A variable, Z, is regressed against variables X and Y and the following equation is estimated: Z = -3.0 + 1.2X - 2.5Y + error. If X = 5 and Y = 3, the estimated value of Z is ________.
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A. B. C. D.D
With the given data, Z = -3 + 1.2*5 - 2.5*3 = -4.5
To find the estimated value of Z, we can use the given regression equation:
Z = -3.0 + 1.2X - 2.5Y + error
We are given the values of X and Y, which are X = 5 and Y = 3. Now, we can substitute these values into the equation:
Z = -3.0 + 1.2(5) - 2.5(3) + error = -3.0 + 6 - 7.5 + error = -4.5 + error
At this point, we can see that the estimated value of Z is -4.5 plus the error term. However, since the error term is not known, we cannot determine the exact value of Z.
Therefore, the answer is B. It cannot be estimated since the error term is unknown.