12.3. Can the percentage of the workforce who are engineers in each U.S. state b

Question

12.3. Can the percentage of the workforce who are engineers in each U.S. state be predicted by the amount of money spent in on higher education (as a percent of gross domestic prod- uct), on venture capital (dollars per $1000 of gross domestic product) for high-tech business ideas, and state funding (in dollars per student) for major research universities? Data for all 50 states and a software package revealed the following results: Estimate Std. Error t value Pr (>|t|) (Intercept) 1.051e+00 1.567e-01 6.708 2.5e-08** Venture cap 9.514e-02 3.910e-02 2.433 0.0189* State funding 4.106e-06 1.437e-05 0.2860.7763 Higher.eD -1.673e-01 2.595e-01 -0.645 0.5223 Residual standard error: 0.3007 on 46 degrees of freedorm Multiple R-squared: 0.1622, Adjusted R-squared: 0.1075 F-statistic: 2.968 on 3 and 46 DF,p-value: 0.04157 (a) Write the equation predicting the percent of engineers in the workforce (b) For a state that has $1 per $1000 in venture capital, spends $10,000 per student on funding for major research universi ties, and spends 0.5% of its GDP on higher education, what percent of engineers do you expect to see in the workforce? (c) If the state in part (b) actually had 1.5% engineers in the workforce, what would the residual be?

Explanation / Answer

Result:

a).

The regression equation is

percent of Engineers = 1.051+0.09514*venture ap+0.000004106*state funding-0.1673*Higher ed

b).

when venture ap=1, state funding=10000, Higher ed=0.5

predicted percent of Engineers = 1.051+0.09514*1+0.000004106*10000-0.1673*0.5

=1.10355

c).

Residual = 1.5 -1.10355

=0.39645

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