Question

PLEASE HELP!! I need to know how to solve these!!!

This table shows 4 observations of a pair of variables (x,y). The variables x and y are positively correlated with a correlation coefficient of 0.99. Find the slope, b, of the least squares regression line, y=ax+b, for these data: x 1 2 3 4
y 1 3 7 10

Answer 1

\[y =\frac{31}{10}x-2.5\]

Answer 2

where did you get these numbers from Mathsboy? I need some steps to follow, I have several like this one!

Answer 3

it is supposed to be a decimal amount with the anser rounded to the nearest hundredth

Answer 4

Take a look at this:
http://en.wikipedia.org/wiki/Simple_linear_regression#Fitting_the_regression_line
It looks quite complicated, but it's simpler than it seems, as long as you know that barred-x is the mean of x, etc.

Answer 5

that is way over my head - can you dumb it down A LOT??? Please?

Answer 6

I can try, it's hard to write on here, the important parts are:
\[y = \alpha + \beta x\]
\[\beta = \frac{\sum_{i=1}^{n}\left(x_i-\bar{x}\right)\left(y_i-\bar{y}\right)}{\sum_{i=1}^{n}\left(x_i-\bar{x}\right)^2}\]

Answer 7

And also:
\[\alpha = \bar{y} - \beta \bar{x}\]

Answer 8

OK - so where do I get the numbers to plug in? I am doing Algebra 2 for a high school class. The teacher is useless, in this case, and I need help!!!

Answer 9

Maybe my method is over complicating things.. in this case, you calculate: \[\bar{x}=(1+2+3+4)/4 = 2.5\]\[\bar{y} = (1+3+7+10)/4 = 5.25\]
And then use the original values in the sums. If you haven't seen the formulae before, I suggest you don't use my method, but that's the only one I'm familiar with unfortunately.

Answer 10

OK, let me see if I can follow you. I add up the x coordinates and find the mean, same with the y values, and then what? How do I find the slope?

Answer 11

The slope is the beta part, you have to use that formula above replacing all xbar with 2.5 and all ybar with 5.25. It's complicated to explain if you don't understand summation yet.

Answer 12

OK - I will have a go at it. Let me run an idea of it on my paper and I will post my result, and maybe you can tell me if i"m remotely close?

Answer 13

Sure.

Answer 14

OK - I got -4.25 How close am I?

Answer 15

what does the correlation coefficient have to do with this? I think that's where the question confuses me!

Answer 16

Honestly... I don't know.

Answer 17

Correlation coeff is not needed. But least squares does not do well if there are outliers. So they are saying least squares is valid here.

Answer 18

That doesn't help me much!

Answer 19

Thanks phi! I thought that was extra information!

Answer 20

Out of curiosity, what approach to solving these problems is the teacher using?

Answer 21

I have no idea. That' why I don't get it. I have the y-hat formula, and the slop formula that states b=r(sy/sx), and I don't really get any of it!

Answer 22

Oooh in that case, the correlation coefficient is probably useful, that's what the r is.

Answer 23

How does that all fit in? Still confused to the rest of it! Can you help?

Answer 24

How do you find the "s" value of the lope? It's with a lowered y or x next to it.

Answer 25

is "s" the standard deviation for this equation?

Answer 26

I'm pretty sure they're the standard deviations of x and y, which of course was not given in the question, and I don't think they're sample standard deviations either, so honestly, unfortunately apart from what I've contributed, I don't think I can help, sorry.

Answer 27

Thanks! I appreciate everything. I would award you more medals for putting up with my questions, but it will only allow me the one! Thanks again!

Answer 28

No problem, sorry I couldn't be of more help.

Answer 29

I steered you wrong.

You are studying this problem in the context of statistics, not calculus nor linear algebra.
What they want you to do is find the standard deviation of y, and the std of x
then the slope (called a in your problem) is a= r * std(y)/std(x)
Here r is the correlation coefficient.

I assume you know how to find the standard deviation?
one way is use wolfram
http://www.wolframalpha.com/input/?i=std+%7B+1%2C2%2C3%2C4%7D