Month$/$Yr$.$ PERIOD PRICE AIP DIFF ADV DEMAND Jan. $2216\mathrm{.}15\mathrm{.}8-0\mathrm{.}36\mathrm{.}922\mathrm{.}225\mathrm{.}7560\mathrm{.}258\mathrm{.}823\mathrm{.}935\mathrm{.}76\mathrm{.}30\mathrm{.}69\mathrm{.}426\mathrm{.}045\mathrm{.}75\mathrm{.}709\mathrm{.}525\mathrm{.}355\mathrm{.}65\mathrm{.}850\mathrm{.}259\mathrm{.}425\mathrm{.}165\mathrm{.}65\mathrm{.}80\mathrm{.}28\mathrm{.}524\mathrm{.}275\mathrm{.}65\mathrm{.}750\mathrm{.}158\mathrm{.}823\mathrm{.}786\mathrm{.}35\mathrm{.}85-0\mathrm{.}459\mathrm{.}021\mathrm{.}396\mathrm{.}45\mathrm{.}65-0\mathrm{.}757\mathrm{.}520\mathrm{.}3106\mathrm{.}26-0\mathrm{.}27\mathrm{.}219\mathrm{.}9115\mathrm{.}96\mathrm{.}10\mathrm{.}28\mathrm{.}521\mathrm{.}2125\mathrm{.}960\mathrm{.}18\mathrm{.}123\mathrm{.}0135\mathrm{.}76\mathrm{.}10\mathrm{.}49\mathrm{.}123\mathrm{.}9145\mathrm{.}756\mathrm{.}20\mathrm{.}459\mathrm{.}025\mathrm{.}7155\mathrm{.}756\mathrm{.}10\mathrm{.}358\mathrm{.}827\mathrm{.}8165\mathrm{.}86\mathrm{.}10\mathrm{.}38\mathrm{.}827\mathrm{.}6175\mathrm{.}76\mathrm{.}20\mathrm{.}59\mathrm{.}227\mathrm{.}1185\mathrm{.}86\mathrm{.}30\mathrm{.}59\mathrm{.}126\mathrm{.}6195\mathrm{.}76\mathrm{.}10\mathrm{.}49\mathrm{.}426\mathrm{.}0205\mathrm{.}85\mathrm{.}75-0\mathrm{.}059\mathrm{.}825\mathrm{.}1215\mathrm{.}85\mathrm{.}75-0\mathrm{.}0510\mathrm{.}124\mathrm{.}8225\mathrm{.}755\mathrm{.}65-0\mathrm{.}110\mathrm{.}724\mathrm{.}8235\mathrm{.}75\mathrm{.}90\mathrm{.}210\mathrm{.}825\mathrm{.}3245\mathrm{.}555\mathrm{.}650\mathrm{.}110\mathrm{.}927\mathrm{.}6255\mathrm{.}66\mathrm{.}10\mathrm{.}511\mathrm{.}628\mathrm{.}3265\mathrm{.}656\mathrm{.}250\mathrm{.}611\mathrm{.}829\mathrm{.}6$

The Fresh Detergent Case

Enterprise Industries produces Fresh, a brand of liquid detergent. In order to more effectively

manage its inventory, the company would like to better predict demand for Fresh. To develop a

prediction model, the company has gathered data concerning demand for Fresh over the last $33$

sales periods. Each sales period is defined as one month. The variables are as follows:

Demand $=$ Y $=$ demand for a large size bottle of Fresh $($in $100,000)$

Price $=$ the price of Fresh as offered by Ent. Industries

AIP $=$ the average industry price

ADV $=$ Ent. Industries Advertising Expenditure $($in $$100,000)$ to Promote Fresh in the sales

period.

DIFF $=$ AIP $-$ Price $=$ the "price difference" in the sales period

$1-$ Download the data from Course Blackboard site into Excel spreadsheet.

$2-$ Make time series scatter plots of all five variables $($five graphs$).$ Insert trend line, equation,

and R$-$squared. Observe graphs and provide interpretation of results.

$3-$ Construct scatter plots of Demand vs$.$ DIFF and Demand vs$.$ ADV, Demand vs$.$ AIP, and

Demand vs$.$ Price. Insert linear fitted line, equation, and R$-$squared. Observe graphs and

provide interpretation. Note that Demand is always on the Y axis.

$4-$ Obtain the correlation matrix for all six variables and rank the variables based on absolute

correlation with Demand. Explain your findings in plain language.

$5-$ Use simple linear regression to perform trend analysis $($time period is X variable$)$ to predict

demand. Is trend analysis suitable for this data? Explain the Excel Regression output $($trend

equation, R$,$ R$-$Squared, goodness of the model$).$

$6-$ Perform simple linear regression analysis with ADV as the independent variable to predict

demand. Write the equation and explain the Excel Regression output.

$7-$ Repeat part $(6)$ with DIFF as the independent variable.

$8-$ Construct multiple linear regression model with Period, AIP, DIFF, and ADV as

independent variables. Formulate the equation and explain the output. Rank variables based

on their degree of contribution to the model. Observe significant F$,$ R$-$squared, and p$-$

values and explain.

$9-$ Perform multiple linear regression analysis with Period, DIFF, and ADV as independent

variables. Formulate the equation. Which variable is the most significant predictor of

demand? Rank the independent variables based on their degree of contribution to the

model. Observe significant F$,$ R$-$squared, and p$-$values and explain.

$10-$ Use the model obtained in parts $9$ and make forecasts for the following months.

Period Price AIP ADV

Oct. $2024(34)$ $$7\mathrm{.}60$ $$7\mathrm{.}35$ $$12\mathrm{.}9$

Nov. $2024(35)$ $$7\mathrm{.}85$ $$7\mathrm{.}40$ $$13\mathrm{.}1$

Dec. $2024(36)$ $$7\mathrm{.}95$ $$7\mathrm{.}85$ $$13\mathrm{.}5$

$11-$ Provide a brief conclusion based on above analysis