e) (15 marks total) Consider the following three potential models where variable Male = 1 for a Male and Male = 0 for a Female: Model 1: MR{PIQ | MRI, Male} = Bo + B,MRI . Model 2: M{PIQ | MRI , Male} = Bo + B,MRI + B2 Male Model 3: M{PIQ | MRI, Male} = Bo + B,MRI + B2 Male + B; MRI * Male Use SPSS output in the following to answer questions 1 and 3. Just write the null and alternative hypothesis, the test statistic, the distribution of the test statistic under the null hypothesis, p-value and your conclusion. 1. (5 marks) Consider the model where mean of PIQ depends on MRI and Male, and where the effect of MRI on mean of PIQ is the same for males and females. Is there significant evidence to conclude that either MRI and/or Male are useful to predict PIQ? Carry out the test. 2. (5 marks) Consider the model where mean of PIQ depends on MRI and Male, and where the differences between genders (Males and females) in mean of PIQ depend on MRI. In this model, carry out a test to determine if the effect of MRI on mean PIQ depend on gender.3. (5 marks) Consider the model where mean of PIQ depends on MRI and Male, and where the differences between genders (Males and females) in mean of PIQ depend on MRI. In this model, carry out a test to determine if gender has any effect on mean of PIQ. Carry out the test. SPSS output for model 1: ANOVAb Sum of Model Squares df Mean Square F Sig 1 Regression 1963.070 1 1963.070 4.098 .053a Residual 13412.796 28 479.028 Total 15375.867 29 a. Predictors: (Constant), MRI b. Dependent Variable: PIQ Coefficients a Standardized Unstandardized Coefficients Coefficients Model B Std. Error Beta F+ Sig. 1 (Constant) 16.778 47.569 353 727 MRI 1.064 525 357 2.024 053 a. Dependent Variable: PIQSPSS output for model 2: ANOVA Sum of Model Squares df Mean Square F Sig. Regression 2612.260 2 1306.130 2.763 081 Residual 12763.606 27 472.726 Total 15375.867 29 a. Dependent Variable: PIQ b. Predictors: (Constant), Male, MRI Coefficients Standardized Unstandardized Coefficients Coefficients Model B Std. Error Beta Sig. (Constant) -8.069 51.793 -.156 877 MRI 1.288 .556 433 2.317 028 Male 9.930 8.474 .219 1.172 251 a. Dependent Variable: PIQSPSS output for model 3: ANOVAb Sum of Model Squares df Mean Square F Sig Regression 3637.967 3 1212.656 2.686 067a Residual 11737.900 26 451.458 Total 15375.867 29 a. Predictors: (Constant), MRIMale, MRI, Male b. Dependent Variable: PIQ Coefficients a Standardized Unstandardized Coefficients Coefficients Model B Std. Error Beta Sig 1 (Constant) -57.176 60.194 -.950 351 MRI 1.817 .647 .611 2.809 .009 Male 169.625 106.270 3.738 1.596 123 MRIMale -1.795 1.191 -3.472 -1.507 144 a. Dependent Variable: PI