In the regression equation y = 1959.71 − 0.46 x₁ + 2.16 x₂,suppose that the you are considering the point (x₁,x₂)= (1.5,0.5),and furthermore,suppose that the variable x₁increases by a factor of 2 (i.e.,it doubles).What must be the change in the variable x₂ so that y remains unchanged? A) 2.16 B) −2.16 C) 0.319 D) −0.319 E) 0.638

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Quizplus · Accepted Answer

When x₁ doubles, its value becomes 1.5*2=3. Therefore the regression equation becomes y = 1959.71 − 0.46 *3 *x₁ + 2.16 x₂= 1959.71 − 1.38 + 2.16 x₂, simplifying further yields y = 1958.33 + 2.16 x₂. For y to remain unchanged from its original value, we need to have: 1959.71 − 0.46 *1.5 *x₁ + 2.16 *0.5 * x₂ = 1958.33 + 2.16 * x₂ Simplifying this, we get: x₂ = 0.319. Therefore, the change in x₂ must be 0.319 for y to remain unchanged. Thus the answer is C.

In the Regression Equation Y = 1959