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 60 30 1995 130 40 120 50 2000 330 130 280 140 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = t
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 60 30 1995 130 40 120 50 2000 330 130 280 140 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = t
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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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 | 60 | 30 |
1995 | 130 | 40 | 120 | 50 |
2000 | 330 | 130 | 280 | 140 |
2005 | 490 | 370 | 460 | 210 |
2010 | 590 | 550 | 830 | 520 |
2012 | 690 | 590 | 1,000 | 900 |
(a)
With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.)
y(x) =
Graph the associated points and regression line.
(b)
What does the slope tell you about the relationship between the number of social science doctorates and the number of education doctorates?
The slope tells us the increase in the number of education doctorates for each additional social science doctorate.The slope tells us the decrease in the number of education doctorates for each additional social science doctorate. The slope tells us the increase in the number of social science doctorates for each additional education doctorate.The slope tells us the decrease in the number of social science doctorates for each additional education doctorate.
(c)
Use technology to obtain the coefficient of correlation r. (Round your answer to three decimal places.)
r =
Does the value of r suggest a strong correlation between x and y?
Since r is close to 1, the correlation between x and y is a weak one.Since r is close to 0, the correlation between x and y is a weak one. Since r is close to 0, the correlation between x and y is a strong one.Since r is close to 1, the correlation between x and y is a strong one.
(d)
Does the graph suggest a roughly linear relationship between x and y? Why or why not?
Yes, the graph suggests a straight line.Yes, the graph suggests a concave-down curve rather than a straight line. Yes, the graph suggests a concave-up curve rather than a straight line.No, the graph suggests a concave-up curve rather than a straight line.No, the graph suggests a concave-down curve rather than a straight line.
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