Referring to the regression model from Exercise 12-3,

(a) Find a 95% confidence interval for the coefficient of spending on higher education.

(b) Is zero in the confidence interval you found in part (a)? What does that fact imply about the coefficient of higher education?

(c) Find a 95% prediction interval for a state that has $1 per $1000 in venture capital, spends $10,000 per student on funding for major research universities, and spends 0.5% of its GDP on higher education.

Exercise 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 product), 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:

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std. Errort value Pr (>|t|) 6.708 2.5e-08 *** 2.433 0.0189 * 0.286 0.7763 -1.673e-01 2.595e-01 -0.645 0.5223 Estimate 1.051e+00 1.567e-01 9.514e-02 3.910e-02 (Intercept) Venture cap state funding 4.106e-06 1.437e-05 Higher.eD Residual standard error: 0.3007 on 46 degrees of freedom Multiple R-squared: 0.1622, Adjusted R-squared: 0.1075 F-statistic: 2.968 on 3 and 46 DF,p-value: 0.04157