WARM UP1. Draw 3 different scatter plots: positive,

negative, and no correlation. (Decide whether you want the positive and negative scatter plots to be weak or strong.)

2. Create a scatter plot from the given data and draw a trend line (line of best fit):

3. Write the equation of the line in slope intercept form that passes through the points (3, 6) and (7, 18).

X Y

5 10

11 32

17 51

22 70

MIDTERM REVIEW QUESTIONS

WORKING WITH SCATTER PLOTS

TREND LINES

Yesterday, we practiced drawing trend lines or lines of best fit.

Those lines are useful when they help us make predictions about what will happen based on the data we already have.

All lines can be represented by equations. But how do we figure out the equation for the

line of best fit for a set of data?

EXAMPLE

A farmer was measuring the height of a plant each day to determine its growth rate and entered his data in the table below.

Stat EditEnter “x” data in L1Enter “y” data in L2StatCalcLinReg (4)Enter Twice

Determine the line of best fit for the data.

YOU TRY

The table below shows the price of one way flights from Charlotte to various cities.

Use your calculator to generate the line of best fit for the data.

YOU TRY After car crashes, police officers use tire skid marks

to determine how fast the person was driving before the crash.

Use your calculator to generate the line of best fit for the data.

WEAK VS. STRONG CORRELATION

We talked yesterday about what makes the difference between weak and strong correlations.

This is important because how STRONG a correlation is tells us how ACCURATE any predictions we make will be.

Stronger correlation More accurate prediction.

So how do we know how strong our correlation is? (How good our line of best fit is)

CORRELATION COEFFICIENT

The correlation coefficient tells us how STRONG or GOOD our correlation and line of best fit are.

Correlation coefficient = r. r falls between 1 and -1 The CLOSER it is to 1 or -1, the STRONGER our

correlation is and the BETTER our line of best fit. Examples: Are the following strong or weak

correlations?r = .95 r = .3 r = -.98 r = -.02

In general, if r > .75 (or < -.75) it is a strong correlation.

CORRELATION COEFFICIENT

Our calculator will give us the “r” value when we do the LinReg

You must turn Diagnostic ON 2nd0 (Catalog) Scroll down to “DiagnosticOn” Enter 2 times

EXAMPLE

Generate the line of best fit for the following data and use the correlation coefficient to determine whether or not it is a good fit (strong correlation).

Study Time (in hours)

1.5 3.0 1.0 2.5 1.5 3.5 4.0

Grade 80 90 70 88 85 95 98

YOU TRY

Years since 1900

Cost (cents)

58 4

63 5

68 6

71 8

74 10

78 15

81 18

The table below lists the cost of postage stamps in years since 1900.

Generate the line of best fit for the following data and use the correlation coefficient to determine whether or not it is a good fit (strong correlation).

MAKING PREDICTIONS

We can make predictions using our line of best fit by plugging in given values.

Note: This is called “extrapolation” (if the given value is OUTSIDE our data set) or “interpolation” (if the given value is INSIDE our data set).

EXAMPLE# of cars

sold18 22 10 11 14 17

Money made ($)

3544 4108 2413 2554 2978 3401

1. Generate the line of best fit.

2. Is there a strong or weak correlation? How do you know?

3. According to your line of best fit, how much money would you make if you sold 30 cars?

YOU TRY

Age 20 26 30 38 45 52 60

Heart beats per minute

200 194 190 182 175 168 160

1. Generate the line of best fit.

2. Is there a strong or weak correlation? How do you know?

3. According to your line of best fit, what is the maximum recommended heart rate for a 16 year old?

4. At what age is the maximum heart rate 150?

The recommended maximum heart rate during exercise is found in the table below.

YOU TRY

Year 1970 1975 1980 1985 1990 1995

Tuition ($)

425 850 1200 1625 2025 2500

The following table shows the cost of annual tuition for state colleges from 1970 to 1995. (Note: What should we make the y-value?)

1. Generate the line of best fit.

2. Is there a strong or weak correlation? How do you know?

3. According to your line of best fit, what will the cost of tuition be in 2015?

4. When will the cost of tuition reach $7,000?

LET’S RUN OUR OWN EXPERIMENTS!

As a class, we are going to collect data, make a scatter plot, and use it to make predictions.

THE QUESTION

Is height related to age? Before we conduct the experiment, what do

you think we’ll find out? We will divide the class in half for this

experiment. You will measure your height in INCHES and

your age in MONTHS. (Example) You are 5’6” and you are 14 years

and 3 months old. Height = 66” (5x12 + 6) and Age = 171

months (14x12 + 3)

YOUR TASK Get the height and age of everyone in your half

of the class, and use that to fill in your data table.

Use your calculator to make a scatter plot and sketch it on the graph.

Use your calculator to determine the line of best fit and the correlation coefficient.

Answer the questions: What type of correlation do we have (positive,

negative, strong, weak, or no correlation) and how do you know?

What can you say about the relationship between height and age based on your data?

Based on your data, how tall would you expect someone who is 18 years and 2 months old to be?

SCENARIO #2

You are working for Willy Wonka and he is developing a new type of gum that allows you to blow a bubble just by blinking, but he’s not sure exactly how yet.

He wants to know if how many bubbles you can blow in a minute is related to how many times you can blink in a minute.

Before we conduct the experiment, what do you think we’ll find out?

YOUR TASK Monitor your partner. First, half of the class will blow

bubbles for 30 seconds while the other half counts how many they get. Then, we’ll trade.

Then, the first half of the class will blink as many times as they can in 30 seconds while the other half counts for them and then we’ll trade.

We’ll share data with each other and then use your calculator to make a scatter plot and sketch it on the graph.

Use your calculator to determine the line of best fit and the correlation coefficient.

Answer the questions: What type of correlation do we have (positive, negative, strong,

weak, or no correlation) and how do you know? What can you say about the relationship between the number of

bubbles you can blow and the number of times you can blink? Based on your data, if a person blinks 150 times in 30 seconds,

how many bubbles could you expect them to blow?

HOMEWORK

p. 163 # 3 – 6 p. 164 # 7 – 10