Assessment Task

Using the Boston data set introduced during LAB work, apply linear regression modelling to predict the per capita crime rate using other variables in the data set. In other words, per capita crime rate is the response and the other variables are predictors.

a)  Use descriptive statistics to explore the dataset.

b.) For each predictor, fit a simple linear regression model to predict the response. Complete regression analysis. Describe your results. In which of the models is there a statistically significant association between the predictor and the response? Create plots to back up your assertions.

c) Fit a multiple regression model to predict the response using all the predictors. Describe your results. For which predictors can we reject the null hypothesis   _₀ := 0? [10]

d.) How do your results from (b) compare to your results from (c)? Create a plot displaying the univariate regression coefficients from (b) on the x-axis, and the multiple regression coefficients from (c) on the y-axis. That is each predictor is displayed as a single point in the plot. Its coefficient in a simple linear regression model is shown on the x-axis, and its coefficient estimate in the multiple linear regression model is shown on the y-axis. [10]

e.) Is there evidence of non-linear association between any of the predictors and the response? To answer this question, for each predictor X, fit a model of the form

=  ₀+  ₁                 +  ₂ ²+  ₃ ³+ Ԑ

Summarise your findings.

Part a) may be completed using any choice of statistical package. Parts b) through e) should be completed using R. A report should be submitted together with supporting software analyses / R-code via online submission on or before Sunday 17^th December 23:55. The grade assessment will be based on the DBS CA grading scheme which has been included in this document