> setwd('c:/Users/jph6366/Desktop/SPATIOTEMPORAL/')
> dataretail <- read.csv("retail.csv")
> head(dataretail)
Period Value
1 Jan-1992 142,051
2 Feb-1992 142,498
3 Mar-1992 154,439
4 Apr-1992 158,430
5 May-1992 164,788
6 Jun-1992 163,417
> tail(dataretail)
Period Value
415 Jul-2026 <NA>
416 Aug-2026 <NA>
417 Sep-2026 <NA>
418 Oct-2026 <NA>
419 Nov-2026 <NA>
420 Dec-2026 <NA>
> class(dataretail)
[1] "data.frame"
> class(dataretail$Value)
[1] "character"
> ourdata <- as.numeric(gsub(",","",dataretail$Value))
> head(ourdata)
[1] 142051 142498 154439 158430 164788 163417
> ts(ourdata, start=c(1992,1), end=c(2026,1))
Time Series:
Start = 1992
End = 2026
Frequency = 1
[1] 142051 142498 154439 158430 164788 163417 164575 165387 159892 168529 166918 203616
[13] 149066 145607 165467 171075 176619 176095 178060 178176 172381 177545 182451 219162
[25] 157262 158247 186925 184025 189261 192034 187716 196791 188722 192462 197408
> autoplot(ts(ourdata, start=c(1992,1), end=c(2026,1)))
Error in autoplot(ts(ourdata, start = c(1992, 1), end = c(2026, 1))) :
could not find function "autoplot"
> library(ggplot2)
> autoplot(ts(ourdata, start=c(1992,1), end=c(2026,1)))
Error in `autoplot()`:
! Objects of class <ts> are not supported by autoplot.
ℹ Have you loaded the required package?
Run `rlang::last_trace()` to see where the error occurred.
> library(fpp2)
── Attaching packages ────────────────────────────────────────────────────────── fpp2 2.5.1 ──
✔ forecast 9.0.1 ✔ expsmooth 2.3
✔ fma 2.5
> autoplot(ts(ourdata, start=c(1992,1), end=c(2026,1)), ylab="Advance Monthly Sales for Retail and Food Services")
> ames <- modeldata::ames
> regfit <- regsubsets(Sale_Price ~ ., data = ames, method = "forward", nvmax = 150)
Reordering variables and trying again:
Warning message:
In leaps.setup(x, y, wt = wt, nbest = nbest, nvmax = nvmax, force.in = force.in, :
6 linear dependencies found
> regfit.s <- summary(regfit)
> ggplot() +
geom_line(aes(x = 1:151, y = regfit.s$bic)) +
labs(y = "BIC", x = "number of features p") +
scale_x_continuous(breaks = seq(0, 150, 10))
. + >
> best_idx <- which.min(regfit.s$bic)
> fs <- names(which(regfit.s$outmat[best_idx, ] == "*"))
> best_idx
[1] 85
> fullmodel<-model.matrix(Sale_Price ~ ., data = ames)
> P<-as.data.frame(fullmodel)
> D<-cbind(Sale_Price=ames$Sale_Price,P[,-1])
> fs <- names(which(regfit.s$outmat[best_idx, ] == "*"))
> selected_fs <- paste(fs, collapse = "+")
> model_bic <- lm(Sale_Price ~ MS_SubClassOne_Story_1945_and_Older+MS_SubClassTwo_Story_1945_and_Older+MS_SubClassDuplex_All_Styles_and_Ages+MS_SubClassOne_Story_PUD_1946_and_Newer+MS_SubClassTwo_Story_PUD_1946_and_Newer+MS_SubClassPUD_Multilevel_Split_Level_Foyer+Lot_Area+Land_ContourHLS+Land_ContourLvl+Lot_ConfigCulDSac+Land_SlopeSev+NeighborhoodEdwards+NeighborhoodSomerset+NeighborhoodNorthridge_Heights+NeighborhoodBrookside+NeighborhoodCrawford+NeighborhoodNorthridge+NeighborhoodStone_Brook+NeighborhoodBriardale+NeighborhoodNorthpark_Villa+NeighborhoodGreen_Hills+Condition_1Norm+Condition_1PosN+Condition_2PosA+Condition_2PosN+Overall_CondBelow_Average+Overall_CondAverage+Overall_CondAbove_Average+Overall_CondGood+Overall_CondVery_Good+Overall_CondExcellent+Year_Built+Year_Remod_Add+Roof_StyleHip+Roof_MatlCompShg+Roof_MatlMembran+Roof_MatlMetal+Roof_MatlRoll+`Roof_MatlTar&Grv`+Roof_MatlWdShake+Roof_MatlWdShngl+Exterior_1stBrkFace+Exterior_1stCemntBd+Exterior_1stHdBoard+Exterior_1stPlywood+Mas_Vnr_TypeNone+Mas_Vnr_TypeStone+Mas_Vnr_Area+FoundationCBlock+Bsmt_CondNo_Basement+Bsmt_ExposureGd+Bsmt_ExposureMn+Bsmt_ExposureNo+BsmtFin_Type_1GLQ+BsmtFin_Type_1Unf+BsmtFin_Type_2GLQ+BsmtFin_Type_2Unf+Bsmt_Unf_SF+Total_Bsmt_SF+Gr_Liv_Area+Bedroom_AbvGr+Kitchen_AbvGr+TotRms_AbvGrd+FunctionalTyp+Fireplaces+Garage_FinishRFn+Garage_FinishUnf+Garage_Cars+Garage_Area+Screen_Porch+Pool_Area+Pool_QCFair+Pool_QCGood+Pool_QCNo_Pool+Pool_QCTypical+Misc_FeatureGar2+Misc_FeatureNone+Misc_FeatureOthr+Misc_FeatureShed+Misc_FeatureTenC+Misc_Val+Sale_TypeNew+Sale_ConditionAdjLand+Sale_ConditionNormal+Longitude, data = D)
> BIC(model_bic)
[1] 68015.1
> AIC(model_bic)
[1] 67494.6
> summary(model_bic)
Call:
lm(formula = Sale_Price ~ MS_SubClassOne_Story_1945_and_Older +
MS_SubClassTwo_Story_1945_and_Older + MS_SubClassDuplex_All_Styles_and_Ages +
MS_SubClassOne_Story_PUD_1946_and_Newer + MS_SubClassTwo_Story_PUD_1946_and_Newer +
MS_SubClassPUD_Multilevel_Split_Level_Foyer + Lot_Area +
Land_ContourHLS + Land_ContourLvl + Lot_ConfigCulDSac + Land_SlopeSev +
NeighborhoodEdwards + NeighborhoodSomerset + NeighborhoodNorthridge_Heights +
NeighborhoodBrookside + NeighborhoodCrawford + NeighborhoodNorthridge +
NeighborhoodStone_Brook + NeighborhoodBriardale + NeighborhoodNorthpark_Villa +
NeighborhoodGreen_Hills + Condition_1Norm + Condition_1PosN +
Condition_2PosA + Condition_2PosN + Overall_CondBelow_Average +
Overall_CondAverage + Overall_CondAbove_Average + Overall_CondGood +
Overall_CondVery_Good + Overall_CondExcellent + Year_Built +
Year_Remod_Add + Roof_StyleHip + Roof_MatlCompShg + Roof_MatlMembran +
Roof_MatlMetal + Roof_MatlRoll + `Roof_MatlTar&Grv` + Roof_MatlWdShake +
Roof_MatlWdShngl + Exterior_1stBrkFace + Exterior_1stCemntBd +
Exterior_1stHdBoard + Exterior_1stPlywood + Mas_Vnr_TypeNone +
Mas_Vnr_TypeStone + Mas_Vnr_Area + FoundationCBlock + Bsmt_CondNo_Basement +
Bsmt_ExposureGd + Bsmt_ExposureMn + Bsmt_ExposureNo + BsmtFin_Type_1GLQ +
BsmtFin_Type_1Unf + BsmtFin_Type_2GLQ + BsmtFin_Type_2Unf +
Bsmt_Unf_SF + Total_Bsmt_SF + Gr_Liv_Area + Bedroom_AbvGr +
Kitchen_AbvGr + TotRms_AbvGrd + FunctionalTyp + Fireplaces +
Garage_FinishRFn + Garage_FinishUnf + Garage_Cars + Garage_Area +
Screen_Porch + Pool_Area + Pool_QCFair + Pool_QCGood + Pool_QCNo_Pool +
Pool_QCTypical + Misc_FeatureGar2 + Misc_FeatureNone + Misc_FeatureOthr +
Misc_FeatureShed + Misc_FeatureTenC + Misc_Val + Sale_TypeNew +
Sale_ConditionAdjLand + Sale_ConditionNormal + Longitude,
data = D)
Residuals:
Min 1Q Median 3Q Max
-309366 -11726 366 11346 169309
