Problem 3. A food supermarket purchases crab from a company in Alaska. Sheet \"problem 3' shows the data of the weight (in pound) and the total price (in $) for the last 15 history orders. # Weight (pound) Price ($) 1 1380 7600 2 3120 21600 3 3520 23800 4 1130 6900 5 1030 5000 6 1720 11900 7 3920 28200 8 1490 8100 9 1860 13200 10 3430 22800 11 2000 14500 12 3660 25100 13 2500 17000 14 1220 7100 15 1390 2900 (a). Fit a linear regression model with weight as the input variable x and the price as the response variable y. Draw the tted regression line along with the scatter dots of the history data. Note: Using any tools and software are accepted, Excel, Python, Maggy, and 9% Manual drawing is NOT accepted. (b). What are the standard errors of the estimates of [30, [31 and the tted regression line at a given point x*=2000, respectively? Using the standard error of 131, test the following hypothesis with given on=0.01. Ho: Bl = 7.0 versus H1: [31 at 7.0 (c). Due to the COVID, the manager has _t_o_ cut down the purchase demand to 800 pounds per order, what is the predicted price? ((1). Assume the error terms 81, 82," .,sn normally distributed with mean zero and standard deviation 0:80. What is the probability that the true price is larger than 3200 when x = 800 pounds