Simple Linear Regression

FORECAST BY SIMPLE LINEAR REGRES

Linear regression attempts to model the relationship between two variables by fitting a line variable is considered to be an explanatory variable, and the other is considered to

Function of Reg a b y 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

240 250 175 186 245 250 260 190 245 250 185 120 135 189 240 261 140 250 165 260 235 197 240 235 245 233 246 250 247 185

225.91 226.40 226.89 227.38 227.87 228.37 228.86 229.35 229.84 230.33 230.82 231.31 231.80 232.29 232.78 233.28 233.77 234.26 234.75 235.24 235.73 236.22 236.71 237.20 237.69 238.19 238.68 239.17 239.66 240.15 240.64 241.13

Error -14.09 -23.60 51.89 41.38 -17.13 -21.63 -31.14 39.35 -15.16 -19.67 45.82 111.31 96.80 43.29 -7.22 -27.72 93.77 -15.74 69.75 -24.76 0.73 39.22 -3.29 2.20 -7.31 5.19 -7.32 -10.83 -7.34 55.15

Forecast the data o

Forecast period

75

Forecasted value: y = 00.225 + 00.00

Data - For 275 250 225 200

Unit

Period (t)Data (y)Forecast

intersection estimate slope estimate data as a function of period

175 150 125 100 75 50 25 0 12 34567891 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 0123 4567890123 45678901234

Errors in F 120 110 100 90 80

33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

241.62 242.11 242.60 243.09 243.59 244.08 244.57 245.06 245.55 246.04 246.53 247.02 247.51 248.00 248.50 248.99 249.48 249.97 250.46 250.95 251.44 251.93 252.42 252.91 253.41 253.90 254.39 254.88

Unit

Errors in F 120 110 100 90 80 70 60 50 40 30 20 10 0 -10 -20 -30 -40

12 3456 7891 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 0123 4567890123 45678901 234

Time

INEAR REGRESSION

variables by fitting a linear equation to observed data. One he other is considered to be a dependent variable. Function of Regression

ction estimate stimate a function of period

225.4194 0.4910 y = 00.225 + 00.000.t

Forecast the data of period m

y = 00.225 + 00.000 x 75

262.24

Data - Forecast Chart

Forecast Observed Data

11 1111112222 22222233333 33333444444 44445555555 5556 23 4567890123 45678901234 56789012345 67890123456 7890

Errors in Forecast

Data? 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0

Errors in Forecast

Error

111 1111112222 22222233333 3 33334444 44 44445555555 55 56 123 4567890123 45678901234 5 67890123 45 67890123456 78 90

Time

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

XXavg YavgX-Xavg Y-Yavg (X-Xavg)^2 <--sum slope est inter.est. 1 15.5 218.3 -14.5 21.7 210.25 2247.5 0.49 225.42 2 -13.5 31.7 182.25 3 -12.5 -43.3 156.25 4 -11.5 -32.3 132.25 5 -10.5 26.7 110.25 6 -9.5 31.7 90.25 7 -8.5 41.7 72.25 8 -7.5 -28.3 56.25 9 -6.5 26.7 42.25 10 -5.5 31.7 30.25 11 -4.5 -33.3 20.25 12 -3.5 -98.3 12.25 13 -2.5 -83.3 6.25 14 -1.5 -29.3 2.25 15 -0.5 21.7 0.25 16 0.5 42.7 0.25 17 1.5 -78.3 2.25 18 2.5 31.7 6.25 19 3.5 -53.3 12.25 20 4.5 41.7 20.25 21 5.5 16.7 30.25 22 6.5 -21.3 42.25 23 7.5 21.7 56.25 24 8.5 16.7 72.25 25 9.5 26.7 90.25 26 10.5 14.7 110.25 27 11.5 27.7 132.25 28 12.5 31.7 156.25 29 13.5 28.7 182.25 30 14.5 -33.3 210.25 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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