Transcript Chapter 4 Describing the Relation Between Two Variables

Chapter 4
Describing the Relation
Between Two Variables
4.2
Least-squares Regression
EXAMPLE Finding an Equation that Describes
a Linear Relation
Using the following sample data:
(a) Find a linear equation that relates x (the
predictor variable) and y (the response variable)
by selecting two points and finding the equation
of the line containing the points.
(b) Graph the equation on the scatter diagram.
(c) Use the equation to predict y if x = 5.
The difference between the observed value
of y and the predicted value of y is the error
or residual. That is
residual = observed - predicted
Compute the residual for the prediction
corresponding to x = 5.
EXAMPLE Finding the Least-squares
Regression Line
Using the sample data:
(a) Find the least-squares regression line.
(b) Interpret the slope and intercept.
(c) Predict y if x = 5.
(d) Compute the residual for x = 5.
(e) Draw the least-squares regression line on the
scatter diagram of the data.
EXAMPLE Computing the Sum of Squared
Residuals
Compute the sum of squared residuals for
the line describing the relation between x
and y that was obtained using two points.
Compute the sum of squared residuals for
the least-squares regression line. Which is
smaller?
EXAMPLE Finding the Least-squares
Regression Line
(a) Find the least-squares regression line
for the drilling data.
(b) Use the line to predict the drilling time
at x = 130 feet.
(c) Should the line be used to predict the
drilling time at x = 400 feet? Why?
(d) Interpret the slope and y-intercept.