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Mathematics CCS West Loop Campus Math 0409: Foundations of Mathematics CRN 92695 Spring 2016 Room: C 258 7:00 9:40 PM Mon and Wed 4 hour lecture course / 64 hours per semester/ 12 weeks Textbook:

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In today's Jude we're going to look at Pearson's product-moment correlation coefficient which is represented by a little R this is used to work out the strength of a relationship or the level of correlation how much two things relate to each other so in the last tube we looked at some graphs and described the strength visually in terms of whether it was strong weak moderate or perfect, and now I'm just going to run through how measuring the strength works when you're doing it more precisely using this R value which is Pearson's product-moment correlation coefficient don't say that five times fast so when we had a scatter plot where the dots fell in a perfect straight line something like that we said that was a perfect relationship and then the next level of strength down from being a perfect relationship was for them to be pretty close to being in a perfect line but just not quite and that we called a really strong relationship, and then they got a little more higgledy-piggledy they got a little more spread out, and we called this a moderate relationship the strength was kind of moderate, and then they spread out even more, and they looked even less like they were in a line, although they still did follow a linear sort of shape, and you could see the relationship it was just kind of all over the shop that we called a fairly weak relationship now the r-value is a way of describing that relationship with a number we give it a statistical number this Pearson's product-moment correlation coefficient number so that we can compare things rather than seeing weak or strong but a bit vague, so a perfect relationship like this where everything falls perfectly in a line that's an r-value of one when you have a strong relationship like this one here where things are quite they follow the trend really nicely we would give that an r-value of 0.75 to 1 somewhere between 0.75 and 1 so for example 0.8 that's a really strong relationship or point-9 something like that moving along when you had a moderate relationship that would be somewhere between 0.5 and 0.75 the weak relationship down here is going to be between 0.25 and 0.5 so 1 is perfect all in a line point 7 5 to 1 is very, very strong 0.5 to 0.75 moderate 0.25 to 0.5 is weak and anything less than 0.25 that's not much of a relationship at all you'd say almost no correlation they hardly relate now if you notice all those relationships that I've drawn on the right there go in a positive direction they go up the hill like that so what happens when we're talking about a negative relationship so for example we have a perfect linear relationship, but they're going down there they're going in a negative direction and again a strong relationship, but it's a bit more on the negative side or a moderate relationship or a weak relationship negative well the nifty thing here is the r-value is just is the same for the positives it's just negative so a perfect relationship that's a negative relationship has an R value...

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