Scatter Plots and Best Fitting Lines

Scatter Plot A graph that is made up of data pairs (points; x, y) that are “scattered” around.

Can you think of any more?? If y tends to increase as x increases, then the data have a positive correlation. Examples: Amount of food you eat/ Weight Age/Height Hours worked/Pay If y tends to decrease as x increases, then the data have a negative correlation. Exercise/Weight Drugs/Brain cells MPH/ Travel Time Can you think of any more??

Causation vs. Correlation A lot of events are correlated, but not all events cause each other. CORRELATED WITHOUT CAUSATION: The number of ski accidents and the number of sales of hot chocolates CORRELATED WITH CAUSATION: The hours you study for a class and your grades in the class.

Correlated with Causation or Correlated Without Causation The attendance at Pope’s Football games and the amount of wins of the football team. The hours you spend on the treadmill and the number of calories you burn. The number of hours of television and your grades on your tests. WITHOUT WITH

Making a Scatter Plot You need a list of data Decide which is your independent variable (x) and which is your dependent variable (y). Then plot the points

Try to make a prediction for the height at: Age (months) Height (inches) 18 76.1 19 77 20 78.1 21 22 78.8 23 79.7 24 79.9 25 81.1 26 81.2 27 82.8 28 29 83.5 Try to make a prediction for the height at: • 21 months • 28 months

Pick two points on your line (NOT NECESSARILY from your data set) and write the equation.

Writing the equation of my best fitting line The points: (18, 76) (22, 79) The slope: Plug in x,y and solve for b: Use m and b to write the equation. This is the equation of your regression line (line of best fit)

y=3/4x+62.5