i) (5 marks) Consider the following three models: Model 1: u{CRE | Diameter} = 3, + ,D1+ $,D2 + ,D3 Model 2: u{CRE | Age, Depth, Gender} = 3, + B,Age + S, Depth + [, Male, L{CRE | Age, Depth, Dose} = 3, + B, D1+ 3,D2 + ,D3 + f,Age + B Depth + }6'6Male' Cary out a test to determine if there are any differences in the mean CRE for four different level of the diameter of clear zone after taking into account variables age, depth, and male. State the null and alternative hypothesis in terms of regression coefficients. Also, identify the residuals sum of squares and degrees of freedom for the models in the null and alternative hypothesis. Calculate the test-statistic, the p-value and identify the distribution of the test- statistic under the null hypothesis. What do you conclude? Model 3: ANOVA table for model 1: ANOVAP Mode Squares df Mean Square F Sig. 1 Regression 233.171 3 77.724 43.017 .000 Residual 738.991 409 1.807 Total 972.162 412 a. Predictors: (Constant), D3, D1, D2 b. Dependent Variable: CRE ANOVA table for model 2: ANOVAb Sum of Model Squares df Mean Square F Sig Regression 8.790 3 2.930 1.244 .293a Residual 963.372 409 2.355 Total 972.162 412 a. Predictors: (Constant), Male, Age, Depth b. Dependent Variable: CRE ANOVA table for model 3: ANOVAb Sum of Model Squares df Mean Square F Sig. 1 Regression 240.835 6 40.139 22.283 000a Residual 731.327 406 1.801 Total 972.162 412 a. Predictors: (Constant), Male, D3, Depth, Age, D2, D1 b. Dependent Variable: CRE