Question

George has found a relationship between the height of a person and his bowling score. The table below shows the data collected by George:


Height
cm 152 160 164 170 180 162 154 158 168
Bowling Score 51 55 57 60 65 55 52 54 59


Part A: What would most likely be the bowling score of a person who has a height of 156 cm? (3 points)

Part B: Predict a possible correlation coefficient for the data in the table and explain why you think your prediction is a good value for the data. (4 points)

i Just need help with B nothing else

Answer 1

@kirbykirby

Answer 2

Well you can plot the data and estimate a value for it. A strong correlation would be probably about 0.8-1

A low correlation maybe 0-0.4

It doesn't seem like they care from the question for an exact value, so I think you could just eye-ball it

Answer 3

Otherwise software would be your best bet to get the correlation coefficient.

Answer 4

what do you mean software?

Answer 5

Bowling score increases with height. Try a linear regression fit.
Since 156 is between 154 and 158, try looking between the corresponding bowling scores.

Answer 6

But you're going to have to put the heights and scores in order from least to greatest.

Answer 7

ok but i just learned what a correlation coefficient is and i still dont understand it that well, can someone explain it?

Answer 8

and i have no idea how to do a linear regression fit

Answer 9

It's pretty much just a wordy way of saying "Look at how the variables fit in with each other when the numbers are in order."

Answer 10

ok and what about the other one

Answer 11

On the left: the fitted line (a.k.a. regression line) fits through the poiints much better than on the right, so the left diagram would have a higher correlation coefficient than the right one

Answer 12

ok but im still confused on how to find the correlation coefficient

Answer 13

Hopefully this will give more useful explanation: http://onlinestatbook.com/2/describing_bivariate_data/pearson.html

Answer 14

The correlation coefficient, aka the cross-correlation coefficient, is a quantity that gives the quality of a least squares fitting to the original data. To really explain the correlation coefficient, you need to consider the sum of squared values \[ss_{xx}\]\[ss_{xy}\] and \[ss_{yy}\] of a set of n data points \[(x_{i}, y{i})\] about their respective means, \[ss_{xx}\]\[= \sum (x_{i}-x)^{2}\]\[= \sum x^{2} - 2 x \sum x + \sum x^{2}\]\[=\sum x^{2} -2 x \sum x + \sum x^{2}\]\[=\sum x^{2}-nx^{2}\]
and so on and so forth. These quantities are basically unnormalized forms of the variances and covariance of X and Y given by
\[ss_{xx} = N var (x)\]\[ss_{yy} = N var (Y)\]\[ss_{xy} = N cov (x,y)\]

Answer 15

Sorry for taking so long, I hate writing equations on hand -.-

Answer 16

ok i think i got it can you help me with one more thing

Answer 17

Sure