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,
[tex]\sum x = 165[/tex]
[tex]\sum y = 140094[/tex]
[tex]\sum x^2 = 3615[/tex]
[tex]\sum y^2 = 2.24\times 10^9[/tex]
[tex]\sum xy = 2756048[/tex]
Since, the equation of a line is, y = ax+b
Where, [tex]a = \frac{\sum y\sum x^2-\sum x\sum xy}{n(\sum x^2)-(\sum x)^2}[/tex]
= [tex]\frac{140094\times 3615-165\times 2756048}{9\times 3615-(165)^2}[/tex]
= 318.0644068
[tex]b = \frac{n(\sum xy)-\sum x\sum y}{n(\sum x^2)-(\sum x)^2}[/tex]
= [tex]\frac{9\times 2756048-165\times 140094}{9\times 3615-(165)^2}[/tex]
= 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,
[tex]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}}[/tex]
= [tex]\frac{9\times 2756048-165\times 140094}{9\times 3615-(165)^2} \sqrt{9\times 2.24\times 10^9-(14094)^2}}[/tex]
= 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.
