$\%$ Load the data

GetEarlyCoronaData;

$\%$ Limit the data to the first $30$ days

mask $=$ days $<=30$;

days $=$ days$($mask$)$;

cases $=$ cases$($mask$)$;

$\%$ Figure $1$: Plot days vs$.$ cases

figure;

figure;

plot$($days$,$ cases, $\text{'}$bo$\text{'})$; $\%$ Plot data points using blue circles

$\%$ Calculate the linear fit $($y $=$ ax $+$ b$)$

p$\_$linear $=$ polyfit$($days$,$ cases, $1)$;

a$\_$linear $=$ p$\_$linear$(1)$; $\%$ Slope

b$\_$linear $=$ p$\_$linear$(2)$; $\%$ Intercept

y$\_$fit$\_$linear $=$ polyval$($p$\_$linear, days$)$;

$\%$ Plot the linear fit line

hold on;

plot$($days$,$ y$\_$fit$\_$linear, $\text{'}$r$-\text{'})$; $\%$ Plot linear fit using red line

legend$(\text{'}$Data points', 'Linear fit'$)$;

title$(\text{'}$Figure $1$: Days vs$.$ Cases with Linear Fit'$)$;

xlabel$(\text{'}$Days$\text{'})$;

ylabel$(\text{'}$Cases$\text{'})$;

$\%$ Add legend and labels

fprintf$(\text{'}$Linear fit equation: y $=\%\mathrm{.}2$f $*$ x $+\%\mathrm{.}2$f

$\text{'},$ a$\_$linear, b$\_$linear$)$;

$\%$ Display linear fit parameters and sum squared errors

SSE$\_$linear $=$ sum$(($cases $-$ y$\_$fit$\_$linear$).^2)$;

fprintf$(\text{'}$Sum squared error for linear fit: $\%\mathrm{.}4$f

$\text{'},$ SSE$\_$linear$)$;

$\%$ Figure $2$: Plot log$($cases$)$ vs$.$ days and calculate the best first$-$order

linear fit

figure;

log$\_$cases $=$ log$($cases$)$;

plot$($days$,$ log$\_$cases, $\text{'}$bo$\text{'})$; $\%$ Plot data points using blue circles

$\%$ Calculate the linear fit for log$($cases$)($log$($y$)=$ ax $+$ b$)$

p$\_$log $=$ polyfit$($days$,$ log$\_$cases, $1)$;

a$\_$log $=$ p$\_$log$(1)$; $\%$ Slope

b$\_$log $=$ p$\_$log$(2)$; $\%$ Intercept

log$\_$fit $=$ polyval$($p$\_$log$,$ days$)$;

$\%$ Plot the linear fit line

hold on;

plot$($days$,$ log$\_$fit, $\text{'}$r$-\text{'})$;

legend$(\text{'}$Data points', 'Log$-$linear fit'$)$;

title$(\text{'}$Figure $2$: Days vs$.$ log$($Cases$)$ with Log$-$Linear Fit'$)$;

xlabel$(\text{'}$Days$\text{'})$;

$1$

ylabel$(\text{'}$log$($Cases$)\text{'})$;

$\%$ Print log$-$linear fit equation and sum squared error

fprintf$(\text{'}$Log$-$linear fit equation: log$($y$)=\%\mathrm{.}2$f $*$ x $+\%\mathrm{.}2$f

$\text{'},$ a$\_$log$,$ b$\_$log$)$;

$\%$ Calculate the sum squared error for the log$-$linear fit

SSE$\_$log $=$ sum$(($log$\_$cases $-$ log$\_$fit$).^2)$;

fprintf$(\text{'}$Sum squared error for log$-$linear fit: $\%\mathrm{.}4$f

$\text{'},$ SSE$\_$log$)$;

$\%$ Figure $3$: Use the log$-$linear fit to calculate the exponential fit and plot

figure;

$\%$ Exponential fit

y$\_$exp$\_$fit $=$ exp$($a$\_$log $*$ days $+$ b$\_$log$)$;

$\%$ Plot the original data and the exponential fit

plot$($days$,$ cases, $\text{'}$bo$\text{'})$; $\%$ Plot data points using blue circles

hold on;

plot$($days$,$ y$\_$exp$\_$fit, $\text{'}$r$-\text{'})$; $\%$ Plot exponential fit using red line

legend$(\text{'}$Data points', 'Exponential fit'$)$;

title$(\text{'}$Figure $3$: Days vs$.$ Cases with Exponential Fit'$)$;

xlabel$(\text{'}$Days$\text{'})$;

ylabel$(\text{'}$Cases$\text{'})$;

$\%$ Calculate the sum squared error for the exponential fit

SSE$\_$exp $=$ sum$(($cases $-$ y$\_$exp$\_$fit$).^2)$;

fprintf$(\text{'}$Sum squared error for exponential fit: $\%\mathrm{.}4$f

$\text{'},$ SSE$\_$exp$)$;

$\%$ Compare the sum squared error terms and conclude which fit is better

if SSE$\_$exp $<$ SSE$\_$linear

fprintf$(\text{'}$The exponential model provides a better fit with smaller sum

squared error.

$\text{'})$;

else

fprintf$(\text{'}$The linear model provides a better fit with smaller sum squared

error.

$\text{'})$;

end

$\%$ Estimate how long it takes to double the number of cases

doubling$\_$time $=$ log$(2)/$ a$\_$log;

fprintf$(\text{'}$Estimated number of days to double the number of cases: $\%\mathrm{.}2$f