4-6 Scatter Plots and Lines of Best Fit

Objective: To graph and interpret points on a scatter plot, to draw and write equations for best-

fit lines and make predictions by using those equations, and to solve problems by using

models.Open Books to page 227.

Drill #78

Write the equation of the line ( in Slope- Intercept form) passing through the following points:

1. (5, 2), ( 7, 6)2. (-2, 4), (0, 5)3. (25, 100), (30, 150)

Find the slope first!

Drill #79

1. Plot the data in the table to the left. (label your axes)

2. Draw a line of best fit through the data

3. Find two points on your line of best fit

4. Find the slope between the two points

5. Write the slope intercept form of the equation of the line of best fit

Make Predictions (Follow-up)

Using the equation of the line of best- fit

How much of an increase in score would you expect if you studied for

1. 3 hours2. 10 hoursHow much would you expect to have studied if

your score increase was:3. 5%4. 15%

(1.) Scatter Plot**

Definition: A graph in which two sets of data are plotted as ordered pairs in the coordinate plane.

Scatter plots can have either a:• Positive correlation,• Negative correlation, OR• No correlationExample #1: page 227

(2.) Positive Correlation**

• When the x and y values are related in the same way (as x increases, y increases) then we say that they have a positive correlation.

(3.) Negative Correlation**

• When the x and y values are related in opposite ways (as x increases, y decreases) then we say that they have a negative correlation.

(4.) No Correlation**

• When there is no relationship between x and y, we say that there is no correlation, or that x and y are independent.

(5.) Line of Best-Fit**

• The Best-Fit line is the line that passes close to most of the data points. It does not have to pass through any of the data points. You can use the best-fit line to make predictions about the data.

Classwork

4-6 Skills Practice #1-4

Directions: If there is a correlation, then draw a line of best fit through the data.

Make Predictions:1. How many calories burned in 60 minutes?2. How many reps at 140 pounds?3. How many newspapers in 2004?

-Plot the following data-

Note: When scaling axes find the maximum and minimum value for each variable. Make sure your axes are slightly bigger than your maximum values and slightly smaller than your minimum values

Scatter Plot: Weak Positive Correlation

Draw the Line of Best-Fit

• The Best-Fit line is the line that passes close to most of the data points. It does not have to pass through any of the data points. You can use the best-fit line to make predictions about the data.

Equation of the line of best-fit

• Find two points on the line: (7, 6) and (1, 0)

• Find the slope:

m = 1• Substitute m and find b:

y = 1x + b• Substitute (1, 0) or (7, 6)

0 = 1(1) + b

-1 = b• y = 1x - 1

17

06

Writing Equations of the Line of Best Fit*

1. Find two points (coordinates) on the line of best fit (they do not have to be data points)

2. Find the slope between the two points

3. Write the equation of the line in point-slope form (use either point)

4. Write the equation in Slope-Intercept Form

Using the Line of Best Fit to Make Predictions

Used Cars: pg 231, #15 – 17

Write an equation.

Use the equation to make predictions…

The Meaning of the Slope*

You can use the following framework to identify the meaning of the slope in the context of the problem:

The slope means that the ___________________y-represents (label)

______________ ___________ ____________Increases/decreases (+/-) slope y-units

every _______________. x-unit

The y-intercept*

The value of the y-intercept (b) tells us what is happening to the y-value when the x-value is 0…

It is the value at the beginning…

• What is the value of x at the y-intercept?

• What does it mean for x to be 0?

• What does x represent?

4-6 Practice

#3 – 5

Plot the data.

Draw a line of best fit.

Find the slope intercept form of the equation.

State the meaning of the slope and the y-intercept.

4-6 Practice

#6 – 8

Plot the data.

Draw a line of best fit.

Find the slope intercept form of the equation.

State the meaning of the slope and the y-intercept.