Quality Quiz from Professor Cleary

Congratulations:
"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 1

Figure 2 shows the plane for the regression equation

Figure 2

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.

Figure 3

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