Chapter 1.4, Problem 31E

(a)

To determine

To calculate: The regression line for number of natural science doctorates as a function of time t and correlation coefficient r also plot the provided points along with the obtained regression line using the technology when the table representing the number of PhD graduates in Mexico every year is as follows:

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

(b)

To determine

The interpretation about the number of natural science doctorates by the help of slope of the regression line which is calculated in part (a). 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

The variation in number of natural science doctorates with time from the graph which is calculated in part (a). When the table representing the number of PhD graduates in Mexico every year is as follows:

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

(d)

To determine

Whether the conclusion is same as concluded in part (c) 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
$1990$	$70$	$10$	$60$	$30$
$1995$	$130$	$40$	$110$	$40$
$2000$	$330$	$130$	$280$	$130$
$2005$	$490$	$370$	$460$	$210$
$2010$	$590$	$550$	$830$	$520$
$2012$	$690$	$590$	$1,000$	$900$