# Example of a real-world situation where multivariate analysis is applicable.

I have searched a lot of site to understand the situation where multivariate analysis is applicable. But not got any easily understandable example.

Would you please give me a real-world example where multivariate analysis is appropriate ?

• Could you tell us what was one of the examples you found, and explain why it is not understandable enough? There are plenty of examples but it's hard to guess which ones you would consider "understandable". – David K Jan 9 '15 at 15:17
• @DavidK for example math.stackexchange.com/questions/1097627/… – user 31466 Jan 10 '15 at 0:56
• There are lots of types of multivariate analysis. Do you mean Principal Components Analysis, Generalized Least Squares? Anything?! – user76844 Jan 12 '15 at 17:03
• @Eupraxis1981 I have been just introduced with multivariate analysis. I don't know type of multivariate analysis. Only what i know is that , the analysis is appropriate when there are several correlated outcomes. And i want to match it with real-world example. – user 31466 Jan 13 '15 at 4:55

## 1 Answer

Here's a simple example:

You have 100 patients for a medical study. You measure 10 different body characteristics (e.g. height, weight, LDL cholesterol, etc) and then monitor each patient for 20 different symptoms over the next 2 years. You would use multivariate analysis to see which groups of body characteristics correlate with which sets of symptoms.

• 100 patients are experimental units. 10 different body characteristics are explanatory variables ($X_1,\ldots,X_{10}$) and 20 different symptoms are dependent variables ($Y_1,\ldots,Y_{20}$) . I have not understood your last line and how are those dependent variables correlated. – user 31466 Jan 13 '15 at 5:18
• In multiple regression analysis, we see if other factors held constant how one unit change in $X_i$ changes in $Y$. But what do we do if it is multivariate analysis ? – user 31466 Jan 13 '15 at 5:25
• @Leaf that is the crux of multivariate analysis. For example, you may find that the combination (5*weight +LDL) correlates strongly with (2*high insulin+3*hypertension). You will end up getting factors (i.e., linear combinations) of explanatory variables and predicted variables that you will be paring up. – user76844 Jan 13 '15 at 5:26
• @Leaf you look at linear combinations of $Y$s, which form "factors" that you can basically treat as a new variable you are trying to predict. – user76844 Jan 13 '15 at 5:27
• I have got my real-world example. But asking you some further questions depending on your comments. (1)As far i know "factors" are controlled independent variables. How does linear combination of $Y$s form factor? And don't we want to predict $Y$, not the factors? – user 31466 Jan 13 '15 at 5:41