Adata set contains three points, and two of the residuals are -12 and 24. what is the third residual?

In regression analysis, a residual value is the difference between a measured value and the corresponding predicted value.

The sum of the residual values either side of the line of best feet is always equal.

That is the sum of the absolute value of the negative residual values must be equal to the sum of the positive residual values.

Given that two of the residual values of a 3-data points are -12 and 24, as can be seen the positive residual value is greater than the absolute  value of the negative residual value, (i.e. 24 > |-12|).

Thus, the third residual value is negative with a magnitude of 24 - |-12| = 24 - 12 = 12.

Therefore, the third residual value is -12.