1. Unit 3.1 Scatter Plots & Line of Best Fit

2. Scatter Plots Scatter Plots are graphs of (X,Y) data They are constructed to show a mathematical relationship between the data. A line of best fit is often drawn to state the mathematical relationship as an equation. The relationship may be negative (negative slope) or positive (positive slope) Also the relationship may be strong or weak. Scatter plot animation Correlation Demo Scatter plot animation Correlation Demo

3. What is correlation? Numerical measure used to show the strength and direction of a linear association between 2 variables Abbreviation for correlation is r. The value of r is always between -1 and 1. Values of -1 or 1 have a strong linear association, while values near 0 have a weak or no correlation. Correlation is NOT RESISTANT, so outliers or extreme values can greatly affect the value of r.

4. Graphs Showing Correlation

5. Do the following graphs have strong/weak and positive/negative correlations?

6. Writing “Line of Best Fit” Graph the (x,y) pairs on the graph. Look for a line (use a ruler) that seems to be in the middle of the data. Does not have to go through any of the points but it might. Find two points on the line and use them to calculate the slope. Use the slope and one of the points to solve for the y intercept. Write equation in slope intercept form. Y = mx + b

7. Accuracy of Line of Best Fit These things affect the accuracy of line of best fit: The more data points you have (bigger sample size), the more accurate your line will be. The fewer extreme values (outliers) you have, the better your line will be. The higher the correlation (closeness of data points to each other in a linear pattern), the better your line will be.

8. Creating a Scatter plot by Hand Chirping crickets - CricketsChirpActivity.pdfCricketsChirpActivity.pdf Excel solution - Temp vs Cricket chirps.xlsTemp vs Cricket chirps.xls