The following data on diagnosis of coronary heart disease $($where $0$ indicating absence

and $1$ indicating presence$),$ serum cholesterol $($in mg$/$dl$),$ resting blood pressure $($in

mmHg$)$ and weight $($in kg$)$ were obtained for $80$ patients to explore the relationship of

coronary heart disease with cholesterol and weight.

S$.$

No$.$

Serum

Cholesterol

$($mg$/$dl$)$

Weight

$($kg$)$

Number of

Patients

having CHD

Total Number

of Patients

$1420601020$

$2450681530$

$340054415$

$451074210$

$54806215$

$($i$)$ Fit a multiple logistic model for the dependence of coronary heart disease on the average

serum cholesterol and weight considering $000$

$0124\mathrm{.}2790\mathrm{.}0350\mathrm{.}172\backslash$beta $,\backslash$beta and $\backslash$beta $$ as

the initial values of the parameters $($solve only for one Iteration$).$

$($ii$)$ Test the significance of the fitted model using Hosmer$-$Lemeshow test at $5\%$ level of

significance.