AP Statistics Question (This was on one of my class tests)

Colleges and Universities A-Z Princeton University
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<p>A scatterplot of a variable Y versus a variable X produced the scatterplot below (it's just a constant value of Y=1 while x increases (perfectly horizontal line)). The value of Y for all values of X is 1.0. The correlation between Y and X is:
A) +1, because the points lie perfectly on a line
B)either +1 or -1, because the points lie perfectly on a line
C) 0, because Y does not change as X increases
D) none of the above</p>

<p>Try and show your work, please. </p>

<p>I'm getting a certain answer, that I don't want to say. This was a test question and the teacher is saying that the answer is (C) but I contend that it can't be. See what you guys get.</p>

<p>P.S. I know this is an active forum and none of the rest really are, so please help. :)</p>

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<p>I got zero as well. If you plug these points into your calculator's list and then do stat->calc->(4)Lin Reg, the r and the r^2 values are left blank, indicating no correlation</p>

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<p>The standard deviation of a line with the points unchanging is 0. y(bar)=1 and all y-values =1. So plug that into the correlation formula of the y-values, (y-(y-bar))/Sy.</p>

<p>(1-1)/0, now you don't even need the x-part or the degrees of freedom, it's undefined.</p>

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<p>also, dont forget:</p>

<p>r = 1/(n-1)* sum((x-xbar)/stand. dev x)(y - ybar)/stand dev. y))</p>

<p>if all the y values are same, standard dev = 0 and you cannot divide by a zero.</p>

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<p>You said exactly what I said but I guess at the same time. SO it is undefined, right?</p>

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<p>Hmm... you put none of the above?
I'm thinking because 0<r<1 that there may be no such thing as an undefined correlation. Ask your stat teacher though.</p>

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<p>She said the same thing "It has to be between -1 and 1," but I was arguing with her. I looked up in the book the definition of a zero standard deviation, which was roughly "all values are the same" which makes sense. So I can prove it's a 0 sd for y, which goes into the equation as divide by 0. So that makes it undefined. Also the TI-89 says the same thing.</p>

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<p>I think you are right actually...</p>

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<p>I remember doing the same exact question last year, and I put something other than 0. But then my teacher said it was 0. =(</p>

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<p>ummmmm.... right.....</p>

<p>Haha, I'm so not a math person... I just studied math so I could get a decent score on the SAT. And that it!!!! No more math for me!</p>

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<p>its just zero, there's no working to be done cause this tests you on your understanding of a basic concept</p>

<p>there are three types of correlation: negative, positive, zero</p>

<p>it makes sense that in this question, it is zero. zero correlation means that independent variable X doesn't affect dependent Variable Y in any way. As X increases, Y remains the same. As X decreases, Y is still the same. So zero correlation.</p>

<p>positive correlation when you get a line with positive gradient. this is the case when as your X increases, your Y increases. As X decreases, Y decreases.</p>

<p>negative correlation when you get a line with a negative gradient. X increases, Y decreases, vice versa</p>

<p>hope that helped :)</p>

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<p>and of course, the value of your product moment correlation depends on how nicely your regression lines coincide</p>

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<p>Welcome back, Calculus.</p>

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<p>Thanks, and btw...albert, check this out from what looks like a professor at Drexel University (who the heck knows where that is). But the site looks very credible if you go to their home page.</p>

<p><a href="http://mathforum.org/library/drmath/view/52771.html%5B/url%5D"&gt;http://mathforum.org/library/drmath/view/52771.html&lt;/a&gt;&lt;/p>

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<p>the professor is saying that slope of the line is undefined??</p>

<p>the slope is undefined for a VERTICAL line. </p>

<p>but we have a HORIZONTAL line here, so the slope is definitely zero.</p>

<p>sorry, i dun get what the professor says, can Calculus please explain thanks. :)</p>

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<p>oh yeah, i think i understood what he meant lol...
sorry</p>

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<p>but i still agree with your teacher though...</p>

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<p>My AP Stats teacher is a first-year teacher who knows seemingly nothing about statistics. Albert, no offense, but you should be caught agreeing with anything my teacher says lol.</p>

<p>I've never had a teacher this bad ever, I'm only kid in school to have taken BC Calculus then wrapped around to take Statistics and she is trying to make it hard for anyone to get an A.</p>

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<p>It shouldn't be C. I also think it is undefined as the division by zero arises.</p>

<p>In reality, a linear model shouldn't be used in the first place. Furthermore, if the correlation is zero, the y values are random with respect to x, not a perfectly horizontal line.</p>