Quality Quiz from Professor Cleary
"A" is correct.
Click here for a more complete video explanation
Kohl Minor should have kept his mouth shut, rather
than botching his interpretation of the printout, which represents
typical output of a multiple regression package. First, it provides
the regression equation indicating the plane that best fits the
dependent variable (Y, or total cost), and the two independent variables
(X1 tons of coal), (X2
depth of shaft). The figure below shows the relationship between
total cost (Y) and depth of shaft (X2)
The equation follows the following format:
The complete model:
It is clear that Kohl had the wrong recipe for interpreting
this multiple regression printout. A better explanation would be
to say that this model describes the relationship between the cost
of mining coal to both the amount of coal mined and the depth of
the mine shaft being mined. The positive sign for b1 (.4) indicates
the rate increase in cost per ton of coal being mined. The positive
sign for b2 (.6) indicates the rate of increase in cost per unit
of depth in the mine shaft.
To gain a conceptual understanding of the regression
equation view Figure 1. This shows the space where the equation
will be represented.
Figure 2 shows the plane for the regression equation
Figure 3 shows 9 data points in the form of people holding balloons
that were used to define the plane. (View the video for further
explanation of these figures.
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