Answer:
y = -0.9x+10.1
Step-by-step explanation:
The equation of the line is:
[tex]y=mx+b[/tex]
You have been asked to stimate m and b. To do so, first find the product between each pair of x and y and the value of x squared:
[tex]\left[\begin{array}{cccc}x&y&x*y&x^2\\1&9&9&1\\3&7&21&9\\5&7&35&25\\7&3&21&49\\9&2&18&81\end{array}\right][/tex]
Then calculate the total sum of all columns:
[tex]\left[\begin{array}{cccc}x&y&x*y&x^2\\1&9&9&1\\3&7&21&9\\5&7&35&25\\7&3&21&49\\9&2&18&81\\\bold{25}&\bold{28}&\bold{104}&\bold{165}\end{array}\right][/tex]
m can be calculated following the next equation:
[tex]m=\frac{\frac{\sum{xy}-\sum{y}}{n}}{\sum{x^2}-\frac{(\sum{x})^2}{n}}[/tex]
where n is the number of (x, y) couples (5 in our case).
Replacing the values calculated previously:
[tex]m=\frac{104-\frac{25*28}{5} }{165-\frac{25^2}{5} }=\frac{104-\frac{700}{5} }{165-\frac{625}{5} } = \frac{104-140}{165-125 } = \frac{-36}{40} = -0.9[/tex]
For b:
[tex]b=\bar{y}- m\bar{x}=\frac{\sum{y}}{n}-m\frac{\sum{x}}{n}=\frac{28}{5}-(-0.9)\frac{25}{5}= \frac{28}{5}+\frac{22.5}{5}=\frac{50.5}{5}=10.1[/tex]
In the figure attached you can see the points given and the stimated line.
