B8IT103 Statistics for Data Analytics

 

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? [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

01                 +  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 17th December 23:55. The grade assessment will be based on the DBS CA grading scheme which has been included in this document

 

Module

 

 

Mark

 

Criteria

 

 

Determinator

 

 

 

Descriptor

 

 

Band

 

 

 

 

within grade band

 

 

A

80-100

 

Displays a thorough and systematic

 

Displaying insight

 

(Outstanding)

 

 

 

 

knowledge of module content, solution and

 

into problem and

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

handover process and documentation.

 

solution presented.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

●   Clear grasp of the issues involved, with

 

 

 

 

 

 

 

 

 

 

 

evidence of innovative and original use of

 

 

 

 

 

 

 

 

 

 

 

learning resources.

 

 

 

 

 

 

 

 

 

 

●   Knowledge beyond module content.

 

 

 

 

 

 

 

 

 

 

●   Clear evidence of independence of thought

 

 

 

 

 

 

 

 

 

 

 

and originality

 

 

 

 

 

 

 

 

 

 

Methodological rigour

 

 

 

 

 

 

 

 

 

 

●   High critical judgement and confident grasp

 

 

 

 

 

 

 

 

 

 

 

of complex issues

 

 

 

 

 

 

 

 

 

 

 

 

A (Clear)

70-79

 

Methodological rigour

 

Methodological

 

 

 

 

 

 

 

Originality

 

rigour

 

 

 

 

 

 

 

Critical judgement

 

 

 

 

 

 

 

 

 

 

●   Use of additional learning resources

 

 

 

 

 

 

 

 

 

 

 

 

B

60-69

 

Very good knowledge and understanding of

 

Extent of use of

 

 

 

 

 

 

 

 

the module content.

 

additional or non-

 

 

 

 

 

 

 

Well-argued answer

 

core learning

 

 

 

 

 

 

 

Some evidence of originality and critical

 

resources

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

judgement

 

 

 

 

 

 

 

 

 

 

Sound methodology

 

 

 

 

 

 

 

 

 

 

●   Critical judgement and some grasp of

 

 

 

 

 

 

 

 

 

 

 

complex issues.

 

 

 

 

 

 

 

 

 

 

 

 

C

50-59

 

Good knowledge and understanding of the

 

Understanding of

 

 

 

 

 

 

 

 

module content.

 

the main issues

 

 

 

 

 

 

 

●   Reasonably well-argued answer

 

 

 

 

 

 

 

 

 

 

●   Largely descriptive or narrative in focus

 

 

 

 

 

 

 

 

 

 

●   Methodological application is not

 

 

 

 

 

 

 

 

 

 

 

consistent or thorough

 

 

 

 

 

 

 

 

 

 

 

 

D

40-49

 

Lacking methodological application

 

Relevance of

 

 

 

 

 

 

 

Adequately argued

 

knowledge

 

 

 

 

 

 

 

Basic understanding and knowledge

 

displayed

 

 

 

 

 

 

 

●   Gaps or inaccuracies but not damaging

 

 

 

 

 

 

 

 

 

 

 

 

E (Fail)

0-39

 

 

 

 

Weakness of

 

 

 

 

 

 

 

 

 

 

understanding

 

 

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