standard:mafs.8.sp.1.2 creating a linear model know that straight lines are widely used to model...

Standard:MAFS.8.SP.1.2

CREATING A LINEAR MODEL

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

Warm Up

A. (6, 15)B. (6, 9)C. (8, 12)D. (9, 7)E. (10, 12)F. (12, 15)

Graph the following points on the coordinate grid

Answer to Warm-Up

Vocabulary• Scatter Plot

• Positive and NegativeCorrelation

• Line of Best Fit

Scatter Plot

• A scatter plot is a graph of a collection of ordered pairs.

• The graph looks like a bunch of points.• The points show the relationship between two

sets of data.• The points on the graph can move in a general

direction.

Positive Correlation

• We call it a positive correlation when both the x-coordinates and the y-coordinates increase simultaneously.

Positive Correlation

The more hours the person worked , the higher the income. Both x and y are increasing simultaneously.

Hours worked daily 2 4 6 8 10 12

Income (in dollars) 16 32 48 64 80 96

Negative Correlation• We have a Negative

Correlation when one variable is increasing and the other is decreasing.

• In this case the graph goes downhill.

x 2 5 8 10 12 14 16 3 2 7

y 20 16 15 14 10 8 7 18 17 16

Negative Correlation

Temperature Outside

10 20 30 35 40 45 50 55 60

Heating Bill 140 115 110 95 80 82 75 55 35

No Correlation

• The points are scattered.

• There is no pattern.• The points are not

related• There is no correlation

No CorrelationWeight Height

3 150

4 110

4 150

5 260

5 160

5 100

5.4 210

5.5 140

6 165

6 100

RecapIdentify the correlation below. Label as positive, negative or

no correlation.

_____________

1 2

3

Line of Best Fit

The line of best fit • is the straight line that best represents the data on a

scatter plot.• may pass through all of the points, some of the

points, or none of the points.• can be used to make predictions as to what can

happen if the trend continues.• represents a relationship between two quantities.

Lines of Best Fit

Guided Practice

Years of experience

1 5 6 10 11 15 20 25 35

Income (hourly wage)

20 29 44 29 49 49 60 45 55

Hours Watch TV

0 1 1.5 2 2.5 3 3.5 4 5

Test Score 92 89 85 80 70 68 60 55 60

2

Answer to Guided Practice

Independent PracticeTime in after school (weekly) 0 1 2 3 4 5

Test scores (average) 60 65 70 75 80 90

1. Label the x and y axis

2. List the ordered pairs

3. Plot the ordered pairs

4. Is there a correlation in the data?

5. Is it positive or negative or no correlation

6. Draw the line of best fit

Independent Practice

• (0,60), (1,65), (2,70), (3,75),

(4,80), (5,90)• The more time spent on

activities, the higher the test scores.

• It is a positive correlation.