# Least Squares regression ```AP Statistics
 Least
Squares regression is a way of finding a
line that summarizes the relationship
between two variables.

A regression line is a
straight line that describes
how a response variable y
changes as an explanatory
variable x changes. We
often use the regression
line for predicting the
value of y for a given
value of x. The least
squares regression line of
y on x is the line that
makes the sum of the
squares of the vertical
distances of the data
points from the line as
small as possible
 In
order to obtain the equation for the least
squares regression line, we must first
calculate the mean and standard deviation of
both x and y denoted x, y, sx , s y
 The equation for the least squares regression
line is the line y  a  bx or y  b0  b1 x
sy
 Where the slope b is b  r
sx
 And
the intercept a is a  y  bx

Ralph has been studying the effect of time someone
studies on time involved in extracurricular activities. The
average time someone studies is 5.7 hours with standard
deviation 19.2. The average time involved in
extracurricular activities is 7.9 hours with standard
deviation 14.5. If the correlation is r = -0.5, find the
equation of the least squares regression line.

Lets calculate the least
squares regression line
for the Sanchez family’s
gas consumption. We
drew the scatterplot in
section 3.1. Here is the
data and the scatterplot
that we obtained.
STEPS FOR THE CALCULATOR
 Make