Given that the calculation for the correlation coefficient is represented by this formula, how could use use this equation to find out other pieces of data we have previously used in this class.

Hint: it might help you to think about the formula in an expanded form. (What does zy stand for?)

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When analyzing the correlation coefficient equation and the corresponding set of raw data we can also find 3 other forms of data. First we can find the mean by using the z-score equation and the raw data. Now that the mean was found, we can consequently find both the varience and standard deviation.

The equation is used to find out if the correlation is weak or strong, and if it is negative or positive. We simply have to plug in our variables in zy and zx. We can use this equation to find the standard deviation and the z score.

we find the correlation which tells us the relationship that exsist between 2 variables.

If for example we have a correlation od .03 we know that there is a little relationship. However, if we find .86, we know that there is a big relationship between the two relation. Nonetheless, we must not get confused and say that correlation is the same thing as causation ( one causes the other to happen every time ).

Then you can find the standard deviation by finding the mean and multiplying each data by the mean then squared the answer , then adding every numbers and dividing it by how many numbers there are.

This formula allows us to calculate the coefficient of the correlation. In order to get the answer we must find the z-score of each data (Zx,Zy. Therefore, this formula can tell the z-score of each data.

This equation is mainly used for solving correlation. If we further expand this formula, we see that Zx and Zy represent the two variables that are being plottled and measured. N, on the other hand, represents the number of data. It tell us whether the correlation is negative or positive and if it is weak, moderate, or strong. If we have our two variables we can also find out with this equation the mean, standard deviation, or the Z scores.

Given the formula used to calculate the correlation coefficient it’s corresponding set of raw data, we are able to find the mean by plugging in all know variables to the z score equation. In finding the mean and using the raw x and y variables we are also able to calculate the variance and therefore the standard deviation. With this one formula and its corresponding data we are able to examine not only the correlation coefficient, but also the z-score, mean, variance, and standard deviation.

The R stands for coefficient correlation. It is the sum of zx and xy divided by the total number of the data. It tells us how close the data are or the opposite. The x and the y stands for variables. The variable y is dependant on the variable x which is independant from the y for most cases. For example, if we have a coefficient correlation of 1, it means that it is a strong positive coefficient correlation. On the other hand, if we have a coefficient correlation of -1, it means that it is a strong negative coefficient correlation. Also, if we have a coefficient correlation of 0.5 or -0.5, it is a moderate coefficient correlation. By having the coefficient correlation of a data, we could guess how the data are spread.

Zy is the z-score of a set y of numbers and Zx is the z-score of a set x of numbers. The previous formula allows us to calculate de correlation between the two sets by dividing the sum of the products of the two z-scores by the total numbers. Also, this formula can be useful to calculate the standard deviation and thus, the variance which is its square.

N is the number of values.

Zx is the sum of all the x values. Zy is the sum of all the y values.

You can then find XY(The Sum of the product of 1st and 2nd Scores), X*2(Sum of square X Scores), and Y*2(Sum of square Y Scores) to use in expanded form.

The formula of the correlation coefficient is related with the formula of z score.

The r depends on variables of x and y (the sum of z score of x and y), and I can find out the z score.

The Zx and the Zy stand for the z-score of the x and y axis. If you have the z-score and all of the raw data, allowing you to find the mean, you can use the equation Z-score= (x-mean)/standard deviation to find the standard deviation.

Zx and Zy stand for the z scores of the data. To calculate the z-score, you take X – meanX over the standard deviation. Through finding the z-score, we find out what the mean of the data is, and the standard deviation. So through using this equation, you can find out the mean, standard deviation, and variance.

The r score/number is the total sum of zx and zy values divided by the total number of data. By finding the r, we could “guess” the others values by adding 1 or by subtracting 1 which is the highest possible value. For instance, the r determines the “slope of the line”, and thereby we could “guess” the others values as well.

Let’s say, we have a r number closes to -1 one, it means that the “slope” tends to negative, so by picking a random number of the x-axis, we are able to determine his y value and so on.

The equation shown above is used to find out if the correlation is a strong or weak one and if it is positive or negative. To find out, you plug in your variables in zx and your other variables in zy. N stands for the frequency / number of data in the equation. R = the strength of the correlation. You can find out the standard deviation from using that data which will show you where you stand in relevance of the mean. You can find the z score also by manipulating zx in relation to zy.

