$2.$ Refer to the $$Regression analysis$$ worksheet. To understand the effectiveness of its marketing strategies, ABC Co$.$ tracks its advertisement expenditures and sales in every marketing campaign. There are $3$ variables contained in the dataset provided by ABC. i Influencer type $$ Macro or Nano ii Sales $($$ thousands$)$ Sales of the marketing campaign iii Social media $($$ thousands$)$ Advertisement expenditures on social media of the marketing campaign $($a$)[5$ marks$]$ Estimate a multiple linear regression model in which the dependent variable is $$Sales$$ and the independent variables are $$Influencer type$$ and $$Social media$.$ What is the estimated regression model? For example, write: Sales $=0\mathrm{.}1+0\mathrm{.}2\backslash$times Macro $+0\mathrm{.}3\backslash$times Social Media $($b$)[5$ marks$]$ Examine the estimated coefficients from the regression model in $($a$).$ Are they statistically significant at the $5\%$ level? How do you interpret them? $($c$)[5$ marks$]$ The marketing manager believes that Macro influencers provide a greater return to sales per advertisement dollar spent. Estimate a multiple linear regression model to test whether the empirical data supports his beliefs. Write down the estimated regression model. Hint: You need to construct a new independent variable. $($d$)[5$ marks$]$ Do the estimated results of the regression model in $($c$)$ support the marketing manager$$s belief? Why?