# Very basic questions on some terms.

#### smarge117

##### New Member
I apologize if this is a little too basic for you, but I'm an RN taking statistics ovr the summer and my brain just doesn't work like this.

My professor has asked to clearly define and explain some terms. This is what I've got, but I have no idea if I'm on the right track or not--the book is not very helpful or clear. If I could ask someone to look at my answers that would be great.

Marginal distribution: Marginal distribution refers to the theory that if you have two variables, you can predict values of one variable, given values of another variable. So if you are predicting a persons height (inches) from his weight (pounds). You’ve got ten people that you know their height and weight. You plot the values on a graph, with weight on the x axis and height on the y axis. If there is a non-perfect linear relationship between height and weight then you would get a cluster of points on the graph which slopes upward. In other words, people who weigh a lot should be taller than those people who are of less weight.

Regression & the regression line: Regression is the study of the measure of the ‘best fit’ line for a set of data. The purpose of regression is to come up with a line that fits through that cluster of points with the least amount of deviations from the line. The regression line is the line that you end up with—the straight line that best represents the relationship between the two measures.

Partial correlation: Partial correlation is based upon observations of differences in scedasticity . We determine what the sub-correlations are and find the average of the sub-correlations. These average out to the original correlation. This is important when we don’t have a consistent correlation.

Multiple correlation: No idea I couldn't keep my eyes open at this point.

if anyone responds, thanks
margaret

#### Dragan

##### Super Moderator
I apologize if this is a little too basic for you, but I'm an RN taking statistics ovr the summer and my brain just doesn't work like this.

Partial correlation: Partial correlation is based upon observations of differences in scedasticity . We determine what the sub-correlations are and find the average of the sub-correlations. These average out to the original correlation. This is important when we don’t have a consistent correlation.

...thanks
margaret

Where on earth are you getting this information from???--Gee whiz.

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I'll pick this question on the topic of partial correlation because I think it's, perhaps, a more complicated question.

Suppose I have a regression model as follows:

Yhat = b0 + b1X1 + b2X2.

where X1 and X2 are the independent variables used to predict Y, and Yhat are the predicted values of Y.

Now, suppose that Y, X1, and X2 are all correlated.

Question: What is the partial correlaton between Y and X1??

We can answer this question by thinking in terms of simple regressions.

More specifically, if I were to perform the following regressions as:

Y = a0 + a1X2 + e1

and

X1 =c0 + c1X2 + e2

where e1 and and e2 are the error terms associated with the two regression lines.

Notice that e1 and e2 are part of Y and X1 but have the linear association of X2 removed from them i.e. the correlations between X2 and e1 and X2 and e2 will be zero.

Thus, if we compute the usual Pearson correlation between e1 and e2 this will be equal to the partial correlation between Y and X1 because the linear association between X2 has been removed (or partialed out) from both variables (Y and X1).

#### smarge117

##### New Member
That information was from the professor.

Thank you for your response, but to be honest with you, nothing makes even a little lightbulb go off in my head.

I think that I'll be able to get through this class, but without any usefull knowledge. If I go for a masters in nursing down the road I'll need a more advanced class, but don't think that anything I've gotten so far is useful.

#### Dragan

##### Super Moderator
That information was from the professor.

Thank you for your response, but to be honest with you, nothing makes even a little lightbulb go off in my head.

I can understand your problem - because what you're being told is jibberish.

Look, let me demonstrate why.

Suppose I have three variables Y, X1, and X2 and they have correlations ry1, ry2 and r12, Mkay.

Now, to compute the partial correlation between Y and X1 it is as I said above or:

PartialCorr(Y,X1) = (ry1 - ry2*r12) / ( Sqrt (1 -ry2) *Sqrt(1 - r12) )

which is algebraically equivalent to what I described above and is Clearly not an average of other so-called "sub-correlations."

I wish you luck.

#### smarge117

##### New Member
I think I'll need it!

thanks for trying to clear it up for me. :yup:

#### Rounds

##### New Member
"but don't think that anything I've gotten so far is useful."

Never judge the content of a class in terms of useful once you agree to be in it. You are hurting yourself when you do. Everything is useful; everything is important. That is a recipe to do well at college.

I can recall teaching Intermediate Algebra and a student asked me why is this useful. And I could just see this student was looking at me for a reason to care. But that reason by and large has to come from within in college or you are risking a lot of your success on the answers you get.

I actually failed that student that day. And that student then failed themselves. Because I didn't give them a reason to care, and apparently without it Intermediate algebra was to hard. Which btw... the only thing you really need to get through Intermediate Algebra is the ability to think it is useful. If you have that it is almost impossible to fail. But you the world is full of people waiting tables that started college but couldn't figure out why their classes were important.

And for a large part of the people I meet, my money is on most of the people in Grad school never dwelled on the question of useful or they managed to fool themselves into thinking it was all useful/important.
I once took a class I didn't think was useful: complex Analysis. I swear to you my perception of that class was a bunch of engineers learning to integrate things I would never have to integrate. It was long division every day only way less likely to come up. And I got a D. Now mind you that I got 800 on the quantitative portion of the GRE. I was sufficiently prepared. It was my last semester of college in an undergrad abstract math program. The only reason I got a D was the perception that it wasn't important. That I was never going to do anything useful with Complex Analysis. It is almost impossible to really take material to heart while you have let yourself believe there is nothing useful going on in it.

So I have never repeated that mistake again in grad school. Everything is important/useful. And I see undergrads struggle all the time now as an instructor for the simple reason that can get the level of concern that comes with thinking material is important or useful.

It is frustrating because they are always a light switch away from doing well. They are concerned about the facts in front of them and its the underlying attitude that it is not useful that is really making it harder to get then it is.

A room gets divided up into grades, but it is rarely divided by IQ. It is more often much more about who cared about the material/who was prepared. If you are prepared that is half the battle. The other half is caring.

#### smarge117

##### New Member
Rounds,

Thank you for that 'reminder' to keep my mind open. Right now, as a nurse it's hard to see how this is going to help me down the road. And maybe I should have qualified it in the beginning, but technically this is a psych class, it's statistics for behaviorial sciences (or something like that). I can do the 'math', but I just don't really understand some of the concepts, they have no context for me yet.

I promise to keep an open mind! ;-)

margaret