The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciencesEngineeringSocialSciencesEducation1990701070301995130401104020003301302801202005490370460210201059055083052020126905901,000900(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) =   (b)Use technology to obtain the coefficient of correlation r. (Round your answer to three decimal places.)r =

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Asked Dec 1, 2019
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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 70 30
1995 130 40 110 40
2000 330 130 280 120
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) = 
 
 (b)
Use technology to obtain the coefficient of correlation r. (Round your answer to three decimal places.)
r = 
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Expert Answer

Step 1

(a)

Step-by-step procedure to obtain the regression equation using Excel:

  • In Excel sheet, enter X in one column and enter Y in one column.
  • In Data, select Data Analysis and choose Regression.
  • In Input Variable y Range, select Education.
  • In Input Variable x Range, select Social Sciences.
  • Click Labels.
  • Click Ok.

Output obtained using Excel is given below:

SUMMARY OUTPUT
Regression Statistics
Multiple R
0.963193763
0.927742225
R Square
Adjusted R 0.909677781
Standard E 103.1793528
Observatic
6
ANOVA
Significance F
df
SS
MS
Regressior
1
546749.418
546749.418 51.35736 0.0020071 18
Residual
42583.91534
10645.97883
Total
589333.3333
Coefficients Standard Error
p-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0 %
t Stat
69.39052052 -1.323544179 0.256233 -284.5003905 100. 81755 16 -284.5003905 100.8175516
0.1203112897.166405287 0.002007
Intercept -91.84141947
Socual Scie 0.862199461
0.52816177 1.196237151
0.52816177 1.196237151
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SUMMARY OUTPUT Regression Statistics Multiple R 0.963193763 0.927742225 R Square Adjusted R 0.909677781 Standard E 103.1793528 Observatic 6 ANOVA Significance F df SS MS Regressior 1 546749.418 546749.418 51.35736 0.0020071 18 Residual 42583.91534 10645.97883 Total 589333.3333 Coefficients Standard Error p-value Lower 95% Upper 95% Lower 95.0% Upper 95.0 % t Stat 69.39052052 -1.323544179 0.256233 -284.5003905 100. 81755 16 -284.5003905 100.8175516 0.1203112897.166405287 0.002007 Intercept -91.84141947 Socual Scie 0.862199461 0.52816177 1.196237151 0.52816177 1.196237151

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Step 2

From the output, the regre...

j-91.8410.862x
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j-91.8410.862x

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