Question

tabulate and find the relationship between the variables ( x and y) for the following patterns​

Answer 1

Answer:

The formula for the correlation (r) is

where n is the number of pairs of data;

are the sample means of all the x-values and all the y-values, respectively; and sx and sy are the sample standard deviations of all the x- and y-values, respectively.

You can use the following steps to calculate the correlation, r, from a data set:

Find the mean of all the x-values

Find the standard deviation of all the x-values (call it sx) and the standard deviation of all the y-values (call it sy).

For example, to find sx, you would use the following equation:

For each of the n pairs (x, y) in the data set, take

Add up the n results from Step 3.

Divide the sum by sx ∗ sy.

Divide the result by n – 1, where n is the number of (x, y) pairs. (It’s the same as multiplying by 1 over n – 1.)

This gives you the correlation, r.

For example, suppose you have the data set (3, 2), (3, 3), and (6, 4). You calculate the correlation coefficient r via the following steps. (Note that for this data the x-values are 3, 3, 6, and the y-values are 2, 3, 4.)

Calculating the mean of the x and y values, you get

The standard deviations are sx = 1.73 and sy = 1.00.

The n = 3 differences found in Step 2 multiplied together are: (3 – 4)(2 – 3) = (– 1)( – 1) = +1; (3 – 4)(3 – 3) = (– 1)(0) = 0; (6 – 4)(4 – 3) = (2)(1) = +2.

Adding the n = 3 Step 3 results, you get 1 + 0 + 2 = 3.

Dividing by sx ∗ sy gives you 3 / (1.73 ∗ 1.00) = 3 / 1.73 = 1.73. (It’s just a coincidence that the result from Step 5 is also 1.73.)

Now divide the Step 5 result by 3 – 1 (which is 2), and you get the correlation r = 0.87.

Step-by-step explanation:

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Answer 2

Answer:

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