library(tidyverse)
# Loaded data
names <-c("Contributor", "Address", "Zipcode", "Price", "Date", "Numbed",
"Numbath", "Yearbuilt", "Sqft", "Lotsize", "Numparking")
housing <- read_csv("Datasets/housing.csv", col_names=names, skip=1)
# Transformed datatypes for some columns that were not read as numbers
# (changed incorrect data to NA)
housing <- housing %>%
mutate(Numbath = as.numeric(Numbath)) %>%
mutate(Lotsize = as.numeric(Lotsize)) %>%
mutate(Numparking = as.numeric(Numparking))
# Duplicate data points are removed
housing$Address <- gsub(",","",housing$Address)
housing$Address <- gsub("\\s+"," ",housing$Address)
housing$Address <- tolower(housing$Address)
housing <- housing[!duplicated(housing$Address),]
# Rows with null values are removed
housingtb <- na.omit(housing)
# Data was written to a file for visual inspection and manual manipulation
# (Commented out after the first time housing.csv was written)
# housing %>%
# write_csv("Datasets/housing.csv")
# Loaded the visually inspected and cleaned data & removed outliers
# housingtb <- read_csv("Datasets/housing.csv")
housingtb <- housingtb %>%
mutate(Age=(2024-Yearbuilt)) %>%
filter(Age >= 0, Sqft > 0, Sqft <= Lotsize, Lotsize <= 100000, Price >= 10000) %>%
select(Price, Numbed, Numbath, Age, Sqft, Lotsize, Numparking)Key Drivers of Housing Prices: Understanding the Impact of Property Features on Sale Value
Introduction: Description of goals
Housing prices are affected by several factors, which include the size, quality, and desirability of a home. To understand the factors that influence housing values, this study aims to investigate the relationship between key characteristics of residential dwellings and their eventual sale prices. The analysis will address two core research questions:
How are the number of bedrooms, number of bathrooms, year built, square footage, lot size, and number of parking spots related to the sale price of a home? Examining these fundamental features of a property will provide insight into which attributes potential home buyers value most when assessing home prices.
Which housing characteristics have the highest impact on sale price? Determining the variables with the highest impacts can indicate which factors are most influential on a home’s market value. These important drivers of price require particular attention.
To analyze these questions, this study will perform a multiple regression analysis using housing sales data containing the aforementioned predictors and sale price as the outcome variable. Regression modeling is well-suited for assessing the individual relationships between potential explanatory variables and the target variable. The resulting regression coefficients and correlation strengths will shed light on the relative importance of various housing attributes in predicting final sale values. These quantitative insights will serve to disentangle the complex factors that interact to determine real estate prices. A data-driven approach will help characterize the true influences of home characteristics on market values. The findings will have implications for homeowners seeking to optimize their property’s value, home buyers evaluating pricing, and policymakers crafting effective housing market measures.
Data Cleaning
Data cleaning consists of largely two steps, i.e., data preprocessing and outlier removal. The preprocessing involves following:
The column names are set by creating a names vector and passing it to read_csv() to ensure proper column labels during import.
The Numbath, Lotsize, and Numparking columns are converted to numeric data types using mutate() and as.numeric(). This fixes cases where they were not initially read as numbers.
Duplicate rows are removed by standardizing the Address column - first removing commas, collapsing whitespace, lowercasing, then filtering out duplicates via !duplicated().
Null values are removed by applying na.omit() to filter out any rows with NA values.
In this step, column data types are fixed, duplicates are removed, and missing values are filtered out. This prepares the raw housing data for analysis by handling several common data quality issues. The result is a clean dataset with consistent formatting and no redundant or missing observations.
Next, outlier removal step includes the following:
The cleaned housing data is loaded from the CSV file into a dataframe housingtb.
A new column ‘Age’ is created by subtracting the Yearbuilt from the current year 2024.
Filters are applied to remove observations with non-sensical or extreme values:
Age is restricted to be greater than or equal to 0 (no future ages)
Sqft must be positive
Sqft cannot exceed Lotsize
Lotsize cannot exceed 100,000
Price must be greater than 10,000
The dataframe is subsetted to only retain the columns that will be used for analysis.
In summary, invalid data such as negative ages or square footages is removed. Extreme upper limits are set for lot size and price to filter outliers based on domain knowledge of reasonable housing values. This cleaning ensures only valid, non-outlier observations remain for modeling. Restricting the data to valid ranges and removing extreme values prepares a high quality dataset for analysis.
Exploratory Data Analysis
Exploratory data analysis (EDA) provides critical initial insights into the housing data prior to modeling. To understand the underlying relationships and patterns, visualizations were used. For this housing data, boxplots and scatterplot matrices visualized the distribution of each variable and the correlations between variables. The boxplots revealed information about the spread, skew, and potential outliers of the individual housing variables while Scatterplot matrices visualized pairwise correlations between the housing variables. The scatterplots revealed linear or nonlinear associations and potential indication of predictive relationships to leverage in modeling.
library(vtable)
sumtable(housingtb, summ.names = c("N", "Mean", "Std Dev" , "Min", "1st Quart",
"Median", "3rd Quart", "Max"),add.median = TRUE)| Variable | N | Mean | Std Dev | Min | 1st Quart | Median | 3rd Quart | Max |
|---|---|---|---|---|---|---|---|---|
| Price | 911 | 376160 | 313509 | 10000 | 194950 | 286000 | 452750 | 3025000 |
| Numbed | 911 | 3.4 | 0.9 | 1 | 3 | 3 | 4 | 7 |
| Numbath | 911 | 2.6 | 1.1 | 0 | 2 | 2 | 3 | 8 |
| Age | 911 | 69 | 36 | 1 | 37 | 68 | 96 | 180 |
| Sqft | 911 | 2194 | 1264 | 672 | 1424 | 1844 | 2501 | 12170 |
| Lotsize | 911 | 14170 | 15178 | 1215 | 6141 | 8712 | 15246 | 98010 |
| Numparking | 911 | 1.7 | 0.97 | 0 | 1 | 2 | 2 | 8 |
housingtb %>%
boxplot()
library(psych)
pairs.panels(housingtb)
- Spatial variables like square footage and lot size exhibited positive skew with some high values.
- Temporal features like age were more symmetrically distributed.
- Although the distribution of Price was highly skewed, the individual values were within the reasonable range considering the consistently increasing house prices.
- Comparing boxplots side-by-side highlighted similarities and differences in the data ranges and distributions.
