Correlations and Lines of Best Fit Scatter Plots

Scatter Plot A scatter plot is a graph of a collection of ordered pairs (x,y). The graph looks like a bunch of dots, but some of the graphs are a general shape or move in a general direction.

Correlation Definition: How closely an equation (for a line of best fit) models the data. Looks Like: A pattern or trend in how the points are plotted. Used To: Show trends and make predictions. Kinds: Positive, Negative, None. Strengths: Strong, Weak, None.

Positive Correlation This means that both numbers are going up. The graph has a positive slope. As x increases, y increases. Example: as the child gets older, the child gets taller

Negative Correlation One number is increasing and one is decreasing. The graph has a negative slope. As x increases, y decreases. Example: as a car gets older, the car is worth less money.

No Correlation This means the two are not related. If there seems to be no pattern, and the points looked scattered, then it is no correlation. Example: your shoe size and grade in Math class.

Line of Best Fit Also called a trend line. It is a straight line that comes closest to all of the dots on the graph. It does not touch all of the dots. It is useful because it lets us make predictions about a set of data.

Draw the line of best fit No correlation – you cannot draw a line of best fit.

Practice Together Value of car in dollars Age of car in years What type of correlation does the data have? Draw the line of best fit. Use the line of best fit to estimate the car’s value when it is 1 year old. Use the line of best fit to estimate the car’s value when it is 7 years old. How much was the car worth when it was brand new? Estimate when the car will be worth $0.