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CHAPTERS Correlation and Regression
What You
Should lear
+ How to find the equation of a
regression line
+ How to pradict y-values using
a regression equation After verifying that tbe. Jinear correlation. between two variables is significant,
the next step is to determine the equation of the tive that best models the data,
“This ling is called 4 regression. fine, and its equation can be. used to predict the
value of y for a given value of x, Although many lines can be drawn through a
set of points, are sion Hine is determined by specific arena
Consider the seatter plot and the line shown below. Bor each data point, 4;
represents the difference between the observed y-value and the predicted
y-value for a given a-value on the Hine, ‘These diftcrences are called residuals
and can be positive, nevative, or zero. When the pomt is above tbe line, d, is
positive. When the point is below the linc, ative. Hi the ¢ ved y-value
uals the predicted y-value, d; = 0. Of all possible lines that can he drawn
throagh « set of painls, Ihe regression line is the tine for which the sum of the
squares of all the residuals
Sai
is a migunum
d
Observed
DEFINI ON
A regression fine, also called a line of best fit, is the line for which the sum
of the squares of the residuals is a minimum
In algebra, you feared that you can write an
equation of a line by finding its slope m and
y-intercept 6. Phe equation has the form,
yume b
Recall that the slope of a Kine is the ratio of its rise
alue of
over its run and the y-intervept is the
the poiatat whieh {he line crosses the y-axis. It is
6
the y-value when x
I
two points to determine the equation of a Hine. a
2 equation
In algebra, you u
statistics, you will use every point in the dara set to determine th
the regression line
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