- Stronger positive correlations were apparent between several attributes like square footage and number of bedrooms.
- Weaker relationships were found between other pairs like age and lot size.
- There was a colinearity between Numbed and Numbath which may need an attention in the regression analysis.
Multiple Linear Regression
A multiple linear regression is conducted with Price as the dependent variable and Numbed, Numbath, Age, Sqft, Lotsize, and Numparking as the predictor variables. The goal is to model the linear relationship between these 6 independent variables characterizing properties and the eventual sales Price of the homes. The regression will estimate the coefficient weights connecting each predictor to Price, quantifying their relative contributions. The R-squared of the model will determine how much of the variation in Price can be accounted for by the home attributes. The regression provides a mechanism to explain Price using the underlying housing features and assess the predictive capacity of the full model. It aims to disentangle the key drivers of home values based on inherent property characteristics.
# Fitted an initial linear regression with all variables
model <- lm(Price ~ Numbed+Numbath+Age+Sqft+Lotsize+Numparking, data=housingtb)
summary(model)
Call:
lm(formula = Price ~ Numbed + Numbath + Age + Sqft + Lotsize +
Numparking, data = housingtb)
Residuals:
Min 1Q Median 3Q Max
-1084792 -97819 -18199 67964 2062379
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.173e+05 3.331e+04 -3.520 0.000453 ***
Numbed -7.271e+03 1.070e+04 -0.680 0.496836
Numbath 1.099e+05 1.020e+04 10.767 < 2e-16 ***
Age 9.556e+01 2.094e+02 0.456 0.648261
Sqft 9.936e+01 8.569e+00 11.595 < 2e-16 ***
Lotsize 1.785e+00 5.118e-01 3.488 0.000510 ***
Numparking -7.862e+03 8.660e+03 -0.908 0.364175
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 209600 on 904 degrees of freedom
Multiple R-squared: 0.5562, Adjusted R-squared: 0.5532
F-statistic: 188.8 on 6 and 904 DF, p-value: < 2.2e-16Based on the initial fitting, the Sqft variable has the largest estimated coefficient. In addition, Numbath, Sqft and Lotsize are statistically significant predictors of the Price. Although Numbed has the second largest magnitude of the coefficient value, it did not result in as a statistically significant predictor. With a suspicion that it could be due to the colinearity, a simple linear regression analysis was done to confirm the impact of Numbed variable.
model1 <- lm(Price ~ Numbed, data=housingtb)
summary(model1)
Call:
lm(formula = Price ~ Numbed, data = housingtb)
Residuals:
Min 1Q Median 3Q Max
-660850 -136541 -42064 76653 2539723
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -209869 35135 -5.973 3.34e-09 ***
Numbed 173787 10070 17.258 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 272200 on 909 degrees of freedom
Multiple R-squared: 0.2468, Adjusted R-squared: 0.246
F-statistic: 297.8 on 1 and 909 DF, p-value: < 2.2e-16The results of the simple linear regression with a setup of the dependent variable, Price, and the predictor, Numbed, show that Numbed is a statistically significant predictor of the Price. Given this information, a multiple regression analysis without Numbath variable was conducted.
model2 <- lm(Price ~ Numbed+Age+Sqft+Lotsize+Numparking, data=housingtb)
summary(model2)
Call:
lm(formula = Price ~ Numbed + Age + Sqft + Lotsize + Numparking,
data = housingtb)
Residuals:
Min 1Q Median 3Q Max
-1686702 -103932 -30238 69810 1937507
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -5.349e+04 3.480e+04 -1.537 0.124637
Numbed 3.348e+04 1.062e+04 3.152 0.001672 **
Age -5.080e+02 2.142e+02 -2.372 0.017924 *
Sqft 1.447e+02 7.924e+00 18.259 < 2e-16 ***
Lotsize 2.104e+00 5.424e-01 3.879 0.000112 ***
Numparking 2.545e+03 9.136e+03 0.279 0.780654
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 222500 on 905 degrees of freedom
Multiple R-squared: 0.4992, Adjusted R-squared: 0.4965
F-statistic: 180.4 on 5 and 905 DF, p-value: < 2.2e-16When a multiple regression is run after removing Numbath as a predictor, Numbed becomes a statistically significant predictor (p<0.01). In the multiple regression, a predictor’s effect is suppressed by other predictors in the model as the predictor shares variance with other predictors, so its unique predictive power decreases. As Numbed is highly correlated with Numbath in the multiple regression, this can make the coefficients unstable and difficult to interpret.
In general, standardization puts all predictors on an equal footing and can lead to a more stable, interpretable, and optimized regression model. To make coefficients comparable and to mitigate multicollinearity, a multiple regression analysis was conducted in standardized units.
# Standardized Multiple Regression
housingtb_unit_normal <- as.data.frame(apply(housingtb,2,function(x){(x-mean(x))/sd(x)}))
model_unit_normal <- lm(Price ~ Numbed+Numbath+Age+Sqft+Lotsize+Numparking, data=housingtb_unit_normal)
summary(model_unit_normal)
Call:
lm(formula = Price ~ Numbed + Numbath + Age + Sqft + Lotsize +
Numparking, data = housingtb_unit_normal)
Residuals:
Min 1Q Median 3Q Max
-3.4602 -0.3120 -0.0580 0.2168 6.5784
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.438e-15 2.215e-02 0.000 1.00000
Numbed -2.079e-02 3.058e-02 -0.680 0.49684
Numbath 3.941e-01 3.660e-02 10.767 < 2e-16 ***
Age 1.103e-02 2.416e-02 0.456 0.64826
Sqft 4.007e-01 3.456e-02 11.595 < 2e-16 ***
Lotsize 8.643e-02 2.478e-02 3.488 0.00051 ***
Numparking -2.428e-02 2.674e-02 -0.908 0.36418
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.6684 on 904 degrees of freedom
Multiple R-squared: 0.5562, Adjusted R-squared: 0.5532
F-statistic: 188.8 on 6 and 904 DF, p-value: < 2.2e-16When the standardized regression is run, the model shows that Numbed, Age, and Numparking are not statistically significant predictors of the Price. Among all the predictors, Lotsize shows the largest regression coefficient. The standardized regression analysis confirms that colinearity may be an issue and suggests we should make a decision to adjust the combination of the predictor variables.
