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Warm-UpWrite the equation of each line.
A B (1,2) and (-3, 7)
Correlation and Lines of Best FitUnit 8 - Statistics
Correlation
•Correlation tells us about the LINEARITY of two quantitative variables
•It is a number, “r”, that can be calculated and is always .
•The closer to 1 or -1 r is, the more linear the scatterplot of the two variables.
Values of “r”• Values close to +1 indicate a positive, linear
correlation• Values close to 0 indicate no correlation or a non-linear
pattern• Values close to -1 indicate a negative, linear
correlation
0
1
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7
x
0 1 2 3 4 5 6 7
Collection 1 Scatter Plot
0
1
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x
0 1 2 3 4 5 6 7
Collection 1 Scatter Plot
0
1
2
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x
0 1 2 3 4 5 6 7
Collection 1 Scatter Plot
r = 1 (positive perfect)
r = -1 (negative perfect)
r 0 (no linear correlation)
Match the r-value to it’s graph
Remember, a low r-value doesn’t mean the variables are not related. It only tells us they are not
LINEARLY related!
Negative very weak
Positive strong
Positive weak
Negative stong
Lines of Best Fit
•Most scatterplot are not perfectly linear, but are close enough for us to model with a line.
•What is a line of Best Fit?Line that approximates the data•Where is it on a scatterplot?Through the “center” of the points•Why do we need one?Predict outcomes that are not found in the data
Finding the Line of Best Fit
1. Plot the points.2. Pick two “center” points and connect
them with a line. ▫ There should be about the same number of data points
above and below the line you draw.
3. Use the two points to calculate a slope.4. Calculate the y-intercept.
▫ Use point-slope formula and convert to slope-intercept form.
Example #1
Approximate a line of best fit for the data. Predict what y would be in x is 20.
0
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x
0 2 4 6 8 10 12 14
Collection 1 Scatter Plot
Practice Modeling
2.
3. y = 2.04x-2.36
Other models
•Match each graph with it’s line of best fit
A DB C
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