Chapter 1. Time-Series Analysis. Pops Icicles Company has been operating for the past 6 years and the owner, Pop, has identified that there is a seasonality in the sales of popsicles and ice-creams. He shares the following data with you and asks you to help him answer the questions below because he looked online for various forms and needs to show this information to a potential buyer of his company. Remember that you can call the seasons quarters and number them according to your wish if you do not want to directly use the seasons he has listed. Remember to round all numbers to 2 decimal places when entering answers for the equation in part (b) and the forecast in part (c).

Year	Season	Sales/week
1	Spring	150
	Summer	250
	Fall	125
	Winter	50
2	Spring	125
	Summer	225
	Fall	150
	Winter	65
3	Spring	136
	Summer	200
	Fall	130
	Winter	65
4	Spring	175
	Summer	235
	Fall	170
	Winter	70
5	Spring	162
	Summer	300
	Fall	150
	Winter	79
6	Spring	150
	Summer	225
	Fall	130
	Winter	72

a. Construct a time series plot (include it in your final submission file at the end of the exam) and identify what the highest sales per week Pop has ever had in a season. popsicles

b. Use the time series linear regression analysis using dummies for Spring, Summer, and Fall to find the parameters of the line that minimizes the MSE for this data. Fill in the blanks below to indicate the corresponding parameter estimates:

Y-hat = + *Spring + *Summer + *Fall

(HINT: Spring = Q1t, Summer = Q2t, and Fall = Q3t if you compare it to the textbook example of snowboots)

c. The forecasted Summer sales in Year 7 would be popsicles.