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2.5 Correlation and BestBest-Fit Lines scatter plot: lot: a graph used to determine whether a correlation exists between paired data positive correlation: y increases as x increases correlation:: y decreases as x increases negative correlation correlation:: data points show no linear pattern relatively no correlation Approximating a BestBest-Fit Line 1.) Draw a scatter plot of the data. 2.) Sketch the line that appears to follow most closely the pattern given by the points. NOTE: There should be as many points above the line as below it. 3.) Choose two points on the line, and estimate the coordinates of each point. NOTE: These two points do not have to be original data points. 4.) Find an equation of the line that passes through the two points from step 3. This equation models the data. Ex: Ex: The table gives the average heights of children for ages 1 – 10. Draw a scatter plot of the data and approximate the best fit line for the data. Also, determine if the correlation is positive, negative or does not exist. 1 73 2 85 3 93 4 100 5 107 Height (cm) Age (years) Height (cm) Age (years) 6 113 7 120 8 124 9 130 10 135 Ex: The table gives the price p (in cents) of a first-class stamp over time where t is the number of years since 1970. Draw a scatter plot of the data and approximate the best fit line for the data. Also, determine if the correlation is positive, negative or does not exist. t = time since 1970 1 8 4 10 5 13 Price (in cents) p = price of stamps (cents) Time (years) (years) 8 15 11 18 11 15 18 21 25 29 20 22 25 29 32 33 Scatter Plots and Regression Lines with the Graphing Calculator In TI 83/84: STAT 1: EDIT ENTER Type in data from “x” into L1 Type in data from “y” into L2. 2nd y = ←Stat Plot Key 1: Plot 1 ENTER ON ENTER TYPE: 1ST graph with dots (scatter plot) ENTER X LIST: L1 2ND 1 Y LIST: L2 2ND 2 MARK: ▫ + . Pick one of these. ENTER ZOOM 9: ZOOMSTAT STAT ENTER CALC 4: Lin Reg (ax +b) ENTER Lin Reg y = ax + b a= b= Equation of Best Fit Line is y = _______ x + _______ ←Type this in y = , then GRAPH.