Model adequacy checking ensures the assumptions of the linear regression model are reasonably satisfied so subsequent analysis is based on a correctly specified model. More critically, it evaluates how well the model actually fits the observed data. The LINE assumptions - linearity, independence, normality, and equal variance - represent ideal conditions for drawing valid inferences from the model. Residual analysis examines the residuals, which are the differences between the response values predicted by the model and the actual observed responses. Patterns or anomalies in the residuals would indicate violations of the LINE assumptions which requires a model refinement.
# Residual plots for models including Numbath and excluding Numbath
library(patchwork)
p1 <- ggplot(model, aes(x = .fitted, y = .resid)) +
geom_point() +
geom_hline(yintercept = 0) +
labs(title = "Residuals vs. Fitted Plot (model)", x = "Fitted Values", y = "Residuals")
p2 <- ggplot(model2, aes(x = .fitted, y = .resid)) +
geom_point() +
geom_hline(yintercept = 0) +
labs(title = "Residuals vs. Fitted Plot (model2)", x = "Fitted Values", y = "Residuals")
p1+p2
The residual plots show funnel shape that would signify unequal error variance.
# QQPlots for models including Numbath and excluding Numbath
par(mfrow=c(1,2))
qqnorm(model$residuals,main="model")
qqline(model$residuals)
qqnorm(model2$residuals,main="model2")
qqline(model2$residuals)
The QQ plots show that both models have heavy-tailed distribution.
To address the issues of violations of equal variance (homoscedasticity) and normality assumptions, the significantly skewed variable (Price) was transformed using log. The new models are then fitted for cross validation and performance comparison.
data_frame <- housingtb %>% as.data.frame()
model3 <- lm(log(Price) ~ Numbed+Numbath+Age+Sqft+Lotsize+Numparking, data=data_frame)
summary(model3)
Call:
lm(formula = log(Price) ~ Numbed + Numbath + Age + Sqft + Lotsize +
Numparking, data = data_frame)
Residuals:
Min 1Q Median 3Q Max
-3.04343 -0.22637 0.00955 0.26783 1.30992
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.152e+01 7.511e-02 153.419 < 2e-16 ***
Numbed 2.702e-02 2.412e-02 1.120 0.2629
Numbath 3.056e-01 2.301e-02 13.282 < 2e-16 ***
Age -1.187e-03 4.722e-04 -2.515 0.0121 *
Sqft 1.048e-04 1.932e-05 5.423 7.51e-08 ***
Lotsize 2.774e-06 1.154e-06 2.403 0.0164 *
Numparking 9.142e-03 1.953e-02 0.468 0.6398
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.4725 on 904 degrees of freedom
Multiple R-squared: 0.5316, Adjusted R-squared: 0.5285
F-statistic: 171 on 6 and 904 DF, p-value: < 2.2e-16model4 <- lm(log(Price) ~ Numbed+Age+Sqft+Lotsize+Numparking, data=data_frame)
summary(model4)
Call:
lm(formula = log(Price) ~ Numbed + Age + Sqft + Lotsize + Numparking,
data = data_frame)
Residuals:
Min 1Q Median 3Q Max
-3.2037 -0.2331 -0.0037 0.3086 1.3776
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.170e+01 8.076e-02 144.883 < 2e-16 ***
Numbed 1.404e-01 2.465e-02 5.695 1.67e-08 ***
Age -2.866e-03 4.971e-04 -5.766 1.11e-08 ***
Sqft 2.309e-04 1.839e-05 12.554 < 2e-16 ***
Lotsize 3.662e-06 1.259e-06 2.909 0.00372 **
Numparking 3.809e-02 2.120e-02 1.796 0.07275 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.5163 on 905 degrees of freedom
Multiple R-squared: 0.4402, Adjusted R-squared: 0.4371
F-statistic: 142.3 on 5 and 905 DF, p-value: < 2.2e-16Model Validation
Cross validation provides insights into how the fitted model may perform when making predictions on new data. It minimizes biases like overfitting that can occur when evaluating fit on the training data alone. For multiple regression, it is a simple and effective technique for validating model quality. The data is split into k equal groups or “folds”. k-1 folds are used to train the model, and the left-out fold serves as the validation set. This is repeated k times, using each fold for validation once. The average validation error over the k folds provides an estimate of the model’s generalization error. Low error indicates the predictors accurately explain the response. High error signals issues with overfitting or poor predictor choices.
In this section, the 2 models (1 with Numbath and 1 without Numbath) are cross-validated and their performances are compared.
library(DAAG)
KCV = cv.lm(data=data_frame, model3, m=5, seed=123)
fold 1
Observations in test set: 182
1 5 13 21 22 29
Predicted 12.5451746 12.2105503 11.8396834 11.96069733 11.9000098 12.0381845
cvpred 12.5466483 12.2163359 11.8635088 11.97666157 11.9167761 12.0500248
log(Price) 12.3458346 12.0810762 11.3850921 12.01370075 11.4616322 12.1547794
CV residual -0.2008137 -0.1352598 -0.4784167 0.03703918 -0.4551439 0.1047545
31 37 39 43 48 52
Predicted 11.8941477 12.0856618 11.9375892 11.9270371 11.8754052 11.9779298
cvpred 11.9089330 12.0908924 11.9476922 11.9393410 11.8944370 11.9928986
log(Price) 12.5317728 11.3265959 11.0020998 12.0494188 12.6915805 11.6952470
