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# Multiple Regression Results For Fast-Growth Firms

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For the 50 states, consider a multiple regression analysis to explain the number of new jobs created, using the number of new firms created and the percentage of fast-growth companies. The variables used are "new jobs" (in thousands), "new firms" (actual number of firms), and pct fast" (in percentage points, so that, for example, 3.15% is represented by the number 3.15. Multiple regression results are shown in Table 12.5.2.

Table 12.5.2 Multiple Regression Results For Fast-Growth Firms

The Regression Equation is:
New Jobs = - 144.764 + 0.099109 *(New Firms) + 78.61557*
(pctFast)

S = 133.7854
R2 = 81.0%
__________________________________________________________________________________
Effect on 95% Confidence Hypothesis std err t
New Jobs Interval Test of coeff statistic
Variable COEFF From To Significant? STD ERR t
Constant -144.76 -282.96 -6.57 Yes 68.6944 -2.11
New Firms 0.0991 0.0825 0.1157 Yes 0.0082 12.04
PCT Fast 78.62 20.04 137.19 Yes 29.1152 2.7

a. Approximately how much of the variation in new creation from one state to another can be explained by the number of new firms and the percent of fast-growth firms?
b. Have "new firms" and "pct fast" explained a significant proportion of the variability in "new jobs"? How do you know?
c. Find the predicted value of "new jobs" and the residual value for Washington state, given that New jobs = 242 (thousand), new firms = 1,741, and Pct fast = 2.44% for this state.
d. What exactly does the regression coefficient 0.0991 for "new firms" tell you?
e. Does the percent of fast-growth firms seem to have an impact on job creation after adjustment for the number of new companies? How do you know?

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#### Solution Preview

a. Approximately how much of the variation in new creation from one state to another can be explained by the number of new firms and the percent of fast-growth firms?
The part of the output that answers this question is the R2. Since R2 in this problem is 81.0% we can say that 81.0% of the variation (or variability) in the number of New Jobs Created can be explained by the ...

#### Solution Summary

Multiple regression results for fast-growth firms are examined.

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