$42.$ Using the data in the table for part calculate the simple linear regression forecast for monthly income for next February. The approximate numeric value of the forecast $($in units of $K$,$ rounded to two $[2]$ decimal places.$)$ a$.$ $$75\mathrm{.}50$K b$.$ $$78\mathrm{.}73$K c$.$ $$74\mathrm{.}95$K d$.$ $$75\mathrm{.}41$K e$.$ $$78\mathrm{.}85$K Question $43.$ According to your regression analysis performed for part $42,$ what is the approximate numerical value of the strength of the linear association between monthly income and month number? $($Round to four $[4]$ decimal places.$)$ a$.0\mathrm{.}8945$ b$.0\mathrm{.}9018$ c$.2\mathrm{.}1500$ d$.0\mathrm{.}4867$Monthly income in thousands of dollars $($$K$)$ at the Acme Law Firm for the $13-$month period from January this year to January next year is listed in the table below. $($For parts $39$ to $47,$ download the Excel file "Exam $2$ time series data" in the "Exam $2$ Excel forecasting file" link in the "Assessments" in the Navigation bar of the Bb course website. Save your completed Excel file containing your calculations for parts $39$ to $47$ for later uploading to Bb$.)$

$\backslash$table$[[$Month$,$Income $($$K$)],[$Jan$,51\mathrm{.}8],[$Feb$,55\mathrm{.}5],[$Mar$,54\mathrm{.}7],[$Apr$,57\mathrm{.}1],[$May$,50\mathrm{.}6],[$Jun$,68\mathrm{.}2],[$Jul$,66\mathrm{.}4],[$Aug$,59\mathrm{.}3],[$Sep$,67\mathrm{.}2],[$Oct$,69\mathrm{.}8],[$Nov$,77\mathrm{.}6],[$Dec$,74\mathrm{.}4],[$Jan$,75\mathrm{.}5]]$