Regression Analysis to Estimate Missing Values

The availability of data for any type of analysis is necessarily potentially limited, but fortunately there are regression analyses with which one can extrapolate numbers with which to estimate missing values.  One relatively simple method for calculating possible values for those missing is the use of a regression line, which can be used to answer the question "what is the most likely value for Y if given a value for X."  One makes the assumption here that the trend in the data will be the same for the missing values, and that the relationship between X and Y will remain constant.

Year	Station B x	Station A y
1931	1005.84	1131.97
1932	1148.08	1269.09
1933	691.39	828.84
1934	1328.25	1442.78
1935	1042.42	1167.23
1936	1502.41	1610.67
1937	1027.18	1152.54
1938	995.93	1122.42
1939	1323.59	1438.29
1940	946.19	1074.47
1941	989.58	1116.30
1942	1124.60	1246.45
1943	955.04	1083.00
1944	1215.64	1334.22
1945	1418.22	1529.50
1946	1323.34	1438.04
1947	1391.75	1503.98
1948	1338.97	1453.11
1949	1204.47	1323.45

  
The above table has rainfall values for two weather stations for the years 1931 through 1949.  The values for Station A in this year range were found using the slope and Y-intercept for the relationship between the stations using the values from 1949-2004.  The formula for the regression line is y = bx + a, where b is the slope, a is the Y-intercept, and x is the given value for Station B for that year.