World Health Organisation's (WHO) specialised cancer agency, the International Agency for Research on Cancer (IARC) has designated fine particulate matter (PM2.5) as carcinogenic to human beings. PM2.5 particles have a diameter of 2.5 micrometers (0.0025 mm) or smaller and they are small enough for people to breath them deeply into lungs and sometimes PM2.5 particles can even enter the bloodstream. Research indicates that temperature in degrees (C), relative humidity in percentage (%), wind speed in kilometers per hour (km/h), and precipitation in millimeters (mm) are potential predictors for PM2.5 concentration in milligram per cubic meter (g/m). A random sample of the annual mean temperature, humidity, wind, precipitation and PM2.5 concentration at 56 test locations was collected. The data is available in the file pm25.csv on iLearn. It is located under Assessment Assignment Assignment datasets. Variable temperature humidity wind precipitation pm25 Description The annual mean temperature in degrees The annual mean relative humidity in percentage The annual mean wind speed in kilometers per hour The annual mean precipitation in millimeters The annual mean PM2.5 concentration in milligram per cubic meter a. [7 marks] Produce a plot and a correlation matrix of the data. Comment on possible relationships between the response and predictors and relationships between the predictors themselves. b. [6 marks] . Fit a model using all the predictors to explain the pm25 response. Using the full model, estimate the impact of humidity on PM2.5 concentration. Do this by producing a 95% confidence interval that quantifies the change in PM2.5 concentration for each extra percentage of relative humidity and comment. c. [14 marks] Conduct an F-test for the overall regression i.e. is there any relationship between the response and the predictors. In your answer: Write down the mathematical multiple regression model for this situation, defining all appropriate parameters. Write down the Hypotheses for the Overall ANOVA test of multiple regression. Produce an ANOVA table for the overall multiple regression model (One combined regression SS source is sufficient). Compute the F statistic for this test. State the Null distribution for the test statistic. Compute the P-Value State your conclusion (both statistical conclusion and contextual conclusion). d. [10 marks] Validate the full model and comment on whether the full regression model is appropriate to explain the PM2.5 concentration at various test locations. e. [2 marks] Find the R2 and comment on what it means in the context of this dataset. f. [3 marks] Using model selection procedures discussed in the course, find the best multiple regression model that explains the data. State the final fitted regression model. g. [3 marks] Comment on the R and adjusted R2 in the full and final model you chose in part f. In particular explain why those goodness of fitness measures change but not in the same way.