As an e$-$commerce retailer, you have obtained some information from several comparable competitors regarding their levels of advertising expenditures and their sales. If you have a goal for $$750,000$ in sales next year, use regression to determine the best amount of advertising dollars you should invest to hit your goal.

Online Store

Monthly E$-$commerce Sales $($in $1000$ s$)$

Online Advertising Dollars

$(1000$ s$)$

$1$

$368$

$1\mathrm{.}7$

$2$

$340$

$1\mathrm{.}5$

$3$

$665$

$2\mathrm{.}8$

$4$

$954$

$5$

$5$

$331$

$1\mathrm{.}3$

$6$

$556$

$2\mathrm{.}2$

$7$

$376$

$1\mathrm{.}3$

Given the historical data of company sales, using linear regression, make a prediction for $2020$ sales revenue.

Year

Sales $($In millions$)$

$2012$

$2\mathrm{.}611$

$2013$

$2\mathrm{.}688$

$2014$

$3\mathrm{.}022$

$2015$

$3\mathrm{.}133$

$2016$

$3\mathrm{.}743$

$2017$

$3\mathrm{.}698$

$2018$

$3\mathrm{.}997$

$2019$

$4\mathrm{.}436$

Develop a brief memorandum to management summarizing your projections with appropriate support. Advise management about the relative risk of relying on historical sales trends to predict sales in recent years. Be sure to describe your linear model and its limitations$.$ Can you say anything about the cause$-$effect relationship between the variables in the correlation analysis? Advise management on what conditions might call for revisiting the prediction.