FormulasSimple linear regressions, Multiple and

correlation

Korelasi

Regresi Linear Berganda

Simple Linear Regression

Musiman dengan regresi dummy

First moving average period is centered at quarter (1+4)/ 2 = 2.5

Centered moving average of the first two moving averages is [7245.01 + 7380.75]/2 = 7312.875

• Smooth the time series to remove random effects and seasonality.

Calculate moving averages.

Step 1:Isolating the Trend Component

Average membership for the first 4 periods = [7130+6940+7354+7556]/4 = 7245.01

Second moving average periodis centered at quarter (2+5)/ 2 = 3.5

Average membership for periods [2, 5]= [6940+7354+7556+7673]/4 = 7380.75

Centered location is t = 3

Trend value at period 3, T3

=AVERAGE(C3:C6,C4:C7)Drag down to D16

Since yt =TtStεt, then the period factor, Stεt is given by

Stet = yt/Tt

Step 2Determining the Period Factors

• Determine “period factors” to isolate the (Seasonal)·(Random error) factor.

Calculate the ratio yt/Tt.

Example:In period 7 (3rd quarter of 1998):

S7ε7= y7/T7 = 7662/7643.875 = 1.002371

=C5/D5Drag down to E16

This eliminates the random factor from the period factors, Stεt This leaves us with only the seasonality component for each season.

Example: Unadjusted Seasonal Factor for the third quarter.S3 = {S3,97 e3,97 + S3,98 e3,98 + S3,99 e3,99}/3 =

{1.0056+1.0024+1.0079}/3 = 1.0053

Step 3Unadjusted Seasonal Factors

• Determine the “unadjusted seasonal factors” to eliminate the random component from the period factors

Average all the yt/Tt that correspond to the same season.

=AVERAGE(E3,E7,E11,E15)Drag down to F6

Paste Special(Values)

Copy F3:F6

Average seasonal factor = (1.01490+.96580+1.00533+1.01624)/4=1.00057

Step 4Adjusted Seasonal Factors

• Determine the “adjusted seasonal factors” so that average adjusted factor is 1

Calculate:

Unadjusted seasonal factors Average seasonal factor

Quarter1234

UnadjustedSeasonal Factor

1.01490 .965801.005331.01624

AdjustedSeasonal Factor

1.014325 .9652521.0047591.015663

Unadjusted Seasonal Factors/1.00057

F3/AVERAGE($F$3:$F$6)Drag down to G18

Step 5The Deseasonalized Time Series

Deseasonalized series value for Period 6

(2nd quarter, 1998)y6/(Quarter 2 Adjusted Seasonal Factor) =

7332/0.965252 = 7595.94

• Determine “Deseasonalized data values”.

Calculate: yt

[Adjusted seasonal factors]t

=C3/G3Drag to cell H18

Step 6The Time Series Trend Component

Regress on the Deseasonalized Time Series Determine a deseasonalized forecast from the

resulting regression equation

(Unadjusted Forecast)t = 7069.6677 + 78.4046t

Period (t)17181920

Unadjusted Forecast (t)8402.558480.958559.368637.76

Step 7The ForecastRe-seasonalize the forecast by multiplying the

unadjusted forecast by the adjusted seasonal factor for each period.

UnadjustedForecast (t)

8402.558480.958559.368637.76

Period17181920

AdjustedForecast (t)

8522.928186.268600.098773.06

AdjustedSeasonal Factor

1.014325 .9652521.0047591.015663

=I19*G3Drag down to J22

SeasonallyAdjustedForecasts