Problem 4 (12 points): A retail store is trying to figure out the relationship between the price (P) and sales (S) of a product. It is assumed that there is a linear relationship between the two, given by S=0+1P+ where N(0,2). To estimate this relationship, each week the store sets a price Pi (in dollars) for the product and notes the sales Si (in hundreds) for that week. The table below summarizes the data collected for six weeks: (a) (4 points ) Find estimates ^0 and ^1 via explicit without using R). Show your work. (b) (3 points) Find an unbiased estimate for 2. Show your work. (c) (3 points) Provide a two-sided 99% confidence interval for 1. Justify your answer. (d) (2 points) Consider the null hypothesis H0:1=2. Will you accept or reject the null at significance level =1% ? Provide clear justification for your