Question Three.

a$)$ Summary statistics for the two variables of a breast cancer study are provided below.

$\backslash$table$[[$UniformCellShape$,,,],[$Class$,$Mean,standard Deviation,Count$],[2,1\mathrm{.}42,\mathrm{.}04,450],[4,6\mathrm{.}51,\mathrm{.}16,238],[$MargAdhesion$,,,],[$Class$,$Mean,standard Deviation,Count$],[2,1\mathrm{.}37,\mathrm{.}05,450],[4,5\mathrm{.}51,\mathrm{.}21,238]]$

Write the hypothesis tests that relate to a comparative analysis of the 'UniformCellShape' variable in relation to class $\text{'}2\text{'}$ and class' $4\text{'}$ of the data.

$(4$ marks$)$

b$)$ A new subject's data is recorded with a value of $3$ in 'UniformCellShape'. In relation to the summary statistics reported in part a$),$ how does the subject relate to the sample class $\text{'}2\text{'}?$

Please provide all calculations with your answer in relation to the classification of the subject in relation to the sample.

$(6$ marks$)$ c$)$ A cancer diagnostic classifier is built using a statistical analysis technique. The output of

the analysis is provided below.

ANOVA

Answer the following four questions in relation to the output provided.

i$)$ What is the Correlation Coefficient?

ii$)$ What is the Coefficient of the Determinant of the Regression?

iii$)$ What is the Linear Regression Model that will be used to classify the data?

iv$)$ What value or values in the output will indicate the accuracy of the performance of the

model to correctly classify the cancers?