CV residual 0.6228397 -0.7642965 -0.9455923 0.1100778 0.7971435 -0.2976516
58 61 75 81 92 97
Predicted 11.9479567 12.2902047 11.555488 12.282161 12.2140369 12.070959
cvpred 11.9651094 12.3064934 11.583838 12.286975 12.2191589 12.098366
log(Price) 12.4684369 12.0435537 9.210340 11.302204 12.1007121 10.596635
CV residual 0.5033275 -0.2629397 -2.373497 -0.984771 -0.1184467 -1.501731
101 102 109 110 115 116
Predicted 11.9885238 11.992775 12.7414993 12.4250918 12.301116642 12.403418
cvpred 12.0019925 12.016270 12.7501838 12.4241535 12.304124367 12.408002
log(Price) 11.3445068 12.173033 13.1519222 11.7117763 12.301382825 13.161584
CV residual -0.6574857 0.156763 0.4017384 -0.7123772 -0.002741541 0.753582
127 129 131 133 140 142
Predicted 12.2429748 12.0072947 12.2332459 12.4974900 12.310565 11.9377397
cvpred 12.2454732 12.0154545 12.2457726 12.5104782 12.325873 11.9457466
log(Price) 11.2897819 11.5607628 12.0725413 12.6776376 12.072541 12.4411448
CV residual -0.9556913 -0.4546918 -0.1732313 0.1671593 -0.253332 0.4953981
146 148 151 155 171 172
Predicted 11.9510550 12.24849453 11.9600810 12.70261408 12.01643 11.9955875
cvpred 11.9693178 12.25129463 11.9682374 12.73716320 12.03809 12.0083653
log(Price) 12.1007121 12.18024189 12.5947306 12.72188581 12.24529 12.3566455
CV residual 0.1313943 -0.07105274 0.6264932 -0.01527739 0.20720 0.3482802
176 181 182 185 186 187
Predicted 12.63012788 12.38895114 11.930675 12.4022755 12.32945817 12.365628
cvpred 12.64814226 12.41667868 11.941316 12.4032838 12.32865649 12.401518
log(Price) 12.67607627 12.44901882 10.915088 12.5706810 12.30138283 12.676076
CV residual 0.02793401 0.03234014 -1.026227 0.1673973 -0.02727367 0.274558
195 197 201 203 207
Predicted 12.0465785 12.35038433 11.9887694 12.3800048 12.1632875
cvpred 12.0567131 12.34811045 12.0017484 12.3850594 12.1694605
log(Price) 12.1750978 12.37792290 12.1281111 12.0698405 12.5845091
CV residual 0.1183848 0.02981245 0.1263627 -0.3152189 0.4150486
217 229 235 236 243 248
Predicted 12.331961056 12.3423322 12.3569361 12.0447694 12.1465032 12.263568
cvpred 12.333564787 12.3400929 12.3710469 12.0573399 12.1563188 12.285697
log(Price) 12.323855681 12.6115378 12.2060726 12.4946293 12.8479265 11.482466
CV residual -0.009709106 0.2714449 -0.1649742 0.4372894 0.6916078 -0.803231
249 250 258 267 268 271
Predicted 12.2976820 12.2624872 12.18188169 12.3216109 11.9530181 12.3491044
cvpred 12.3106248 12.2598317 12.18592788 12.3422756 11.9620356 12.3478541
log(Price) 11.8844890 11.9511804 12.12757042 12.4529327 12.6835483 12.4684369
CV residual -0.4261358 -0.3086513 -0.05835746 0.1106571 0.7215127 0.1205828
272 277 280 281 285 286
Predicted 12.38036674 12.34289423 12.35331664 12.4474535 12.2966119 12.318896
cvpred 12.38195997 12.33915509 12.36180470 12.4590124 12.2996159 12.321021
log(Price) 12.39255221 12.31492705 12.32385568 12.6443276 12.7337554 11.289782
CV residual 0.01059224 -0.02422804 -0.03794902 0.1853151 0.4341395 -1.031239
291 295 296 302 306 308
Predicted 12.40813711 12.6947501 12.47511891 12.6901961 12.3134748 12.3390518
cvpred 12.41508887 12.6880114 12.46895851 12.6858298 12.3147493 12.3374899
log(Price) 12.38002595 12.4684369 12.40819683 12.5425449 11.8565152 11.7597855
CV residual -0.03506291 -0.2195745 -0.06076168 -0.1432849 -0.4582342 -0.5777044
311 313 336 341 353 359
Predicted 11.9884842 12.2952939 12.39920816 12.4666284 12.652992 12.2848662
cvpred 12.0017152 12.3005038 12.40727897 12.4651284 12.642168 12.2873959
log(Price) 11.8130301 13.1441249 12.49874226 12.1547794 12.468437 12.8266491
CV residual -0.1886851 0.8436211 0.09146329 -0.3103491 -0.173731 0.5392532
362 368 370 375 387
Predicted 12.25027232 12.49903019 12.37232787 12.35104100 12.814475
cvpred 12.24798420 12.49803582 12.36782487 12.35986327 12.828558
log(Price) 12.27373129 12.52815614 12.34147728 12.31940133 13.017003
CV residual 0.02574709 0.03012033 -0.02634758 -0.04046194 0.188445
388 390 392 395 397 406
Predicted 11.9562172 12.370993 12.4020967 12.3625259 12.6242437 12.3073433
cvpred 11.9625050 12.399697 12.4168866 12.3582192 12.6284538 12.3077331
log(Price) 12.6603279 12.240474 12.1415341 12.0719697 13.4444469 12.8346813
CV residual 0.6978229 -0.159223 -0.2753525 -0.2862495 0.8159931 0.5269482
409 412 434 438 440 441
Predicted 12.3515634 12.5633045 12.723417 12.6985588 12.28167114 12.3206560
cvpred 12.3594728 12.5593943 12.713070 12.6930011 12.27892348 12.3224278
log(Price) 12.7685415 12.0051797 13.142166 12.4684369 12.34539971 12.6603279
CV residual 0.4090687 -0.5542146 0.429096 -0.2245642 0.06647623 0.3379001
465 468 471 479 480 484
Predicted 12.7090963 12.6791710 12.72814685 12.3583714 12.76987230 12.3610934
cvpred 12.7043840 12.6737151 12.73100983 12.3828014 12.76456802 12.3770331
log(Price) 12.5421877 12.3764903 12.67607627 11.9183906 12.69158046 12.1807548
CV residual -0.1621963 -0.2972248 -0.05493356 -0.4644108 -0.07298756 -0.1962782
485 486 487 497 499 510
