If a quadratic regression model is Yi =β0 + β1 X1i +β2 X1i2 + ε, what should be the alternate hypothesis (H1) for testing the quadratic effect?
The alternative hypothesis (H1) for testing the quadratic effect would be that the coefficient β2 is not equal to zero. In other words, the quadratic term X1i2 has a significant effect on the dependent variable Yi.
The alternate hypothesis (H1) for testing the quadratic effect in the quadratic regression model Yi = β0 + β1X1i + β2X1i^2 + ε can be stated as follows:
H1: β2 ≠ 0
This means that there is a non-zero quadratic effect in the model, indicating that the relationship between the response variable (Yi) and the predictor variable (X1i) is not strictly linear.
To determine the alternate hypothesis for testing the quadratic effect in a quadratic regression model, we need to consider the null hypothesis and the research question.
In this case, the null hypothesis (H0) would state that the quadratic effect of the independent variable on the dependent variable is non-existent, meaning that the coefficient β2 is equal to zero.
The alternate hypothesis (H1) would then state that there is a quadratic effect of the independent variable on the dependent variable, implying that the coefficient β2 is not equal to zero.
Therefore, the alternate hypothesis (H1) for testing the quadratic effect in this quadratic regression model would be:
H1: β2 ≠ 0