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In: Statistics and Probability

1) Is ryx = rxy? That is, will the sample correlation coefficient be the same if...

1) Is ryx = rxy? That is, will the sample correlation coefficient be the same if you exchange continuous random variables X and Y? Why or why not?

2) What type of association does the correlation coefficient, ryx, quantify?

3) Should the estimated correlation be extrapolated beyond the observed ranges of the variables?

4) Is the sample correlation coefficient, ryx, sensitive to extreme outliers? Explain.

5) Can you calculate the sample correlation coefficient, ryx, if all X values are the same? If all the Y values are the same? Explain in terms of the formula for ryx.

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Expert Solution

Result:

1) Is ryx = rxy? That is, will the sample correlation coefficient be the same if you exchange continuous random variables X and Y? Why or why not?

Yes, ryx = rxy. The sample correlation coefficient be the same if we exchange continuous random variables X and Y.

The result is the same because the correlation formula is not dependent on the symbols.

2) What type of association does the correlation coefficient, ryx, quantify?

The correlation coefficient, ryx, quantify the linear relation.

3) Should the estimated correlation be extrapolated beyond the observed ranges of the variables?

No, estimated correlation should not be extrapolated beyond the observed ranges.

4) Is the sample correlation coefficient, ryx, sensitive to extreme outliers? Explain.

Yes, sample correlation coefficient, ryx, sensitive to extreme outliers.

An outlier that falls near where the regression line would normally fall would necessarily increase the size of the correlation coefficient. An outlier that falls some distance away from the original regression line would decrease the size of the correlation coefficient.

5) Can you calculate the sample correlation coefficient, ryx, if all X values are the same? If all the Y values are the same? Explain in terms of the formula for ryx.

sample correlation coefficient, ryx could not be calculated if all X values are the same.

If all X values are the same then standard deviation of x is 0.

Therefore denominator in the correlation formula r= cov(x,y)/ (sx*sy) will be zero and the value is indeterminant.

orchestra answered 2 years ago
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