A recruiter for Big Box stores has collected the data in the file BigBox.xlsx summarizing the amount of money the company spent on print, web, and TV advertising in California over the past $22$ months and the resulting number of applications received from job applicants during the same months. The recruiter would like to build a regression model to predict the number of applications the company should expect based on a given advertising mix. a$.$ Prepare scatter plots showing the relationship between the number of applications received and each of the independent variables. What sort of relationship does each plot suggest? b$.$ If the recruiter wanted to build a regression model using only one independent variable to predict the number of applications received, what variable should be used? c$.$ What set of independent variables results in the highest value for the adjusted R$2$ statistic? d$.$ Suppose the recruiter chooses to use the regression function with all independent variables X$1,$ X$2$ and X$3.$ What is the estimated regression function? e$.$ Suppose the recruiter wants to generate $800$ applications in the next month. According to the model estimated in part $($d$),$ what is the least costly way to achieve this objective? f$.$ What problem, if any, do you see with the answer obtained in part $($e$)$ and what might be done to avoid it$?$