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.
