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

$\backslash$table$[[$Year$,1,2,3,4,5,6,7,8,9,10],[\backslash$table$[[$Number of Patients$],[$Robbery Rate$],[$per $1,000$ Population$]],37,33,40,42,41,54,58,54,51,62]]$

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

hat$(y)=+t$

Where hat$(y)=$ Dependent Variable and $x=$ Independent Variable.

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

Using linear regression, the number of patients Dr$.$ Fok will see in year $12=$ patients $($round your response to hwo decimal places$).$

The coefficient of determination for the linear regression model is $0\mathrm{.}8817.$ This shows that there is a relationship between the "Number of Patients" and "Yoar:"