Hi all, this is my first post on these forums, I should make clear now I'm not after answers or anything just a nudge in the right direction and hopefully some helpful guidance...anyway I have some stats coursework all regarding the general linear model and I am completely stumped on where entirely to begin, I have made an attempt based on examples I have done previously but I doubt they are right...I should also state I am much more of a pure mathematician than statistician hence my confusion! Anyways the question is as follows and as stated I have no idea where to begin
Three possible models were considered:
(i) There is a difference between cholesterol levels for urban and rural males, and the relationship between cholesterol and age also differs between the two groups.
(ii) There is a difference between cholesterol levels for urban and rural males, but the relationship between cholesterol and age is the same for the two groups.
(iii) Both the cholesterol levels and the relationship between cholesterol and age are the same for urban and rural males.
The models are to be fitted in the general linear model framework
where the notation in the course notes applies.
(a) Give the matrix formulation of each of the three models, explaining all notation and the meaning of the parameters you are trying to estimate. For each model you should give the response vector, the design matrix, the parameter vector and the error vector. You should explain why you have chosen this particular set of parameters. State any assumptions clearly. You should aim to make the parameter systems as similar as possible for the three models: this will make model comparison easier.
(b) Fit model (ii) above to these data using the matrix operations available in Excel (or another computer package)
You should provide:
• parameter estimates
• a table of observed values, fitted values and residuals
• anything else you think might be useful
On the basis of these results, comment on the hypothesis that urban and rural cholesterol levels do not differ. What other analyses do you think would be helpful here?
You should check your results using a specialist statistics package (e.g. MINITAB).
Area Age Cholesterol
rural 46 181
rural 52 228
rural 39 182
rural 65 249
rural 54 259
rural 33 201
rural 49 121
rural 76 339
rural 71 224
rural 41 112
rural 58 189
rural 18 137
rural 44 173
rural 33 177
urban 78 241
urban 51 225
urban 43 223
urban 44 190
urban 58 257
urban 63 337
urban 19 189
urban 42 214
urban 30 140
urban 47 196
urban 58 262
urban 70 261
urban 67 356
urban 31 159
urban 21 191
urban 56 197
....So any help, or guidance to references or examples would be greatly appreciated, and as said this is my first post so be gentle!
Many thanks.