MTH 303 Linear Statistical Models 2023-2024 S1
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MTH 303
Linear Statistical Models
2023-2024 S1
Task 2(50 marks)
A statistician wants to model the total number of customers at one Caffe Nero situated on Oxford Road in Manchester between 8 am and 8:15 am.They can think of three explanatory variables:if it is rainy or not,if it is during the semester or not,and the temperature(temp) in degrees Celsius.The statistician has data for 28 days,given in the file named nero.RData, and believes that the response variable(Customer)follows a Poisson distribution.
1.Loading the data into R. (2 marks)
2.State the linear predictor corresponding to models specified with the following R code,
explaining all relevant terms:
(a)temp+semester
(b)temp*semester
(c)temp*semester +rainy (8 marks)
3.Fit a Poisson Generalized Linear Model (GLM)with log link to the data set for the model in part 2(c).Label this model as Model1.Comment on the significance of the parameters based on the summary of the fitted model. (9 marks)
4.Fit an improved model by substracting non-significant variable(s)based on your analysis
in 3.Label this improved model as Model2. (3 marks)
5.Justify why Model2 improves Modell by referring to the R output. (4 marks)
6.You are given a new Poisson GLM(Model3)with log link function,specified by the following R code:
temp+temp*semester
(a)Justify why Model3 outperforms Modell and Model2 by referring to the R output. (4 marks)
(b)Use plot function to draw“Residuals vs.Fits”plot,for the residuals of Model3,and comment on the validity of Model3. (8 marks)
(c)Quantile residuals are the useful residuals of choice for generalized linear models. Make Q-Q plot with quartile residuals and comment on it.(Hint:you may need to install statmod package first.) (8 marks)
(d)Use R to calculate the predicted total number of customers during the semester at rainy day with a temperature of 0 degree Celsius,using Model3. (4 marks)
2023-12-11