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.256e+07 2.093e+06 -6.002 2.20e-09 ***
MS_SubClassOne_Story_1945_and_Older 6.960e+03 2.485e+03 2.801 0.005131 **
MS_SubClassTwo_Story_1945_and_Older 9.630e+03 2.649e+03 3.635 0.000283 ***
MS_SubClassDuplex_All_Styles_and_Ages -1.614e+04 3.960e+03 -4.076 4.70e-05 ***
MS_SubClassOne_Story_PUD_1946_and_Newer -2.242e+04 2.272e+03 -9.866 < 2e-16 ***
MS_SubClassTwo_Story_PUD_1946_and_Newer -3.044e+04 3.008e+03 -10.119 < 2e-16 ***
MS_SubClassPUD_Multilevel_Split_Level_Foyer -3.421e+04 6.397e+03 -5.348 9.60e-08 ***
Lot_Area 4.102e-01 7.613e-02 5.388 7.70e-08 ***
Land_ContourHLS 1.758e+04 3.107e+03 5.657 1.69e-08 ***
Land_ContourLvl 6.015e+03 2.019e+03 2.979 0.002913 **
Lot_ConfigCulDSac 4.156e+03 1.954e+03 2.127 0.033488 *
Land_SlopeSev -2.532e+04 7.690e+03 -3.293 0.001005 **
NeighborhoodEdwards -6.354e+03 2.072e+03 -3.067 0.002181 **
NeighborhoodSomerset 2.672e+04 2.254e+03 11.855 < 2e-16 ***
NeighborhoodNorthridge_Heights 4.820e+04 2.463e+03 19.570 < 2e-16 ***
NeighborhoodBrookside 8.362e+03 2.530e+03 3.305 0.000962 ***
NeighborhoodCrawford 1.517e+04 2.747e+03 5.523 3.64e-08 ***
NeighborhoodNorthridge 3.523e+04 3.317e+03 10.622 < 2e-16 ***
NeighborhoodStone_Brook 6.295e+04 3.862e+03 16.300 < 2e-16 ***
NeighborhoodBriardale 2.342e+04 5.435e+03 4.309 1.69e-05 ***
NeighborhoodNorthpark_Villa 3.137e+04 5.690e+03 5.513 3.85e-08 ***
NeighborhoodGreen_Hills 1.202e+05 1.722e+04 6.978 3.71e-12 ***
Condition_1Norm 8.958e+03 1.414e+03 6.336 2.72e-10 ***
Condition_1PosN 1.624e+04 4.336e+03 3.745 0.000184 ***
Condition_2PosA 9.590e+04 1.228e+04 7.811 7.92e-15 ***
Condition_2PosN -9.927e+04 1.294e+04 -7.671 2.33e-14 ***
Overall_CondBelow_Average 1.294e+04 3.864e+03 3.349 0.000821 ***
Overall_CondAverage 2.141e+04 3.215e+03 6.660 3.28e-11 ***
Overall_CondAbove_Average 2.775e+04 3.264e+03 8.503 < 2e-16 ***
Overall_CondGood 3.710e+04 3.395e+03 10.926 < 2e-16 ***
Overall_CondVery_Good 4.039e+04 3.870e+03 10.436 < 2e-16 ***
Overall_CondExcellent 5.508e+04 5.184e+03 10.626 < 2e-16 ***
Year_Built 4.950e+02 3.481e+01 14.220 < 2e-16 ***
Year_Remod_Add 1.094e+02 3.536e+01 3.094 0.001992 **
Roof_StyleHip 5.719e+03 1.285e+03 4.452 8.84e-06 ***
Roof_MatlCompShg 6.685e+05 3.301e+04 20.250 < 2e-16 ***
Roof_MatlMembran 7.147e+05 4.196e+04 17.033 < 2e-16 ***
Roof_MatlMetal 6.992e+05 4.192e+04 16.678 < 2e-16 ***
Roof_MatlRoll 6.665e+05 4.107e+04 16.227 < 2e-16 ***
`Roof_MatlTar&Grv` 6.650e+05 3.319e+04 20.035 < 2e-16 ***
Roof_MatlWdShake 6.585e+05 3.394e+04 19.404 < 2e-16 ***
Roof_MatlWdShngl 7.416e+05 3.397e+04 21.831 < 2e-16 ***
Exterior_1stBrkFace 1.545e+04 2.797e+03 5.523 3.63e-08 ***
Exterior_1stCemntBd 8.285e+03 2.474e+03 3.348 0.000823 ***
Exterior_1stHdBoard -5.282e+03 1.416e+03 -3.730 0.000196 ***
Exterior_1stPlywood -7.136e+03 1.985e+03 -3.595 0.000330 ***
Mas_Vnr_TypeNone 7.630e+03 1.465e+03 5.208 2.04e-07 ***
Mas_Vnr_TypeStone 6.928e+03 1.910e+03 3.628 0.000290 ***
Mas_Vnr_Area 3.854e+01 4.048e+00 9.523 < 2e-16 ***
FoundationCBlock -2.398e+03 1.301e+03 -1.843 0.065364 .
