Question

Short answer

Step-by-step solution

Step-by-Step SolutionStep 1: Estimating sample estimates

Least square prediction method

Step 3:Sum of square of residuals ,mean squared of error, and   S2

$$\begin{gathered} {\mathbf{S}}^{\mathbf{2}}\mathbf{=}\frac{\mathbf{SSE}}{\mathbf{n}\mathbf{-}\mathbf{(}\mathbf{k}\mathbf{+}\mathbf{1}\mathbf{)}} \\ \mathbf{=}\frac{\mathbf{151},\mathbf{016}}{\mathbf{20}\mathbf{-}\mathbf{(}\mathbf{2}\mathbf{+}\mathbf{1}\mathbf{)}} \\ \mathbf{=}\frac{\mathbf{151},\mathbf{016}}{\mathbf{17}} \end{gathered}$$

Interpretation: Value of s close to 0 indicates that the data is clustered around the mean. However, high value of s indicates that the data points are clustered above the mean value. Also, approximately 95% of the observations should fall between the range of +/- 2s

Therefore,$\mathbf{s}\mathbf{=}\sqrt{\mathbf{8883}\mathbf{.}\mathbf{294}}\mathbf{=}\mathbf{94}\mathbf{.}\mathbf{251}$

 Testing the significance of  β1

Confidence interval for β2

Step 6:  R2and adjusted   R2

The value of $R^2$and adjusted is calculated using $R^2$

Testing the overall significance of the model

Using the given hypothesis testing, overall significance of the model can be found as;

 Overall significance of the model

To comment on the overall significance of the model, F statistic can be found like

The observed 5% significance level for the test conducted in part g would be

${\mathbf{F}}_{\mathbf{\alpha }\mathbf{,}\mathbf{16}\mathbf{,}\mathbf{16}}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{33}$

Since F test statistic > F observed value, reject the null hypothesis that ${\mathbf{\beta }}_{\mathbf{1}}\mathbf{=}{\mathbf{\beta }}_{\mathbf{2}}\mathbf{=}\mathbf{0}$

Therefore, the data provides strong evidence that at least one of the coefficients in the model is a nonzero number.