A secondary school teacher wants to know if the marks of students in Specialist Mathematics can...

 

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A secondary school teacher wants to know if the marks of students in Specialist Mathematics can be predicted from their marks in General Mathematics. A linear model is assumed, and the following data is obtained from nine students: General Mathematics Specialist Mathematics ID 1 2 86 85 85 97 3 89 76 4 82 79 56788 84 76 86 99 84 49 9 72 83 78 92 (a) Write down the linear model as a matrix equation, writing out the matrices in full. (b) Calculate the least squares estimate of the parameters. (c) Calculate the sample variance s. (d) Calculate the standardised residuals for all students. (e) Calculate the Cook's distances for all students. (f) Predict (using a point estimate) the mark of Specialist Mathematics for a student whose mark for General Mathematics is 90. A secondary school teacher wants to know if the marks of students in Specialist Mathematics can be predicted from their marks in General Mathematics. A linear model is assumed, and the following data is obtained from nine students: General Mathematics Specialist Mathematics ID 1 2 86 85 85 97 3 89 76 4 82 79 56788 84 76 86 99 84 49 9 72 83 78 92 (a) Write down the linear model as a matrix equation, writing out the matrices in full. (b) Calculate the least squares estimate of the parameters. (c) Calculate the sample variance s. (d) Calculate the standardised residuals for all students. (e) Calculate the Cook's distances for all students. (f) Predict (using a point estimate) the mark of Specialist Mathematics for a student whose mark for General Mathematics is 90.