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If I wanted to maximize two variables can I just rank the two variables from the sample as a point system and then sum the points? I know this probably isn't the most mathematically correct way. For example, if I have an average and a variance for 150 different samples from one population and I rank each average and variance and then add the points from both rankings could I maximize the sum?

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  • $\begingroup$ What does maximising variables mean? $\endgroup$
    – copper.hat
    Jun 6, 2019 at 17:52
  • $\begingroup$ @copper.hat I want to maximize average and variance $\endgroup$ Jun 6, 2019 at 18:32
  • $\begingroup$ @copper.hat and instead of trying to write a multivariate optimization program I was wondering if you could just rank each variable using a point system and then just sum the points and maximize $\endgroup$ Jun 6, 2019 at 18:33
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    $\begingroup$ Can you write an expression for what your ranking and point system would be? Also can you clarify - do you have 1 average across 150 samples or are you saying you have 150 averages? $\endgroup$
    – E. Tucker
    Jun 6, 2019 at 21:50
  • $\begingroup$ Also, I agree with copper.hat. I'm not sure what your variables are. $\endgroup$
    – E. Tucker
    Jun 6, 2019 at 22:08

1 Answer 1

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Based on our conversation in the comments of your post (=trying to find the data point with the highest combo of 2 components), yes, it would be correct to calculate the combination for each data point, order these, and select the highest value.

For example, if $\alpha \in [0,1]$ were the weight of the $x$ components, you could

  • Calculate the score for each data point as $z_i, \forall i\in 1..150$:

$\alpha*x_1+(1-\alpha)*y_1 = z_1$

$\alpha*x_2+(1-\alpha)*y_2 = z_2$

and so on until $z_{150}$

  • Order all the values of $z_i$ from highest to lowest.
  • Select the highest value of $z_i$ and find the associated $x_i$ and $y_i$
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