Enterprise Industries produces Fresh, a brand of liquid laundry detergent. In order to manage its inventory more effectively and make revenue projections, 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 30 sales periods (each sales period is defined to be one month). Here, for each sales period,
• y = the demand for the large size bottle of Fresh (in hundreds of thousands of bottles) in the sales period
• x1 = the price (in dollars) of Fresh as offered by Enterprise Industries in the sales period
• x2 = the average industry price (in dollars) of competitors' similar detergents in the sales period
• x3 = Enterprise Industries' advertising expenditure (in hundreds of thousands of dollars) to promote Fresh in the sales period
1. Please generate the descriptive statistics monthly average and monthly standard deviation for y, x1, x2 and x3 based on the data provided.
2. Please analyze the correlation between y and x1, the correlation between y and x2, and the correlation between y and x3 based on the data provided. Draw three appropriate graphs in excel to show the relationship between two.
3. Assuming Fresh predicts the average future monthly demand for the large size bottle of Fresh is 9 (hundreds of thousands of bottles) based on the data provided, examine whether his prediction is accurate. Please use the hypothesis testing I to conduct the examination by following steps below.
(a)State the null (Ho) and alternative (Ha) hypotheses. Explain briefly what they mean.
(b)Does it involve a one-tailed test or a two-tailed test? Why do you say that?
(c)What is your calculated t-score? What is the critical t-score?
(d)Assess the calculated and critical t-scores (as sentences in a paragraph): based on their values, will you keep the Ho or reject it and go for Ha? (e)Interpret: what does your chosen hypothesis says (the findings)?
4. To help Enterprise Industry predict a more accurate future monthly demand for its
Fresh product, please construct six following linear regression models(please report
its ??2, ???????????????? ??2, and coefficients of ??0, ??1, ??2, ??3)
?????????? 1 : ?? = ??0 + ??1??1
?????????? 2 : ?? = ??0 + ??2??2
?????????? 3 : ?? = ??0 + ??3??3
?????????? 4 : ?? = ??0 + ??1??1 + ??2??2
?????????? 5 : ?? = ??0 + ??1??1 + ??3??3
?????????? 6 : ?? = ??0 + ??1??1 + ??2??2 + ??3??3
Compare those 6 models and comment which model gives a better prediction of demand for Fresh.