Question

TEST TOMMOROW, sigma notation in systems of equations help needed dearly. PLS

Answer 1

What's the question

Answer 2

Its a graph, idk how to put it in, points are (0, 5.4) (1,4.8) (3, 3.5) (5, 2.5)

Answer 3

Ive been stuck for hours on this stuff

Answer 4

WHat are you supposed to do with those points?

Answer 5

Find the least squares regression line, y=ax+b and then solve for a and b by solving using
the summatic notation

Answer 6

Im gonna sgnal for help

Answer 7

@cwrw238

Answer 8

Oh ok so you have the formulas for the regression line parameters right? that being:
\[b=\frac{\sum_{i=1}^n(x_i-\bar{x})(y_i-\bar{y})}{\sum_{i=1}^n(x_i-\bar{x})^2} \] and \[ a=\bar{y}-b\bar{x}\] those right?

Answer 9

Yea, exactly

Answer 10

Ok first find \(\bar{x}\), which is the average of the x-coordinates
Then find \(\bar{y}\), which is the average of the y-coordinates and tell me what you get.

Answer 11

2.25 for x and 15.7 for y

Answer 12

o.o are you sure (for the \(\bar{y}\))? Did you maybe forget a decimal place for one of your y-values when finding that

Answer 13

3.925 didnt divide

Answer 14

I get 16.2 / 4 = 4.05. But that's probably just a small mistype. The next part, let's focus on the numerator. You have to basically take the first x-value subtract it with \(\bar{x}\), and multiply that with first y-value and subtract \(\bar{y}\). Then you basically write \(+\) and do the same procedure for the 2nd x and y-values. And here \(n=4\) since you have 4 points.

So: \[ \sum_{i=1}^4(x_i-\bar{x})(y_i-\bar{y})=(0-2.25)(5.4-4.05)+(1-2.25)(4.8-4.05)\\
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~+(3-2.25)(3.5-4.05)+(5-2.25)(2.5-4.05) \]

Answer 15

So think of it this way: Do everything you see after the sigma notation using 1 value, then write + and skip to the next value, until you go through your whole list

Answer 16

Does it make sense so far?

Answer 17

Y= -.58x+54
? is that the answer

Answer 18

I get -0.586x + 5.369

Answer 19

\(a=\bar{y}-b\bar{x}=4.05-(-0.586)(2.25)=5.369\)