Scatterplots and Correlation

Scatter Plots and Correlation Scatter plots =discrete graph which shows relationships between two sets of data. Correlation = describes the type of relationship represented Strong Correlation = if the points (dots) are close to the line Weak Correlation = if the points are further from the line (spread out) Positive Correlation / “Trend”= both data sets increase together (an increasing graph) Negative Correlation / “Trend”= as one data set increases, the other decreases (a decreasing graph) Positive Correlation No correlation Negative Correlation

Patterns in scatter plots Scatter Plots show Linear Associations when the points cluster along a straight line. Linear Association Linear Association

Patterns in scatter plots Scatter Plots show Non-Linear Associations when the points do not cluster along a straight line Non- Linear Association Non- Linear Association

Patterns in scatter plots Outliers are values much greater or much less than the others in a data set. They lay outside the cluster of correlation Scatter plots do not always contain outliers. Do you notice any outliers in these scatter plots?

Linear Associations Line of Best Fit = is the line that best approximates the linear relationship between two data sets (comes closest to all of the dots on the graph) Linear Regression Equation = the equation that describes the line of best fit Linear Regression = models the relationship between two variables in a data set by producing a line of best fit

Placing a Line of Best Fit Select which line is the correct Line of Best Fit / Linear Regression A. A. A. A. B. B. B. B.

Correlation Coefficient Correlation Coefficient= indicates how closely data points are to forming a straight line (shows the strength of correlation). “r” represents the correlation coefficient Only for scatter plots that appears to have a linear association The value of the correlation coefficient is -1 ≤ r ≤ 1 +1 is perfect positive correlation, very strong (an actual line) 0 is no correlation -1 is perfect negative correlation, very strong (an actual line with negative slope).

Perfect straight decreasing line Perfect straight increasing line

Estimate r value (correlation coefficient) Speed of Car & Fuel Efficiency Cost of Property & Number of Spaces from GO on Monopoly Game Board The correlation coefficient is r = 0.9 This means that there is a STRONG Positive Correlation. The correlation coefficient is r = 0.7 This means that there is a MODERATE Positive Correlation.

Estimate r value (correlation coefficient) Price of a Used Car and Number of Miles on the Odometer Amount of Gas to Heat a House and Average Monthly Outdoor Temperature The correlation coefficient is r = -0.6 This means that there is a MODERATE Negative Correlation. The correlation coefficient is r = -0.8 This means that there is a STRONG Negative Correlation.

Estimate r value (correlation coefficient) Duration of a Rollercoaster Ride & the Height of the First Drop GPA & Weight of Student The correlation coefficient is r = 0.3 This means that there is a WEAK Positive Correlation. The correlation coefficient is r = 0 This means that there is a NO Correlation.

Paycheck & Hours Worked Estimate r value (correlation coefficient) Paycheck & Hours Worked If you had a job and made $8.25 per hour, the graph at the right would show the amount of your paycheck after working x number of hours. In this example, r = 1 because the hours you work and the amount of money you earn, show PERFECT Positive Correlation. The slope is 8.25 not 1. The r value and the slope are two different things. The correlation coefficient will have the SAME sign as the slope but rarely the same value.