91影视

${\mathbf{尾}}_{\mathbf{0}}$indicates the y-intercept term of the curve. It means it gives the value of E(y) when${\mathbf{x}}_{\mathbf{1}}\mathbf{=}\mathbf{0}$

${\mathbf{尾}}_{\mathbf{1}}$indicates the magnitude of the shift in parabola due to changes in the value of x (shift parameter)

${\mathbf{尾}}_{\mathbf{2}}$indicates the rate of curvature of the parabola. (Shape parameter).

The value of${\mathbf{R}}^{\mathbf{2}}$given here is 0.226 which denotes that about 23% of the variation in the variables can be explained by the model. A higher value of${\mathbf{R}}^{\mathbf{2}}$means that the model is a good fit for the data while a lower value suggests otherwise.

Here, 23% is a very low value for${\mathbf{R}}^{\mathbf{2}}$meaning the model is not a good fit for the data.

When a straight-line model was fitted to the data, the value of ${\mathbf{R}}^{\mathbf{2}}$was 18% while when a quadratic model is fitted to the data, the value of ${\mathbf{R}}^{\mathbf{2}}$increases to 23%. This means that the quadratic model is a better fit for the data than a straight-line model. However, 23% is still a lower value meaning a better quadratic model can be used to fit the data.

To test whether a quadratic model is a good fit for the data, F-test needs to be done wherethe null hypothesis is whether the model parameters are explaining the model where the beta values are zero and the alternate hypothesis is whether the beta values are non-zero.

Mathematically,

${\mathbf{H}}_{\mathbf{0}}\mathbf{:}{\mathbf{尾}}_{\mathbf{1}}\mathbf{=}{\mathbf{尾}}_{\mathbf{2}}\mathbf{=}\mathbf{0}$

${\mathbf{H}}_{\mathbf{a}}$:At least one of the parameters${\mathbf{尾}}_{\mathbf{1}}$or${\mathbf{尾}}_{\mathbf{2}}$is non zero