Dr$.$ Lillian Fok, a New Orleans psychologist, specializes in treating patients who are agoraphobic $(1.$e$.,$ afraid to leave their homes$).$ The following table indicates how many patients Dr$.$ Fok has seen each year for the past $10$ years. It also indicates what the robbery rate was in New Orleans during the same year.

$\backslash$table$[[$Year$,1,2,3,4,5,6,7,8,9,10],[$Number of Patients,$37,33,41,41,41,54,62,53,57,62],[$Robbery Rate per,$57\mathrm{.}8,61\mathrm{.}4,72\mathrm{.}6,75\mathrm{.}7,78\mathrm{.}5,89\mathrm{.}0,101\mathrm{.}5,94\mathrm{.}8,102\mathrm{.}2,117\mathrm{.}2]]$

The simple linear regression equation that shows the best relationship between the number of patients and year is $($round your responses to three decimal places$)$:

hat$(y)=30\mathrm{.}467+3\mathrm{.}206x$

where hat$(y)=$ Dependent Variable and $x=$ Independent Variable,

Using linear regression, the number of patients Dr$.$ Fok will see in year $11=$ patients $($round your response to two decimal places$).$