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

Question

In regression model: y = β₀ + β₁x₁ + β₂

In regression model: y = β0 + β1x1 + β2 + 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.

In regression model: y = β<sub>0</sub> + β<sub>1</sub>x<sub>1</sub> + β<sub>2</sub> <sub> </sub> + ε ,if β<sub>2</sub> < 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.

+ 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 the coefficient of x in the second term of the model equation (β₁x₁) is positive, it implies that the relationship between y and x is initially positive. However, since β₂ is negative, it suggests that there exists a point after which the relationship between y and x becomes negative. 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 + β2

In Regression Model: Y = β₀ + β₁x₁ + β₂