In regression model: y = β₀ + β₁x₁ + + ε ,if β₂

Question

In regression model: y = β₀ + β₁x₁ + + ε ,if β₂ < 0,then the value of y is expected to increase with x until x reaches a certain point after which the value of y is expected to decrease.

Quizplus · Accepted Answer

Since β₂ is negative, the coefficient of the second term is negative. Therefore, as x increases and the second term becomes larger, the value of y will increase. However, at some point, the negative coefficient of the second term will overpower the positive coefficient of the first term, causing the value of y to decrease. Therefore, y is expected to increase with x until a certain point after which it is expected to decrease.

In Regression Model: Y = β0 + β1x1

In Regression Model: Y = β₀ + β₁x₁