Simple Linear Regression
Brethren of CodeAbbey are running several small businesses to support the Monastery. One of them is the Winemaking.
One of the interesting issues here is that the price of the wine is not constant. At some years customers are ready to buy more barrels and pay higher, while at other years they are reluctant and brotherhood needs to lower prices to get rid of wine stores.
It was found that the reason for such behavior is simple - after rainy years grapes yield wine of better quality and people are more eager to purchase it.
This gives monks the idea - they need to find the formula for calculating more just price depending on weather records from the preceeding year, so that trade will run more smoothly. (the wine which is sold this year was prepared from the grapes picked the year before)
You are to help them in finding this formula. To keep things simple let us try approximating the dependency with the linear function in the form
Y = K * X + B
X is the amount of rainy days and
Y is the price.
You will be given a list of records, each containing the number of rainy days during previous year along with the average price for which the wine was sold during current year.
Input data contains starting
A and ending
B year in the first line.
Then lines follow for each year in form
YYYY: D P where
YYYY is the mark of year,
D is the number of rainy days
(in previous season) and
P is the wine price (in crowns per barrel).
Answer should contain values for
B with accuracy of
1e-7 or better.
input data: 1925 1947 1925: 89 257 1926: 75 226 1927: 83 235 1928: 52 173 1929: 148 332 1930: 109 268 1931: 129 306 1932: 115 289 1933: 102 265 1934: 99 269 1935: 50 228 1936: 102 265 1937: 91 256 1938: 79 238 1939: 118 298 1940: 134 311 1941: 61 155 1942: 146 340 1943: 108 274 1944: 96 242 1945: 89 232 1946: 143 328 1947: 133 303 answer: 1.54053779316 107.312854273
By the way, google for "wine price bordeaux linear regression" and you will see that the problem is not invented out of nothing, but instead have similar real application.