Correlations: Describing Scatter Plots and Lines of Best Fit
Positive, Negative or no Correlation?
/ A scatter plot shows a ______correlation when the pattern rises up to the right.This means that the two quantities increase together.
/ A scatter plot shows a ______correlation when the pattern falls down to the right.
This means that as one quantity increases the other decreases.
/ A scatter plot shows ______correlation when no pattern appears.
Hint:
If the points are roughly enclosed by a circle, then there is no correlation.
Strong or Weak?
Hint:To visualize this, enclose the plotted points in an oval.
If the oval is thin, then the correlation is strong.
If the oval is fat, then the correlation is weak.
· If the points nearly form a line, then the correlation is ______.
· If the points are dispersed more widely, but still form a rough line, then the correlation is ______.
Practice
Write two or three key words to describe each relation: strong or weak, positive or negative, linear or non-linear correlation. In the event that there is no correlation, simply state so.
a. / b. / c.d. / e. / f.
Line of Best Fit
To be able to make predictions, we need to model the data with a line or a curve of best fit.
Guide for drawing a line of best fit:
1. The line must follow the ______.
2. The line should ______through as many points as possible.
3. There should be ______of points above and below the line.
4. The line should pass through points all along the line, not just at the ends.
Interpolate
When you interpolate, you are making a prediction ______the data.
Hint:You are interpolating when the value you are finding is somewhere between the first point and the last point.
Extrapolate
When you extrapolate, you are making a prediction ______the data. It often requires you to ______the line.
Independent Practice:
A. A basketball team recorded the number of points each player scored vs. the number of shots they took.
Shots / 25 / 32 / 24 / 15 / 34 / 67 / 19 / 10 / 30 / 50Points / 40 / 54 / 36 / 24 / 60 / 108 / 34 / 20 / 45 / 85
a) Identify the independent variable and the dependent variable. Explain.
b) Draw a scatter plot by hand on graph paper and find the line of best fit.
c) Describe the correlation and the relationship between the variables.
d) If a person shot 40 times, how many points would they receive? Is this interpolating or extrapolating?
e) If a person got 90 points, how many shots did they take? Is this interpolating or extrapolating?
f) If a person shot 80 times, how many points would they receive? Is this interpolating or extrapolating?