(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 r-value to three decimal places.) y(t)= 43.460x−86554.2 r= Graph the associated points and regression line. (b) What does the slope tell you about the number of social science doctorates? The number of social science doctorates has been increasing at a rate of about 43 per year.The number of social science doctorates has been increasing at a rate of about 70 per year. The number of social science doctorates has been decreasing at a rate of about 43 per year.The number of social science doctorates has been decreasing at a rate of about 70 per year. (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? 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.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-down 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.The data points suggest a straight line, indicating that the number of doctorates has been growing at a more-or-less constant rate. (d) If r had been equal to 1, could you have drawn the same conclusion as in part (c)? Explain. 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.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. 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.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.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.

(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 r-value to three decimal places.) y(t)= 43.460x−86554.2 r= Graph the associated points and regression line. (b) What does the slope tell you about the number of social science doctorates? The number of social science doctorates has been increasing at a rate of about 43 per year.The number of social science doctorates has been increasing at a rate of about 70 per year. The number of social science doctorates has been decreasing at a rate of about 43 per year.The number of social science doctorates has been decreasing at a rate of about 70 per year. (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? 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.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-down 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.The data points suggest a straight line, indicating that the number of doctorates has been growing at a more-or-less constant rate. (d) If r had been equal to 1, could you have drawn the same conclusion as in part (c)? Explain. 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.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. 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.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.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.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...

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Related questions

Question

The following table shows the annual number of PhD graduates in a country in various fields.

	Natural Sciences	Engineering	Social Sciences	Education
1990	70	10	50	30
1995	130	40	110	40
2000	330	130	270	130
2005	490	370	450	210
2010	590	550	830	520
2012	690	590	1,000	900

(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 r-value to three decimal places.)

y(t)=

43.460x−86554.2

Graph the associated points and regression line.

(b)

What does the slope tell you about the number of social science doctorates?

The number of social science doctorates has been increasing at a rate of about 43 per year.The number of social science doctorates has been increasing at a rate of about 70 per year. The number of social science doctorates has been decreasing at a rate of about 43 per year.The number of social science doctorates has been decreasing at a rate of about 70 per year.

(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?

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.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-down 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.The data points suggest a straight line, indicating that the number of doctorates has been growing at a more-or-less constant rate.

(d)

If r had been equal to 1, could you have drawn the same conclusion as in part (c)? Explain.

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.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. 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.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.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.

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