Question

Consider the following table.

Answer 1

Answer:

y = -0.9x+10.1

Step-by-step explanation:

The equation of the line is:

$y=mx+b$

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:

$\left[\begin{array}{cccc}x&y&x*y&x^2\\1&9&9&1\\3&7&21&9\\5&7&35&25\\7&3&21&49\\9&2&18&81\end{array}\right]$

Then calculate the total sum of all columns:

$\left[\begin{array}{cccc}x&y&x*y&x^2\\1&9&9&1\\3&7&21&9\\5&7&35&25\\7&3&21&49\\9&2&18&81\\\bold{25}&\bold{28}&\bold{104}&\bold{165}\end{array}\right]$

m can be calculated following the next equation:

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

where n is the number of (x, y) couples (5 in our case).

Replacing the values calculated previously:

$m=\frac{104-\frac{25*28}{5} }{165-\frac{25^2}{5} }=\frac{104-\frac{700}{5} }{165-\frac{625}{5} } = \frac{104-140}{165-125 } = \frac{-36}{40} = -0.9$

For b:

$b=\bar{y}- m\bar{x}=\frac{\sum{y}}{n}-m\frac{\sum{x}}{n}=\frac{28}{5}-(-0.9)\frac{25}{5}= \frac{28}{5}+\frac{22.5}{5}=\frac{50.5}{5}=10.1$

In the figure attached you can see the points given and the stimated line.