Question

You are a consultant assisting a crop scientist in understanding the grain characteristics of peanuts. For each plot under study, at the end of the season, you record, X1= Yield plot weight (kg), X2=Sound mature kernels (gms). You stored the data as csv file in a safe location, however due to a cyber-attack, the original data is lost. Fortunately you have a print copy of mean them. (μYou 1 & μalso 2 and variance σ ,σ for each measurements, and the correlation (ρ) between notice that the crop scientist prefers to use pounds as the unit of measurement instead of kg, where 1 pound is equal to 0.4535 kilograms. What is the best way of assisting the crop scientist in this adverse situation, by presenting the mean, variances and correlation between measurements?

Answer 1

ANSWER::

Given

It is given that we have lost teh original data and only a print copy of mean, variance and the correlation are available.

From the theory of central tendency, we know that variance and covariance is invariant to location and the standard deviation and mean is affected by scale. The mean will change as per the scale ie if each observation is multiplied by teh same quantity, the mean will In this case, the weight in kilograms will be converted to pounds the values for mean and the standard deviation will change.

Since correlation

  

The numerator will be changed since Y is converted to pounds and in the denominator also teh same effect and hence gets cancelled and the correlation doesn't change.

Therefore, the correlation coefficient = as in the print-out.

Mean of gms

Mean of Y = pounds

SD of gms

SD of Y = pounds

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