Predicted 12.36785 12.6290764 12.3562158 12.7260238 12.3252205 12.757294432
cvpred 12.37437 12.6199779 12.3648996 12.7259403 12.3481787 12.771223856
log(Price) 12.50618 12.4780064 12.7068479 13.0058296 12.1652507 12.765402678
CV residual 0.13181 -0.1419715 0.3419483 0.2798892 -0.1829281 -0.005821177
516 521 533 535 543 552
Predicted 12.3917198 12.6226826 12.3566524 12.4041267 12.75365494 13.0367281
cvpred 12.3883198 12.6194357 12.3653492 12.4184126 12.73711090 13.0298988
log(Price) 12.2783933 12.7278382 12.5947306 13.0269532 12.67294638 13.4828311
CV residual -0.1099265 0.1084025 0.2293815 0.6085405 -0.06416452 0.4529323
555 562 567 570 575 577
Predicted 12.6508474 12.30768594 12.6623414 12.6338493 12.3617940 12.7093354
cvpred 12.6407587 12.29820034 12.6603753 12.6287448 12.3694440 12.7132246
log(Price) 13.2445810 12.34147728 12.8609986 12.7854911 11.7791285 13.0389818
CV residual 0.6038223 0.04327694 0.2006233 0.1567462 -0.5903155 0.3257572
579 585 589 590 594 595
Predicted 12.6928752 12.4230356 12.6930577 12.7519289 12.7156405 12.4731952
cvpred 12.6914357 12.4195520 12.7064421 12.7489064 12.7328097 12.4794740
log(Price) 13.3533164 12.5425449 11.9316358 12.5061772 12.5058068 12.8992198
CV residual 0.6618806 0.1229929 -0.7748063 -0.2427292 -0.2270029 0.4197459
605 609 610 613 623 631
Predicted 12.81050451 12.6638744 12.66604286 12.7688601 12.904709 12.7349490
cvpred 12.80450818 12.6634070 12.65984845 12.7610313 12.900771 12.7363653
log(Price) 12.70684793 12.4529327 12.75708006 12.3458346 13.018113 12.8557903
CV residual -0.09766025 -0.2104743 0.09723161 -0.4151967 0.117342 0.1194249
633 638 658 661 666 667
Predicted 13.0797658 12.7041426 12.5785192 12.7089737 12.9121552 12.9121552
cvpred 13.0526110 12.6982952 12.5852863 12.7048415 12.9084718 12.9084718
log(Price) 13.2878778 13.4588356 12.3238557 13.2655975 12.8346813 12.8346813
CV residual 0.2352668 0.7605404 -0.2614307 0.5607561 -0.0737905 -0.0737905
671 672 675 676 684 690
Predicted 12.7200033 12.7342707 12.8296084 12.7755060 12.8707008 13.1720944
cvpred 12.7241900 12.7129470 12.8182488 12.7631652 12.8840973 13.1614456
log(Price) 13.0147782 12.3544927 12.9945300 12.4450895 12.5245264 13.0389818
CV residual 0.2905882 -0.3584543 0.1762812 -0.3180757 -0.3595709 -0.1224639
691 693 694 695 704 722
Predicted 13.33762094 13.1571681 13.1571703 13.0576206 12.9896374 12.5640101
cvpred 13.33817561 13.1491186 13.1491209 13.0505813 12.9786277 12.5666654
log(Price) 13.25339164 13.4758332 13.4758332 13.3179302 13.1470560 13.1711535
CV residual -0.08478397 0.3267146 0.3267122 0.2673488 0.1684283 0.6044881
737 747 760 771 772 778
Predicted 12.94920865 13.1545083 12.72533357 13.531133 12.8821030 12.9236608
cvpred 12.95398809 13.1319871 12.71118962 13.495609 12.8699860 12.9118693
log(Price) 12.89420728 14.0662693 12.79385931 14.030622 12.7654027 13.7991271
CV residual -0.05978081 0.9342822 0.08266969 0.535013 -0.1045833 0.8872578
781 783 790 793 794 795
Predicted 12.9449839 12.8524700 13.0867720 13.1866298 12.9218984 13.55293709
cvpred 12.9417565 12.8273127 13.0690104 13.1621879 12.9022331 13.51741580
log(Price) 12.9189612 13.4730202 12.9480100 12.7656884 13.1709630 13.49805633
CV residual -0.0227953 0.6457075 -0.1210004 -0.3964995 0.2687299 -0.01935947
798 799 805 809 816 819
Predicted 12.825604 12.8940670 13.245574 13.1820753 13.193067 13.5053093
cvpred 12.848627 12.8749295 13.214476 13.1590834 13.178357 13.4799785
log(Price) 10.558414 13.0960194 13.120361 13.0170029 14.221042 13.9332936
CV residual -2.290213 0.2210899 -0.094115 -0.1420805 1.042685 0.4533151
833 837 842 844 855 859
Predicted 13.2260717 13.1977560 13.0408883 13.184633898 13.3616996 13.165314
cvpred 13.1947008 13.1865462 13.0195806 13.165534083 13.3265734 13.139690
log(Price) 13.0562236 13.8145101 12.6729464 13.171153542 13.1806323 14.457364
CV residual -0.1384773 0.6279639 -0.3466342 0.005619458 -0.1459412 1.317674
863 865 866 869 873 889
Predicted 13.4457597 13.2421541 13.2421541 13.5784979 13.8926565 13.8640518
cvpred 13.4155084 13.2118424 13.2118424 13.5434486 13.8629981 13.8256336
log(Price) 13.0604880 13.5276951 13.5276951 13.7642173 13.3692235 14.4032972
CV residual -0.3550204 0.3158528 0.3158528 0.2207687 -0.4937747 0.5776636
893 894 903 904
Predicted 13.612501 14.0034263 14.1551269 14.555789
cvpred 13.544773 13.9394447 14.0877912 14.476151
log(Price) 14.922422 13.8254609 14.8451300 13.319574
CV residual 1.377648 -0.1139839 0.7573388 -1.156578
Sum of squares = 47.63 Mean square = 0.26 n = 182
fold 2
Observations in test set: 183
4 18 23 25 27 28
Predicted 12.2152987 11.9202146 12.2378360 11.9888907 12.000878 11.8955277
cvpred 12.1947523 11.8928110 12.2184911 11.9612687 11.999254 11.8637404
log(Price) 12.0810762 12.1007121 11.4131051 12.5776362 10.373491 11.9703503
CV residual -0.1136762 0.2079011 -0.8053859 0.6163675 -1.625763 0.1066099
32 38 44 46 49 53
Predicted 11.9477034 12.2464622 11.9732563 12.2792100 11.9457733 11.9865175
