I’m sorry:
The correct answer is “A”
Polly was actually right this time!
Another application of multiple regression is to standardize the raw data. This is done by subtracting data values from the mean, then dividing it by the standard deviation.
This process would be repeated for each independent variable (in this case, , amount of coal mined, and , the depth of the shaft) and for the dependent variable y, cost of mining coal.
= value for Y
= mean value of Y
S = standard deviation of the variable Y
where
and
raw value for
mean value for
standard deviation of
standardized value for
raw value for
mean value for
standard deviation for
standardized value for
Software used for the calculation now takes the standardized values instead of the raw data, and uses the least square method to derive a new regression equation.
Regression for cost (y-bar)
Variable |
Coefficient |
Beta coefficient |
Standard error |
t-value |
p-value |
Constant |
2 |
0 |
1.067 |
<0.001 | |
Tons mined |
0.4 |
1 |
1.581 |
3.162 |
0.007 |
Shaft size |
0.6 |
3 |
1.005 |
5.969 |
<0.001 |
R-squared |
0.7526 |
||||
R-squared (adj) |
0.7196 |
where
standardized value for Y
0 = Y intercept
1 = standardized (beta) coefficient for
3 = standardized (beta) value for
The first question is why the y intercept is equal to 0 (stay tuned for this).
What does the beta coefficient of 1 for mean? If , the amount of coal mined, were increased by one standardized unit of coal mined, the cost of mining would increase by one standardized unit. Thus the coefficient of depth of mines equal to three means that if the depth of the mine increases by one standardized unit, the cost of mining would increase by three standardized units.
Another way to look at this is to observe that the cost of mining is three times more sensitive to change in the depth of the mine than to the amount of coal mined. Beta coefficients help to understand the relative importance of independent variables with respect to the dependent variables.
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