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Q: Find the value for the correlation coefficient r X 5 1 4 2 3 Y 5 10 12 4 8?
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What is a coefficient?

A coefficient is a number in front of a variable (i.e. multiplied by it).For example, in the expression x2 - 10x + 25, the coefficient of x2 is 1 and the coefficient of x is -10. The third term, 25, is a constant.If the expression were -x2 + 10x + 25, the coefficient of x2 would be -1, and the coefficient of x would be 10.


How do you simulate an AR1 process using Microsoft Excel?

This can be done fairly easily using Excel's random number generator and a couple of simple equations. First, you need to specify the auto correlation coefficient you wan to use and the mean value and error variance of the AR1 process. For example, you could say that the auto correlation coefficient is 0.5, and that the mean = 100 and the errors are ~ N ( 0, 102 ); i.e., the errors are normally distributed with a mean of 0 and a standard deviation of 10. Keep in mind that for the AR1 series to be stationary, the absolute value of the auto correlation coefficient must be less than 1. Then using Excel's random number generator you would generate an array of error terms equal in length to the AR1 series you want to create. This is done as follows: 1) Type the following formula into the first cell of the error array, say cell B11 = NORMINV(RAND(), 0, 10) [Note: The values 0 and 10 in the above equation represent the mean and standard deviation of the error distribution. Ordinarily errors have a mean of 0, but you should substitute a relative cell reference for the standard deviation so that it can be changed without re-entering the formula.] 2) Copy the formula to as many cells as you want to have terms in the AR1 series 3) Now, start the AR1 series in a separate array, say cell C11. Begin by making the first term equal to the mean value; for example, = 100. Then in cell C12 type = 100 + 0.5*C11 + B11 [Note: The values 100 and 0.5 in the above equation represent the mean and auto correlation values. As before you should substitute a relative cell reference so that they can be changed without re-entering the formula. Be careful to make sure that the cell containing the mean value is the same in both formulas.] 4) You should then copy that formula down the entire array for the AR1 series. To make sure you have done everything correctly you can check your AR1 series as follows: The mean of an AR1 process = mean/(1 - auto correlation coefficient). In this case, with a mean of 100 and an auto correlation coefficient of 0.5 the mean value = 200. Thus, if you take the average of the AR1 array, it should be approximately = 200. The variance of an AR1 process = error variance/(1 - autocorr2 ). In this case with a variance of 100 and an auto correlation coefficient of 0.5 we would get 133.33 for a variance or about 11.55 for a standard deviation. Thus if you take the standard deviation of the AR1 series you should get 11.55. Hope this helps. This can be done fairly easily using Excel's random number generator and a couple of simple equations. First, you need to specify the auto correlation coefficient you wan to use and the mean value and error variance of the AR1 process. For example, you could say that the auto correlation coefficient is 0.5, and that the mean = 100 and the errors are ~ N ( 0, 102 ); i.e., the errors are normally distributed with a mean of 0 and a standard deviation of 10. Keep in mind that for the AR1 series to be stationary, the absolute value of the auto correlation coefficient must be less than 1. Then using Excel's random number generator you would generate an array of error terms equal in length to the AR1 series you want to create. This is done as follows: 1) Type the following formula into the first cell of the error array, say cell B11 = NORMINV(RAND(), 0, 10) [Note: The values 0 and 10 in the above equation represent the mean and standard deviation of the error distribution. Ordinarily errors have a mean of 0, but you should substitute a relative cell reference for the standard deviation so that it can be changed without re-entering the formula.] 2) Copy the formula to as many cells as you want to have terms in the AR1 series 3) Now, start the AR1 series in a separate array, say cell C11. Begin by making the first term equal to the mean value; for example, = 100. Then in cell C12 type = 100 + 0.5*C11 + B11 [Note: The values 100 and 0.5 in the above equation represent the mean and auto correlation values. As before you should substitute a relative cell reference so that they can be changed without re-entering the formula. Be careful to make sure that the cell containing the mean value is the same in both formulas.] 4) You should then copy that formula down the entire array for the AR1 series. To make sure you have done everything correctly you can check your AR1 series as follows: The mean of an AR1 process = mean/(1 - auto correlation coefficient). In this case, with a mean of 100 and an auto correlation coefficient of 0.5 the mean value = 200. Thus, if you take the average of the AR1 array, it should be approximately = 200. The variance of an AR1 process = error variance/(1 - autocorr2 ). In this case with a variance of 100 and an auto correlation coefficient of 0.5 we would get 133.33 for a variance or about 11.55 for a standard deviation. Thus if you take the standard deviation of the AR1 series you should get 11.55. Hope this helps.


What are the parts of a number in scientific notation?

In scientific notation, a number is represented as the product of a coefficient and a power of 10. The coefficient is a decimal number between 1 and 10, and the power of 10 indicates the number of places the decimal point is moved. For example, in the number 4.2 x 10^3, "4.2" is the coefficient and "3" is the power of 10.


How do we know if a correlation is significant or not?

There are several statistical measures of correlation: some require only a nominal scale, that is, data classified according to two criteria; others require an ordinal scale, which is the ability to determine whether one measurement is bigger or smaller than another; others require an interval scale, which allows you to determine the difference in values but not the ratio between them. [A good example of the latter is temperature measured in any scale other than Kelvin: the difference between 10 degrees C and 15 degrees C is 5 C degrees, but 15 C is not 1.5 times as warm as 10 C.]The contingency coefficient, which is suitable for nominal data, has a chi-squared distribution.The Spearman rank correlation, requiring ordinal data, has its own distribution for small data sets but as the number of units increases to n, the distribution approaches Student's t-distribution with n-2 degrees of freedom.The Kendall rank correlation coefficient can be used in identical situations and gives the same measure of significance. However, the Kendall coefficient can also be used to test partial correlation - whether the correlation between two variables is "genuine" or whether it arises because both variables are actually correlated to a third variable.The Pearson's product moment correlation coefficient (PMCC) is the most powerful but requires measurement on an interval scale as well as an underlying bivariate Normal distribution.The significance levels of these correlation measures are tabulated for testing.A simple "rule of thumb" for testing the significance of PMCC is that values below -0.7 or above 0.7 are highly significant. Values in the ranges (-0.7, -0.3) and (0.3, 0.7) are moderate, and values between -0.3 and +0.3 are not significant.


What is the coefficient of 10xy?

The numerical part, 10.


What is the numerical coefficient of the term 10x?

It is: 10


What Simplify and determine the coefficient of (-x)(5y)(-2x).?

The simplified term is 10x2y so that the coefficient is 10.


What is coefficient of expansion of steel?

13*10^-6


What is n in scientific notation?

In scientific notation, "n" represents the coefficient or mantissa, which is a number between 1 and 10. It is multiplied by a power of 10, denoted by the exponent, to give the overall value of the number.