Line of Best Fit Equation (by hand)

[Pages:2]Line of Best Fit Equation (by hand)

o Graph the coordinates on a scatterplot. o Draw a line going through the approximate center of the data. o Find two coordinates on the line (they don't have to be points you plotted) o Use the two coordinates to find the slope o Substitute the slope and one coordinate into y=mx+b form to find the y-intercept. o Substitute the slope and y-intercept into y=mx+b form to get your final equation.

Line of Best Fit/Linear Regression and Correlation Coefficient (by graphing calculator)

o "2ND" "Y=" highlight "PLOT 1...Off" "ENTER" highlight "On" "ENTER" o "Y=" Clear any equations o "STAT" "Edit..." Highlight L1 "CLEAR" "ENTER" Repeat for any other "L" columns

with data entered o Replace "_ _ _ _ _ _" under L1 with first x value "ENTER" Repeat until all x values are

entered o Replace "_ _ _ _ _ _" under L2 with matching y value "ENTER" Repeat until all y

values are entered o Make sure each L1 value is paired with an L2 value o "Mode" Scroll to "Stat Diagnostics" Highlight "On" and hit "Enter" o "STAT" "CALC" "LinReg(ax + b)" "ENTER" "Calculate" "Enter"

You will get something that looks like: y=ax+b a = 3 (slope) b = 5 (y-intercept) r2 = .9216 r = .96 (correlation coefficient)

Correlation Coefficient (r)

- a number in the range -1 < r < 1, that indicates how well a regression equation truly represents data being examined

o If r is close to 1 (or -1), the model is considered a "good fit". o If r is close to 0, the model is "not a good fit". o If r = ?1, the model is a "perfect fit" with all data points lying on the line. o If r = 0, there is no linear relationship between the two variables.

A correlation greater than 0.8 is generally described as strong, whereas a correlation less than 0.5 is generally described as weak.

Line of Best Fit & Correlation Coefficients

Plot the points below on the given coordinate plane

Year

1930 1940 1950 1960 1970 1980 1990 2000

Life Expectancy 59.7 62.9 68.2 69.7 70.8 73.7 75.4 77.0

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