height (inches)

Weight (lbs)

62 125

66 140

67 152

70 149

Our calculators can make scatterplots too!

Here’s how: STAT EDIT Type the values for the first

variable (x) in L1 Type the values for the second

variable (y) in L2 2nd Y= ENTER ON ZOOM 9: STAT

Example #1:

X Y

10 3

20 15

30 9

40 19

Example #2:

Week Average Temperatur

e

1 56

2 63

5 78

8 71

10 75

You Do!

Height (inches)

Weight (lbs)

62 125

66 140

67 152

70 149

Trend Lines

In order to actually use scatter plots to help them figure out things about real life data, economists and business people figure out the actual equation of the line that matches their scatter plot.

This is called a trend line or a line of best fit.

Drawing Trend Lines

We will use our calculators to get the exact line of best fit tomorrow.

For now, we will draw them by hand.

Example #1:

X Y

10 3

20 15

30 9

40 19

Example #2:

Week Average Temperatur

e

1 56

2 63

5 78

8 71

10 75

You Do!

Height (inches)

Weight (lbs)

62 125

66 140

67 152

70 149

Mini-Quiz

You may use your notes, but not your neighbors.

I want to see what YOU know! Put it in the box when you are

finished and return to your seat.

Homework

Workbook p. 163 (1, 2), p. 164 (11-15)