multivariate analysis

a) A discriminant analysis was carried out to classify the interest of school pupils whether they want to become a scientist or not (1=yes O=no) based on three criteria which are, science content knowledge, self-efficacy, and self-regulation. Some of the SPSS outputs are given below. Prior Probabilities for Groups Cases Used in Analysis Be a scientiest Prior Unweighted Weighted No 470 31 31.000 Yes .530 35 35.000 Total 1.000 66 66.000 Classification Function Coefficients Be a scientiest No Yes Science knowledge - 007 .134 Self-Efficacy 6.190 7.016 Self-Regulation 6.076 4.968 (Constant) -26.747 -25.686 Fisher's linear discriminant functions Original Classification Results Predicted Group Membership Be a scientiest No Yes Count No 20 11 Yes 13 22 % No 64.5 35.5 Yes 37.1 62.9 Total 31 35 100.0 100.0 i) Write down the Fisher's linear discriminant function for each category. (2 marks) ii) State the rules for assigning a new school pupil to one of the categories. (2 marks) iii) Calculate the misclassification rate. Comment on the performance of the discriminant function based on the value obtained. (2 marks) iv) Suggest other analysis that can be used to classify the school pupil into these two categories. State the differences between these two analyses. (4 marks) a) A discriminant analysis was carried out to classify the interest of school pupils whether they want to become a scientist or not (1=yes O=no) based on three criteria which are, science content knowledge, self-efficacy, and self-regulation. Some of the SPSS outputs are given below. Prior Probabilities for Groups Cases Used in Analysis Be a scientiest Prior Unweighted Weighted No 470 31 31.000 Yes .530 35 35.000 Total 1.000 66 66.000 Classification Function Coefficients Be a scientiest No Yes Science knowledge - 007 .134 Self-Efficacy 6.190 7.016 Self-Regulation 6.076 4.968 (Constant) -26.747 -25.686 Fisher's linear discriminant functions Original Classification Results Predicted Group Membership Be a scientiest No Yes Count No 20 11 Yes 13 22 % No 64.5 35.5 Yes 37.1 62.9 Total 31 35 100.0 100.0 i) Write down the Fisher's linear discriminant function for each category. (2 marks) ii) State the rules for assigning a new school pupil to one of the categories. (2 marks) iii) Calculate the misclassification rate. Comment on the performance of the discriminant function based on the value obtained. (2 marks) iv) Suggest other analysis that can be used to classify the school pupil into these two categories. State the differences between these two analyses. (4 marks)