A company selling a perishable good (so theres no need to worry about inventory) has been doing some research on the demand and its sensitivity to price. Theyve been pricing their product at $5.00 for a long time and have seen demand fluctuate randomly. The most recent 30 weeks of sales data are contained in the table below:

Week	Sales		Week	Sales		Week	Sales
1	417		11	413		21	352
2	376		12	366		22	398
3	406		13	397		23	404
4	348		14	425		24	405
5	402		15	418		25	468
6	400		16	417		26	379
7	400		17	430		27	408
8	345		18	385		28	443
9	380		19	427		29	359
10	431		20	407		30	432

The problem is that theyre not sure how their profits would respond if they were to try different prices. The company agrees to explore a few different prices. The following table summarizes the prices they tried and the demand they observed.

Price	Observed Demand
$4.00	494
$6.00	344

In such a small price window, its generally safe to assume that the demand is a linear function of the price with an additive stochastic element with a mean of zero:

To understand how to properly price and supply their product, the company needs to know the mean and standard deviation at all prices.

Your current task is to find the estimates, and , that minimize the sum of squared residuals.

Question 1 Part 3

What is the estimate of the slope ( ) that minimizes the sum of squared residuals?