Question

Using Multiple regression, the relationship of Y to four other variables was established as: Y = 12 + 3X₁ – 5X₂ + 7X₃ + 2X₄ When X₁ increases 2 units and X₂ increases 1 unit, while X₃ and X₄ remain unchanged, using this model what change would you expect in your estimate of Y?

Answer 1

The estimate of Y changes by -2 or decreases by 2.

Explanation:

We are given the following information:

Using Multiple regression, the relationship of Y to four other variables was established as:

`Y = 12 + 3X_1- 5X_2 + 7X_3 + 2X_4`

`X_1` increases 2 units and
`X_2` increases 1 unit, while
`X_3` and
`X_4` remain unchanged.

Predicted Y =

`Y_p = 12 + 3(X_1+2) - 5(X_2+1) + 7X_3 + 2X_4`

Change in Y =

`Y_p - Y \\= 12 + 3(X_1+2) - 5(X_2+1) + 7X_3 + 2X_4-(12 + 3X_1 - 5X_2 + 7X_3 + 2X_4)\\= 12-12+3(X_2+1-X_2)-5(X_2+1-X_2) + 7X_3 - 7X_3 + 2X_4 - 2X_4\\=3 - 5\\= -2`

The estimate of Y changes by -2 or decreases by 2.