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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.
