1. Georgetown Middle School Math
Summer 2017

2. Standards: 8.DSP.1 - Investigate bivariate data.
Collect bivariate data.
Graph the bivariate data on a scatter plot.
Describe patterns observed on a scatter plot, including clustering, outliers, and association (positive, negative, no correlation, linear, nonlinear).
8.DSP.2 - Draw an approximate line of best fit on a scatter plot that appears to have a linear association and informally assess the fit of the line to the data points.
8.DSP.3 - Apply concepts of an approximate line of best fit in real-world situations.
Find an approximate equation for the line of best fit using two appropriate data points.
Interpret the slope and intercept.
Solve problems using the equation.

3. Vocabulary Scatterplot Correlation Coefficient Explanatory variable
Response Variable
Outlier
Least-squares regression line
slope
y-intercept
Interpolation
Extrapolation

4. Three Key Features of a Scatterplot
Form: linear vs. nonlinear
Association: positive vs. negative vs. none
Strength: strong vs. moderate vs. weak

5. Scatterplots

6. The Correlation Coefficient, r
The correlation coefficient is a number, r, that measures the strength of the linear association between two variables.
-1 ≤ r ≤ 1
If r is close to 1, then there is a strong positive linear association.
If r is close to -1, then there is a strong negative linear association.
If r is close to 0, then there is a weak or no association.

7. Positive Correlation

8. Negative Correlation

9. Weak or No Correlation

10. Correlation…...Did you know?
Correlation has no units!!
Correlation is the same regardless of how you assign the x and y variables.
Correlation does not imply causation!!!!

11. Correlation has no units!!
Its value does not depend on the units of the two variables
Multiplying all x’s or all y’s by a constant does not change r.
Adding the same constant to all x’s or all y’s does not change r.
Changing units such as in→cm or ºF→ºC does not change r.

12. Correlation is the same regardless of how you assign the x and y variables.
r for life expectancy Women vs. Men: r = 0.977
r for life expectancy Men vs. Women: r = 0.977

13. Correlation does not imply causation!!!
Do not use the words, “causes”, “makes”, “will”, “because”, etc. when making regression analysis based conclusions.
Do use the words, “predict”, “tends”, and “on average”.

14. Writing clear descriptions based on association:
Always use a phrase like “tends to” when describing an association because the trend you are describing has variability – the association you are describing may not be true for all individuals.
Always point out any data points that appear to be unusual or not part of the general pattern.

15. Interpreting Correlation:
The correlation between daily swim suits and ski jackets purchased in an apparel store is r = Interpret this correlation.

16. Interpreting Correlation:
The correlation between daily swim suits and ski jackets purchased in an apparel store is r = -0.96
There is a strong negative correlation between daily swim suits and ski jackets purchased.
On days with strong swim suit sales, one predicts that ski jacket sales would be weak.
This does not mean that people who buy swim suits are causing potential ski jacket buyers to not buy.

17. Slope
Rise/Run means that if x is increased by 1, then y is predicted or increases by an average of the slope value.
The slope is only meaningful if the data follows a linear model.

18. y-intercept The y-intercept is the value of y when x is 0.
Use the y-intercept to interpret the data only when:
It makes sense to have a value of 0 for x.
The calculated y-intercept value is meaningful.
The data include values equal to or close to 0.

19. Slope and Causation
Interpret the slope and y-intercept: Predicted Salary = 22, ,000 College Years

20. Influential observations (outliers)
occur when the x-value is relatively low or high compared to the rest of the data and do not fit the overall trend.
These observations have a large “influence” on the regression analysis.

21. Interpolation
using the regression equation to predict values inside the observed range of the explanatory variable.

22. Extrapolation
using the regression equation to predict values outside the observed range of the explanatory variable.

23. Big Questions: What is the best way to investigate bivariate data?
What patterns can be observed by a scatterplot?
How is a line of best fit determined?
What does a line of best fit tell us about a data set?
What does a line of best fit tell us about data beyond the set?

24. Monopoly
In the game of Monopoly, dollar values paid for assets appear to correlate with their physical distance form “GO” as you move around the board in the direction of play.
In the board game, Monopoly, does a property’s distance from GO correlate to its rent when you land on it ?
Is your intuition about what to own on the monopoly board accurate?

25. Data

26. Scatterplot
Create a scatter plot comparing the number of spaces a property is from GO and the cost to purchase the property from the bank.

27. Monopoly Scatterplot

28. Extension
Make an additional scatter plot comparing the number of spaces a property is from GO and the cost to an opponent for rent with a hotel for that property.
Which properties should you buy based on cost to purchase and income for hotel.