cvpred 11.9215463 12.2269921 11.9486142 12.2793613 11.9192415 11.9789981
log(Price) 12.0610469 11.6656466 12.0662357 12.0725413 11.6868788 11.6868788
CV residual 0.1395005 -0.5613455 0.1176215 -0.2068201 -0.2323627 -0.2921193
59 60 62 65 66 69
Predicted 11.854530 12.27674521 12.2306823 11.99897422 12.1917044 12.5882217
cvpred 11.815526 12.26697821 12.2156301 11.98570521 12.1552627 12.5866457
log(Price) 10.235880 12.20106010 12.1145055 11.91772368 12.7585199 11.9009053
CV residual -1.579646 -0.06591811 -0.1011247 -0.06798152 0.6032573 -0.6857404
76 78 87 89 90 91
Predicted 12.1826462 12.2851817 11.8534308 12.2839007 12.055120100 12.2166215
cvpred 12.1534236 12.2757336 11.8044099 12.2739313 12.063170540 12.1910595
log(Price) 12.0137008 11.8130301 12.4292162 12.4968748 12.072541253 12.0725413
CV residual -0.1397228 -0.4627036 0.6248063 0.2229435 0.009370713 -0.1185182
98 104 108 111 114 122
Predicted 11.9160114 12.3583152 12.3365070 12.2954120 12.6489154 12.0861295
cvpred 11.8840196 12.3540746 12.3280767 12.2818082 12.6623053 12.0593392
log(Price) 12.1542529 12.5425449 12.2160230 11.7117763 12.5245264 12.3673408
CV residual 0.2702333 0.1884703 -0.1120538 -0.5700319 -0.1377789 0.3080016
123 124 128 132 138 145
Predicted 12.30455859 11.9745047 12.33627832 12.2514168 12.0060795 12.2891197
cvpred 12.29625273 11.9558253 12.33808850 12.2364524 11.9894828 12.2781623
log(Price) 12.20557252 11.5617156 12.25486281 12.6915805 12.1007121 12.7938593
CV residual -0.09068021 -0.3941097 -0.08322569 0.4551281 0.1112293 0.5156971
147 150 153 168 169 180
Predicted 12.2419313 12.3429878 11.9910787 12.2425664 12.527298 12.3475660
cvpred 12.2242784 12.3294030 11.9732554 12.2329869 12.523751 12.3484310
log(Price) 12.7158978 11.8130301 12.2548628 11.6952470 12.136187 12.7742233
CV residual 0.4916194 -0.5163729 0.2816075 -0.5377399 -0.387564 0.4257924
188 204 208 218 234 253
Predicted 12.0166420 12.2152400 12.2571300 12.30712749 12.43030809 12.3101218
cvpred 11.9997270 12.1949221 12.2315164 12.29792691 12.41702195 12.2990982
log(Price) 12.1007121 12.0045683 12.5567295 12.32385568 12.48748510 12.7798731
CV residual 0.1009852 -0.1903538 0.3252131 0.02592877 0.07046316 0.4807749
260 263 266 269 276 287
Predicted 12.2728674 12.3075579 12.6545757 12.0364869 12.34526914 12.35795203
cvpred 12.2571143 12.2955275 12.6617614 12.0213695 12.34256288 12.35870708
log(Price) 12.9831013 12.8531759 11.8130301 11.7440372 12.38971000 12.30138283
CV residual 0.7259871 0.5576484 -0.8487313 -0.2773323 0.04714713 -0.05732426
289 293 300 301 304 316
Predicted 12.3834650 12.1340916 12.2986169 12.2680039 12.35906326 12.2609047
cvpred 12.3797466 12.1147028 12.2849325 12.2500137 12.36807009 12.2401274
log(Price) 12.5245264 12.3327053 12.9360338 13.1123130 12.31492705 12.0317193
CV residual 0.1447797 0.2180025 0.6511013 0.8622993 -0.05314304 -0.2084081
325 326 328 330 332 333
Predicted 12.3322126 12.2751116 12.24500847 12.6048355 12.6651903 12.585928
cvpred 12.3213715 12.2651338 12.26389117 12.6066028 12.6532925 12.585243
log(Price) 12.8615180 11.6526874 12.20106010 12.1579323 12.3194013 12.948010
CV residual 0.5401464 -0.6124464 -0.06283107 -0.4486705 -0.3338912 0.362767
335 337 356 358 361 363
Predicted 12.7391252 11.9868092 12.7093376 12.1972116 12.2948404 12.24972590
cvpred 12.7602988 11.9631664 12.7246608 12.1841498 12.2783508 12.21981063
log(Price) 12.6443276 11.7360690 12.5245264 12.3013828 13.1470560 12.27373129
CV residual -0.1159712 -0.2270974 -0.2001344 0.1172331 0.8687052 0.05392067
373 374 385 398 403 417
Predicted 12.6752556 12.7211982 12.300316 12.7242452 12.5900065 12.6244715
cvpred 12.6832044 12.7267194 12.297773 12.7521313 12.5788464 12.6263788
log(Price) 13.0919042 12.4874851 11.983554 12.8674711 12.3673408 12.8992198
CV residual 0.4086997 -0.2392343 -0.314219 0.1153398 -0.2115056 0.2728411
419 424 427 428 429 439
Predicted 12.7421714 11.986860 12.06895240 12.06895240 12.181222 12.7540202
cvpred 12.7665465 11.961696 12.05076729 12.05076729 12.174034 12.7940107
log(Price) 12.5061772 12.821258 12.11724143 12.11724143 11.112448 12.6915805
CV residual -0.2603692 0.859562 0.06647414 0.06647414 -1.061586 -0.1024302
442 443 444 445 452 454
Predicted 12.3206583 12.3313253 12.0380515 12.3636861 12.7528115 12.3295860
cvpred 12.3053808 12.3224753 12.0272527 12.3537916 12.7776618 12.3228398
log(Price) 12.5947306 11.8844890 12.6443276 11.6952470 12.5425449 12.4780064
CV residual 0.2893498 -0.4379863 0.6170749 -0.6585445 -0.2351169 0.1551665
456 457 460 473 481 482
Predicted 12.4186835 12.3558138 12.517414 12.9816293 12.355663 12.31975644
cvpred 12.4247700 12.3609809 12.533751 12.9904711 12.358656 12.30189942
log(Price) 12.7454857 12.8609986 10.820038 13.5278285 13.399995 12.20607265
CV residual 0.3207157 0.5000177 -1.713713 0.5373574 1.041339 -0.09582677
483 493 495 500 504 506
Predicted 12.6431349 12.5539430 12.38440148 12.3316596 11.9981846 12.8644075
