1. 5.7 Scatter Plots and Line of Best Fit I can write an equation of a line of best fit and use a line of best fit to make predictions.

2. Scatter Plots A scatter plot is a graph that displays two sets of data as ordered pairs. Scatter plots can help show whether or not two sets of data are related.

3. Making a Scatter Plot Make a scatter plot for the data What’s a car worth? Age (yr) Value (dollars) Age (yr) Value (dollars) 311,000115,000 212,00048,000 73,00057,000 81,00036,000 210,00066,000

4. Correlation A correlation is a relationship between the sets of data Also called a trend Positive correlation or trend

5. Correlation Negative correlation or trend

6. Correlation No correlation or trend

7. Line of Best Fit A line you draw on a graph to approximate the relationship between data sets. Also called a trend line A line of best fit should have an equal number of data points on each side If there is no correlation, you cannot draw a line of best fit

8. You Try! Create a scatter plot for the data and draw the trend line. 22 54 33.5 74.5 95 64

9. Making Predictions What is the approximate weight of a 7 month old panda? We have just used interpolation to estimate a value between two unknown values using a line of best fit. Extrapolation is used to predict a value outside the range of known values. Ex: Use your model to find the body weight of a 3-year old panda.

10. Using a Calculator Correlation coefficient (r) can be found using a graphing calculator. – Ranges between -1 and 1 – The nearer r is to 1 or -1, the more closely the trend line fits the data – r close to 1 shows a strong positive correlation – r close to -1 shows a strong negative correlation – r close to 0 means a weaker correlation or no correlation

11. Using a Calculator Press STAT and then 1 to select EDIT Enter x-values into L1 and y-values into L2 – (if x-values are years, do not enter the year, but enter 1 for one year from the start, 2 for 2 years from start, etc.) Press STAT then move Right to the CALC menu Move Down to LinReg(ax+b) and press Enter Press Enter again – a will represent slope – b will represent the y-intercept – And r will show the correlation coefficient (NOT r 2 )

12. Causation A change in one quantity causes a change in the second quantity. Correlation does not always imply causation

13. Assignment ODDS P.341 #7-9, 13-19