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 40 100 40 2000 330 130 280 130 2005 490 370 470 210 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.)
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
| Natural Sciences |
Engineering | Social Sciences |
Education | |
|---|---|---|---|---|
| 1990 | 70 | 10 | 50 | 30 |
| 1995 | 130 | 40 | 100 | 40 |
| 2000 | 330 | 130 | 280 | 130 |
| 2005 | 490 | 370 | 470 | 210 |
| 2010 | 590 | 550 | 830 | 520 |
| 2012 | 690 | 590 | 1,000 | 900 |
r =
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