Question

Problem: Use a graphing calculator to find the equation of the line of best fit for the data below. Let x = 0 represent 1980, x = 10 represent 1990, x = 15 represent 1995, and so on.
Florida Resident Population (in thousands)
Year 1980 1990 1995 2000 2002 2003 2004 2005 2006
Population 9,746 12,938 14,538 15,983 16,682 16,982 17,367 17,768 18,090
What is the equation of the line of best fit? Describe how you found this equation.

What is the slope of the line of best fit? What does this value tell you about Florida’s population growth? (2 points)

What is the correlation coefficient? What does this value tell you about your data? (1 point)

According to the data, what will the estimated resident population be in the year 2018? Be sure to show how you arrived at your answer. (2 points)
Can someone help me awnser these asap.

Answer 1

Answer:  First question: Equation of the line, 318.64468 x + 9734.81209

Second question: Slope of the line, 318.64468

Third question: Correlation coefficient, 0.9997017489

Fourth question:  21821.2595484 is approximate population Florida in 2018

Step-by-step explanation:

Here, x represents the number of years after 1980 and y represents the population after x years.

According to the given table,

$\sum x = 165$

$\sum y = 140094$      

$\sum x^2 = 3615$      

$\sum y^2 = 2.24\times 10^9$      

$\sum xy = 2756048$      

Since, the equation of a line is, y = ax+b

Where, $a = \frac{\sum y\sum x^2-\sum x\sum xy}{n(\sum x^2)-(\sum x)^2}$

= $\frac{140094\times 3615-165\times 2756048}{9\times 3615-(165)^2}$

= 318.0644068

$b = \frac{n(\sum xy)-\sum x\sum y}{n(\sum x^2)-(\sum x)^2}$

= $\frac{9\times 2756048-165\times 140094}{9\times 3615-(165)^2}$

= 9734.81209

1) Thus, the equation of the given line,

y = 318.044068 x + 9734.81209

2) compare the equation with the general equation of line y = mx +c

m = 318.044068

Which is the slope of the line.

3) The correlation coefficient,

$r = \frac{n(\sum xy)-\sum x \sum y}{\sqrt{n\sum x^2-(\sum x)^2} \sqrt{n\sum y^2-(\sum y)^2}}$

=  $\frac{9\times 2756048-165\times 140094}{9\times 3615-(165)^2} \sqrt{9\times 2.24\times 10^9-(14094)^2}}$

= 0.9997017489

Therefore, there is a strongly positive relation between x and y.

4) For 2018,

x = 38

y = 318.0644068 × 38 + 9734.8129 = 21821.2595484 thousands.

Thus, the population of Florida in 2018 is 21821.2595484 thousands.