Chapter 1.4, Problem 34E

(a)

To determine

The variation in number of education doctorates with time using the variation of education doctorates with the social science doctorate and the variation of social science doctorate with the time from the table representing the number of PhD graduates in Mexico every year is as follows:

	Natural Sciences	Engineering	Social Science	Education
$1990$	$70$	$10$	$60$	$30$
$1995$	$130$	$40$	$110$	$40$
$2000$	$330$	$130$	$280$	$130$
$2005$	$490$	$370$	$460$	$210$
$2010$	$590$	$550$	$830$	$520$
$2012$	$690$	$590$	$1,000$	$900$

(b)

To determine

Whether the conclusion is same for the variation of number of education doctorates with the number of social science doctorates as concluded in part (a) if r is equal to $1$. When the table representing the number of PhD graduates in Mexico every year is as follows:

	Natural Sciences	Engineering	Social Science	Education
$1990$	$70$	$10$	$60$	$30$
$1995$	$130$	$40$	$110$	$40$
$2000$	$330$	$130$	$280$	$130$
$2005$	$490$	$370$	$460$	$210$
$2010$	$590$	$550$	$830$	$520$
$2012$	$690$	$590$	$1,000$	$900$

(c)

To determine

Whether the conclusion is same for the variation of number of social science doctorates with the time as concluded in part (a) if r is equal to $1$. When the table representing the number of PhD graduates in Mexico every year is as follows:

	Natural Sciences	Engineering	Social Science	Education
$1990$	$70$	$10$	$60$	$30$
$1995$	$130$	$40$	$110$	$40$
$2000$	$330$	$130$	$280$	$130$
$2005$	$490$	$370$	$460$	$210$
$2010$	$590$	$550$	$830$	$520$
$2012$	$690$	$590$	$1,000$	$900$