The following table shows the annual number of PhD graduates in a country in various fields. 1000 1990 800 1995 600 2000 400 2005 y 200 2010 Natural Sciences 70 130 330 5 490 590 690 Engineering 10 40 Graph the associated points and regression line. 10 130 370 550 590 Social Sciences 2012 (a) Use technology to obtain the regression equation and the coefficient of correlation r for the number of social science doctorates as a function of time t in years since 1990. (Round coefficients to three significant digits. Round your value to three decimal places.) y(t) = 15 70 20 120 280 460 830 1000 800 PKIZK 600 400 200 20 25 1,000 Education 30 40 130 25 O 210 520 900 y 1000 800 600 400 200 5 10 15 (b) What does the slope tell you about the number of social science doctorates? O The number of social science doctorates has been decreasing at a rate of about 52 per year. O The number of social science doctorates has been decreasing at a rate of about 43 per year. O The number of social science doctorates has been increasing at a rate of about 52 per year. O The number of social science doctorates has been increasing at a rate of about 43 per year. 10 15 20 25 O The data points suggest a concave-up curve rather than a straight line, indicating that the number of doctorates has been growing at a slower and slower rate. The data points suggest a concave-up curve rather than a straight line, indicating that the number of doctorates has been growing at a faster and faster rate. O The data points suggest a straight line, indicating that the number of doctorates has been growing at a more-or-less constant rate. 1000 O 800 600 400 200 (c) Judging from the graph, would you say that the number of social science doctorates is increasing at a faster and faster rate, a slower and slower rate, or a more-or-less constant rate? Why? O The data points suggest a concave-down curve rather than a straight line, indicating that the number of doctorates has been growing at a slower and slower rate. O The data points suggest a concave-down curve rather than a straight line, indicating that the number of doctorates has been growing at a faster and faster rate. 5 (d) If r had been equal to 1, could you have drawn the same conclusion as in part (c)? Explain. O No, if r had been equal to 1, then the points would lie exactly on the regression line, which would indicate that the number of doctorates is growing at a constant rate. O No, if r had been equal to 1, then the points would lie exactly on the regression line, which would indicate that the number of doctorates is growing at a faster and faster rate. O No, if r had been equal to 1, then the points would lie exactly on the regression line, which would indicate that the number of doctorates is growing at a slower and slower rate. O Yes, if r had been equal to 1, then the points would lie exactly on the regression line, which would indicate that the number of doctorates is growing at a constant rate. O Yes, if r had been equal to 1, then the points would lie exactly on the regression line, which would indicate that the number of doctorates is growing at a faster and faster rate. 10 15 20 t 25