Question

Is the number of games won by a major league baseball team in a season related to the team batting average? The table below shows the number of games won and the batting average of 8 teams.
Team - Games Won - Batting Average
1- 115- 0.285
2- 66- 0.267
3- 66- 0.263
4- 103- 0.274
5- 62- 0.26
6- 76- 0.282
7- 71- 0.266
8- 110- 0.282

Using games won as the independent variable x, do the following:
(a) The correlation coefficient is
r = _________________
(b) The equation of the least squares line is

y = _________ + _____________ x
1 hour ago - 4 days left to answer.

Answer 1

What's your plan? Won't you need \(\sum x\;and\;\sum y\;and\; \sum xy\)? That's a good place to start.

Answer 2

That's the thing. I'm not sure how to get those. I can't seem to get any closer to solve this. Any help with how to approach this is appreciated.

Answer 3

What do you mean you can't get those. Just add them up!

115 + 66 + 66 + 103 + 62 + 76 + 71 + 110 = Sum of the x's

Answer 4

Okay, I found that x = 669 and y = 2.179

What should my next step be? I'm not sure how to find the correlation coefficient.

Answer 5

Sum of the xy. Multiply the two and than add up all those.

You will also need the sum of the x^2 and y^2

It can be a little tedious.

Answer 6

669 * 2.179 = 1457.751
669 + 2.179 = 671.179
669^2 * 2.179^2 = 2125037.978001

I think my numbers should be right.

Answer 7

You should get:

\(n = 8\)
\(\sum x = 2.185\)
\(\sum y = 669\)
\(\sum xy = 183.807\)
\(\sum x^{2} = 0.597319\)
\(\sum y^{2} = 59307\)

I can't really tell what you are doing. Maybe you are forgetting that \(\sum xy \ne \sum x \cdot \sum y\)

Answer 8

Whoops! I'm backwards. Trade x and y. That doesn't actually change anything, except which is independent and which is dependent.

Answer 9

Oh, I see where I messed up. Thank you for that. I assume my next step should be to plug the numbers in an equation correct?

Answer 10

I sincerely hope you already have the equation. I know I don't want to type it all. :-)

Answer 11

It's this one, correct?

Also thank you so much for the help, you're really helping me out of a jam. :)

Answer 12

Yes, that's it.

How about that least squares equation?

Answer 13

You already have all the numbers. Just different equations.

Answer 14

No, that equation I don't have.

Answer 15

Okay, I'll type in the formulas for a and b, given y = ax+b

Denominator for Both = \(\left(\sum x \right)^{2} - n\cdot \sum x^{2}\)

a-numerator = \(\sum x\sum y - n\sum xy\)

b-numerator = \(\sum x \sum xy - \sum x^{2} \sum y\)

That's all. Just calculate those two ratios.

Answer 16

Oh my gosh, thank you so much! You were such a big help!