The equation shown above is used to find out if the correlation is a strong or weak one and if it is positive or negative. To find out, you plug in your variables in zx and your other variables in zy. N stands for the frequency / number of data in the equation. R = the strength of the correlation. You can find out the standard deviation from using that data which will show you where you stand in relevance of the mean. You can find the z score also.

Zx stands for : (x- mean)/standard deviation

knowing that, we can find the standard deviation of the data.

From this we can obtain the standard deviation of data since Zy represents z scores. From there, standard deviation can give us the mean the mode and the median.

we will find the z-score and then multipli by y and z and mutliply that by the some of all the raw data. that will give us the nominator and then we multiplie by n. this is going to give us the correlation

Zy represents data used on the y axis which correlates with Zx which is the data along the x axis. I presume to find r we divide all the correlated z scores on the x and y axis by the number cases or people.

Well, one could find the z-scores of the correlated data sets x and y, since they are included in the formula, and you can also find the standard deviation through an expansion of the z score formula, by plugging in the z score itself in the z score equation to isolate the standard deviation. By finding the standard deviation, one can also find the mean and the number of cases in the respective set of data by isolating each piece of the z score formula. Thus, it is possible to uncover all the formulas we have looked at in class.

If zx and zy are z scores of two different things that want to be correlated then if we have the correlation between 2 z-scores and 1 z score we could find out the other one missing in the problem. That is if N is a constant i guess. The formula could be the sum of 2 z-score over a constant or mean which gives correlation.

ZY represents the Z-score for the y-axis and ZX represents the z-score for the x-axis, therefore if we could iscolate either of these functions we could determine the z-scores for a certain set of numbers. As long as there is only one variable that is unidentified it would be possible to calculate many things from this equation. Including the standard deviation.

By using the formula above, with the correlation and the number of scores, you can find the z-scores by isolating it in the formula. Therefore, you can find other values such as the z-score even though the formula is meant to find the correlation.

At face value, the formula for the correlation coefficient (R) states that r is equal to the sum of the difference between the z score and the mean of ONE distribution, and the z score and the mean of a SECOND distribution. All divided by the total number of values.

This can be used as a way to measure the relationship between different classes taught under the same conditions.

Hope this debauchery of a simple concept isn’t a public comment.

In class Quiz

the equation for the Z score is

and the equation for R is

Zy is the Zscore of the Y axis. With this equation we can isolate the Z score of the 2 different axis and we can isolate the stander deviation(S). we can also find the mean.

With the given formula you can rearange it in order to figure out all the numbers. If you are only given 2/3 numbers you are capable of finding the answers. You can find out what r is if you have z and n, you can find out n if you have r and z . Just by rearanging the formula you can find all the data necessary to solve the equation

with the r formula you can also conclude the z score of y(zy), the z score of y(zx), and the total number of data(n).

This formulacan uses the z-scores of the x and y numbers to calculate the correlation.

after that, we can use the z-scores to find the standard deviation

because this method uses the zscores of the x (zx) and y(zy) variables to calculate the correlation coefficient, we can use the z-scores to isolate and find the standard deviation

We use standard deviation to help us find the z-scores and now we need the z-scores to find the Correlation Coefficient. If all of the data in a standardized graph are under the area of the curve in an unskewed manner, then it is probable that the Correlation Coefficient(r) will be a strong positive or negative correlation.

r=Sum((all Z of X)(all Z of Y))/Number of data

By using the correlation coefficient formula, we can find other pieces of data we have previously used. I.E. the z-score, variance, standard deviation, the mean and when we know that the correlation is normal we can also find the median.

zy stands for the z-scores of the y axis and the zx stands for the z-scores of the x axis.

Through the coefficient formula we can find the z-scores of the of all the values of the data set. also, we can figure out the mean of the data set as well as the standard deviation.

Cont’d

By reversing the r-correlation formula (r=ΣZxZy/N) we can obtain the z-score for both the X series and Y series. In doing so, we get the standard deviation and mean of these series. For example, if r calculated the correlation between age (x) and IQ (y) we can find the z-score for an age or IQ, plus the their average and standard deviation.

We could use this equation to find the z-scores of the given variables and find out where they stand and how far from the average they are in their respective sets of data.

Because this method uses the z-score of the x (Zx) and y (Zy) variables to calculate the correlation coefficient, we can use the z-score to isolate and find the standard deviation.