Chapter 1.4, Problem 33E

(a)

To determine

The variation in number of engineering doctorates with time using the variation of engineering doctorates with the natural science doctorate and the variation of natural 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 engineering doctorates with the number of natural 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 natural 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
$1990$	$70$	$10$	$60$	$30$
$1995$	$130$	$40$	$110$	$40$
$2000$	$330$	$130$	$280$	$130$
$2005$	$490$	$370$	$460$	$210$
$2010$	$590$	$550$	$830$	$520$
$2012$	$690$	$590$	$1,000$	$900$