cvpred 12.6512421 12.5596777 12.37036330 12.3220323 11.9644411 12.8811911
log(Price) 13.0170029 12.9945300 12.46843691 11.6082356 12.4292162 12.5686303
CV residual 0.3657607 0.4348523 0.09807361 -0.7137967 0.4647751 -0.3125608
513 515 518 519 526 528
Predicted 12.3476753 12.6686961 12.9871135 12.6332621 12.6722772 12.36719721
cvpred 12.3593256 12.6639338 12.9864067 12.6311907 12.6747351 12.35347040
log(Price) 13.2861815 12.9715405 12.1947589 13.3845738 13.2267234 12.29225034
CV residual 0.9268559 0.3076066 -0.7916478 0.7533831 0.5519883 -0.06122005
529 530 532 538 547 550
Predicted 12.2922167 12.6909805 12.76308017 12.6879427 12.7492516 12.8727717
cvpred 12.2610885 12.6974018 12.78545514 12.6799558 12.7682107 12.8898589
log(Price) 12.4292162 12.4912516 12.70987365 12.5591913 12.6280671 12.7882883
CV residual 0.1681277 -0.2061502 -0.07558149 -0.1207646 -0.1401437 -0.1015706
556 561 565 572 581 588
Predicted 12.3916621 12.9533468 12.387204 12.3605386 12.8039345 12.40655744
cvpred 12.4040846 12.9952761 12.375949 12.3551764 12.8247951 12.40267263
log(Price) 12.1388639 12.5425449 12.882582 12.8103886 12.6915805 12.43718437
CV residual -0.2652208 -0.4527312 0.506633 0.4552122 -0.1332147 0.03451174
599 604 608 611 612 616
Predicted 12.7183737 13.04004817 12.7464935 12.6192166 12.6739752 12.6228388
cvpred 12.7298630 13.05739431 12.7555727 12.6354126 12.6694738 12.6266123
log(Price) 13.2339048 12.96336765 12.2642142 12.9116423 12.5281561 12.7656884
CV residual 0.5040418 -0.09402666 -0.4913585 0.2762297 -0.1413177 0.1390761
626 628 635 640 641 646
Predicted 12.713928 12.7224292 12.7547166 12.8807663 12.7710090 12.85513488
cvpred 12.723576 12.7258795 12.7740759 12.8875844 12.7852556 12.89238167
log(Price) 13.253392 12.1547794 13.0497927 12.7868906 12.3059180 12.92391244
CV residual 0.529816 -0.5711002 0.2757168 -0.1006938 -0.4793376 0.03153076
652 653 662 663 665 669
Predicted 12.7578049 12.6047666 13.1474295 12.762748 12.5194998 12.7200033
cvpred 12.7500604 12.6165280 13.1795540 12.785401 12.5108142 12.7290826
log(Price) 12.0435537 13.4588356 12.9116423 11.736069 13.0389818 13.0147782
CV residual -0.7065067 0.8423077 -0.2679116 -1.049332 0.5281676 0.2856955
679 682 696 700 711 715
Predicted 13.1100320 12.7263809 13.3410860 12.8421664 12.3901464 12.8290747
cvpred 13.1389156 12.7507411 13.4187058 12.8653737 12.3868004 12.8476291
log(Price) 12.6587394 13.0167806 12.9831013 13.1221634 11.6952470 12.6115378
CV residual -0.4801763 0.2660395 -0.4356045 0.2567897 -0.6915534 -0.2360913
717 723 726 727 733 736
Predicted 12.8448919 13.04409228 12.7327134 12.831706 13.1011774 12.94920643
cvpred 12.8653049 13.06948182 12.7250761 12.841845 13.1118145 12.96612095
log(Price) 13.0919042 13.15192218 12.9945300 13.322852 13.2360491 12.89420728
CV residual 0.2265992 0.08244036 0.2694539 0.481007 0.1242346 -0.07191367
741 753 756 757 762 764
Predicted 12.61554002 12.8178237 12.7835637 13.37146736 13.2925937 13.2010038
cvpred 12.62364798 12.8294201 12.8275611 13.40328071 13.3239073 13.2249386
log(Price) 12.70654486 13.3645249 13.0280527 13.30468493 13.1768516 12.9360338
CV residual 0.08289688 0.5351048 0.2004916 -0.09859578 -0.1470557 -0.2889048
775 777 787 788 789
Predicted 12.87403489 12.89107668 13.1601712 12.6334821 13.2179847
cvpred 12.89048215 12.91447373 13.1795814 12.6393923 13.2586598
log(Price) 12.93603380 12.97386337 12.6931177 12.8739020 12.8891695
CV residual 0.04555165 0.05938964 -0.4864637 0.2345097 -0.3694903
797 803 807 811 813 829
Predicted 13.12357191 13.1808044 12.747320 13.27086215 13.23844894 13.5377377
cvpred 13.13021565 13.2075256 12.728754 13.31049998 13.26492034 13.5643116
log(Price) 13.21767356 13.9978321 13.864301 13.27936713 13.28787782 13.8726052
CV residual 0.08745791 0.7903065 1.135546 -0.03113286 0.02295747 0.3082936
830 835 839 841 843
Predicted 13.6275047 13.27895517 13.65615314 12.5235127 12.9942057
cvpred 13.6748542 13.30826487 13.71536968 12.5061764 13.0165225
log(Price) 13.3374748 13.23569206 13.66317490 12.6115378 13.1223634
CV residual -0.3373795 -0.07257281 -0.05219479 0.1053613 0.1058409
847 849 860 879 886 890
Predicted 13.42593065 13.5557242 13.2660236 13.5630240 14.5889338 14.2266576
cvpred 13.46845327 13.5805800 13.3149056 13.6220252 14.6717972 14.2917283
log(Price) 13.38133729 14.0824796 13.1711535 13.5144055 14.0778748 13.8145101
CV residual -0.08711598 0.5018996 -0.1437521 -0.1076198 -0.5939224 -0.4772183
896 900 905 906 908
Predicted 13.9330854 13.8657018 12.9814355 14.707590 14.77965
cvpred 13.9934177 13.9310770 12.9653664 14.773206 14.88379
log(Price) 13.1587628 13.7953079 12.2783933 14.222281 13.45540
CV residual -0.8346549 -0.1357692 -0.6869731 -0.550925 -1.42839
Sum of squares = 41.98 Mean square = 0.23 n = 183
fold 3
Observations in test set: 182
14 26 40 47 50 54
Predicted 11.8396844 12.2471076 12.22378004 11.8733000 12.2786292 11.9397276
cvpred 11.8369298 12.2542095 12.22230398 11.8675250 12.2876439 11.9421839
