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Does this mean that as long as the student has good gpa and good gre even though his Alma Mater's prestige is low - he will get admitted in a college

Any additional things i can interpret from below ?

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    $\begingroup$ Correlation refers to a technique used to measure the relationship between two or more variables.When two things are correlated, it means that they vary together.Positive correlation means that high scores on one are associated with high scores on the other, and that low scores on one are associated with low scores on the other. Negative correlation, on the other hand, means that high scores on the first thing are associated with low scores on the second. Negative correlation also means that low scores on the first are associated with high scores on the second... $\endgroup$ – Aditya May 21 '18 at 4:57
  • $\begingroup$ "even though his Alma Mater's prestige is low", we see a negative correlation between his prestige and the admission criteria, hence try to classify the admissibility based on those features to gain more insights $\endgroup$ – Fadi Bakoura May 21 '18 at 8:12
  • $\begingroup$ Thanks guys for your comments - really helped me understand better $\endgroup$ – Patrick May 21 '18 at 15:34
  • $\begingroup$ Also keep in mind that correlation shows linear relation between two variables; nonlinearities are not shown by it. Therefore correlation might be low but nonlinear relations may still exist between two variables. Apart from that, you cannot understand the "direction" of the relation, i.e. if variable "a" inflicts the change on variable "b" or vice versa. Lastly, "correlation does not imply causation", don't forget! $\endgroup$ – pcko1 May 28 '18 at 17:38
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No. From this correlation matrix you cannot draw the conclusion that

as long as the student has good gpa and good gre even though his Alma Mater's prestige is low - he will get admitted in a college

The reason is that correlation is a measure of association between single pairs of variables. The conclusion you draw above - on the contrary - is based on a combination of three different variables plus the outcome variable.

If you want to get an estimation of the probability that a student will be admitted to college based on her gpa, gre and prestige the right way is to create a logistic regression model. Here's an example in R (provided that admit is a binary variable, with admit=1 indicating that the student is admitted and admit=0 that she is not admitted)

model <- glm(admit ~.,family=binomial(link='logit'),data=data)

With this fitted model you can then compute the probability that a student is admitted given her particular combination of gpa, gre and prestige.

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