Bsmt_CondNo_Basement 1.919e+04 4.151e+03 4.622 3.98e-06 ***
Bsmt_ExposureGd 1.632e+04 2.022e+03 8.069 1.04e-15 ***
Bsmt_ExposureMn -8.068e+03 2.008e+03 -4.018 6.01e-05 ***
Bsmt_ExposureNo -6.497e+03 1.415e+03 -4.590 4.62e-06 ***
BsmtFin_Type_1GLQ 8.136e+03 1.480e+03 5.496 4.23e-08 ***
BsmtFin_Type_1Unf 6.609e+03 1.637e+03 4.037 5.56e-05 ***
BsmtFin_Type_2GLQ 1.437e+04 4.561e+03 3.151 0.001643 **
BsmtFin_Type_2Unf 5.736e+03 1.589e+03 3.610 0.000311 ***
Bsmt_Unf_SF -2.201e+01 1.829e+00 -12.031 < 2e-16 ***
Total_Bsmt_SF 4.606e+01 2.115e+00 21.777 < 2e-16 ***
Gr_Liv_Area 6.104e+01 2.096e+00 29.123 < 2e-16 ***
Bedroom_AbvGr -5.697e+03 8.748e+02 -6.513 8.70e-11 ***
Kitchen_AbvGr -1.562e+04 3.530e+03 -4.424 1.00e-05 ***
TotRms_AbvGrd 1.811e+03 6.195e+02 2.924 0.003484 **
FunctionalTyp 1.596e+04 1.949e+03 8.191 3.87e-16 ***
Fireplaces 5.582e+03 8.733e+02 6.391 1.91e-10 ***
Garage_FinishRFn -7.783e+03 1.252e+03 -6.214 5.92e-10 ***
Garage_FinishUnf -3.963e+03 1.345e+03 -2.947 0.003234 **
Garage_Cars 3.516e+03 1.448e+03 2.429 0.015204 *
Garage_Area 1.814e+01 5.009e+00 3.622 0.000298 ***
Screen_Porch 4.114e+01 8.319e+00 4.946 8.02e-07 ***
Pool_Area 1.780e+01 5.919e+01 0.301 0.763687
Pool_QCFair -8.308e+04 3.209e+04 -2.589 0.009679 **
Pool_QCGood -7.913e+04 2.773e+04 -2.854 0.004347 **
Pool_QCNo_Pool -9.473e+04 2.452e+04 -3.864 0.000114 ***
Pool_QCTypical -9.696e+04 1.963e+04 -4.940 8.28e-07 ***
Misc_FeatureGar2 5.681e+05 3.177e+04 17.882 < 2e-16 ***
Misc_FeatureNone 5.722e+05 4.071e+04 14.055 < 2e-16 ***
Misc_FeatureOthr 5.932e+05 3.832e+04 15.479 < 2e-16 ***
Misc_FeatureShed 5.724e+05 3.973e+04 14.409 < 2e-16 ***
Misc_FeatureTenC 5.282e+05 5.148e+04 10.260 < 2e-16 ***
Misc_Val 1.018e+00 1.847e+00 0.551 0.581567
Sale_TypeNew 2.225e+04 2.459e+03 9.049 < 2e-16 ***
Sale_ConditionAdjLand 2.175e+04 7.402e+03 2.939 0.003321 **
Sale_ConditionNormal 7.251e+03 1.604e+03 4.521 6.42e-06 ***
Longitude -1.088e+05 2.259e+04 -4.819 1.52e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 23960 on 2844 degrees of freedom
Multiple R-squared: 0.9127, Adjusted R-squared: 0.91
F-statistic: 349.6 on 85 and 2844 DF, p-value: < 2.2e-16
> best_cp_f_idx <- which.min(regfit.s$cp)
> cat("Forward Cp optimal size:", best_cp_f_idx, "\n")
Forward Cp optimal size: 135