log(Price) 11.3850921 12.6765449 12.27839331 12.2307653 11.7675677 12.5245264
CV residual -0.4518377 0.4223354 0.05608933 0.3632403 -0.5200762 0.5823424
57 68 73 86 96 99
Predicted 11.947565 11.9790110 11.904527 12.0057594 12.288435 12.36175889
cvpred 11.953206 11.9918867 11.905517 12.0197260 12.297145 12.37756346
log(Price) 11.127263 11.8705999 10.596635 11.9183906 11.884489 12.41268023
CV residual -0.825943 -0.1212868 -1.308882 -0.1013354 -0.412656 0.03511677
107 112 113 119 126 130
Predicted 12.4976409 12.2954120 12.36626 12.29570 12.2998180 12.141106
cvpred 12.4878358 12.3007691 12.37391 12.30095 12.3055521 12.151237
log(Price) 12.7656884 11.7117763 12.42922 11.86710 12.1547794 10.915088
CV residual 0.2778526 -0.5889928 0.05531 -0.43385 -0.1507727 -1.236149
134 139 156 158 160 165
Predicted 11.8239882 12.601677 12.1867929 12.27469598 12.0241423 11.97956768
cvpred 11.8095654 12.606114 12.2012401 12.28017896 12.0431644 11.98525087
log(Price) 12.1441972 11.561716 11.8493977 12.19095901 11.9447079 12.07254125
CV residual 0.3346319 -1.044399 -0.3518424 -0.08921996 -0.0984565 0.08729038
166 167 173 175 183 190
Predicted 12.2263926 12.2587886 11.9797179 11.96129120 12.1070469 12.28660020
cvpred 12.2228983 12.2627461 11.9901749 11.96926507 12.1123299 12.29289678
log(Price) 11.3621026 12.8212583 12.2060726 11.89478071 12.3327053 12.38002595
CV residual -0.8607957 0.5585122 0.2158977 -0.07448436 0.2203754 0.08712917
192 199 209 212 213 214
Predicted 12.2804089 12.17168973 11.9830505 12.6651168 12.2842999 11.9631260
cvpred 12.2857268 12.18329342 11.9923241 12.6746843 12.2886938 11.9703767
log(Price) 12.7038130 12.21602298 11.8493977 12.9384405 12.7038130 12.1001564
CV residual 0.4180863 0.03272956 -0.1429264 0.2637562 0.4151192 0.1297798
215 219 223 231 232 233
Predicted 12.2326566 12.2863547 12.1660984 12.2218130 12.3892243 12.36222302
cvpred 12.2328021 12.2917349 12.1765919 12.2464748 12.4044301 12.37271394
log(Price) 11.3504065 12.8479265 11.7076695 12.5776362 12.6603279 12.45097769
CV residual -0.8823956 0.5561916 -0.4689224 0.3311614 0.2558978 0.07826375
238 242 245 251 255 257
Predicted 12.38160349 12.4121944 12.1290385 12.388690 12.36879815 12.3658833
cvpred 12.39636358 12.4213004 12.1348683 12.403198 12.38490593 12.3813017
log(Price) 12.45293272 12.2548628 12.3458346 12.206073 12.32385568 12.2783933
CV residual 0.05656914 -0.1664376 0.2109663 -0.197125 -0.06105025 -0.1029084
270 274 278 288 290 292
Predicted 12.3434238 12.33933187 13.008129 12.295685 12.6710398 12.47511780
cvpred 12.3529112 12.34538380 13.013388 12.300469 12.6833245 12.49333138
log(Price) 11.8493977 12.38797745 12.409013 13.134292 12.3458346 12.40819683
CV residual -0.5035135 0.04259365 -0.604375 0.833823 -0.3374899 -0.08513455
294 297 307 309 312
Predicted 12.47967380 12.39245591 12.43240245 11.9976262 12.6254090
cvpred 12.49005506 12.40465091 12.44492179 12.0067229 12.6282092
log(Price) 12.40860524 12.49125159 12.52452638 11.8130301 12.4568314
CV residual -0.08144981 0.08660068 0.07960458 -0.1936928 -0.1713779
318 334 338 340 343 344
Predicted 12.2002032 12.1570790 12.3358669 12.6631658 12.5027261 12.37603213
cvpred 12.2123876 12.1639776 12.3439403 12.6687814 12.5176234 12.38715988
log(Price) 11.2885311 13.1421660 12.0940231 12.4799093 12.3966930 12.32829028
CV residual -0.9238565 0.9781884 -0.2499172 -0.1888721 -0.1209303 -0.05886961
350 366 371 376 377 378
Predicted 12.3551498 12.6838206 12.7339967 12.324767 12.70892678 12.6209908
cvpred 12.3640792 12.6905245 12.7443607 12.334940 12.71542238 12.6213214
log(Price) 12.4760998 12.5496623 12.6378551 12.549662 12.62970506 13.2621253
CV residual 0.1120206 -0.1408621 -0.1065057 0.214722 -0.08571733 0.6408039
379 382 384 399 400 401
Predicted 12.0556195 12.3336808 12.2402738 12.7242424 12.7207128 12.3120765
cvpred 12.0468156 12.3388080 12.2586193 12.7322865 12.7347937 12.3154014
log(Price) 12.9360338 11.7745202 12.3673408 12.8674711 12.6181823 12.1164214
CV residual 0.8892182 -0.5642878 0.1087215 0.1351846 -0.1166114 -0.1989799
404 408 411 414 416 420
Predicted 12.42805791 12.3186879 12.3974281 12.3262664 12.6752811 12.5266938
cvpred 12.42573606 12.3228491 12.4054932 12.3305765 12.6843244 12.5355447
log(Price) 12.36734079 13.1203614 12.8609986 12.5637471 12.8866410 12.3925522
CV residual -0.05839526 0.7975123 0.4555054 0.2331706 0.2023166 -0.1429924
431 432 436 447 448 450
Predicted 12.34836891 12.5488450 12.3739132 12.3878616 12.92952 12.2720232
cvpred 12.35857948 12.5575598 12.3824186 12.3975180 12.94671 12.2666634
log(Price) 12.27839331 12.2060726 12.1547794 11.8493977 12.81968 12.9598444
CV residual -0.08018617 -0.3514872 -0.2276392 -0.5481203 -0.12703 0.6931811
451 455 459 463 467 469
Predicted 12.2720257 12.34586520 12.3711803 12.39522904 13.0248552 12.6254780
cvpred 12.2666659 12.35135493 12.3792350 12.40356208 13.0294321 12.6283522
log(Price) 12.9598444 12.44901882 11.7752897 12.44901882 13.1900220 12.9831013
CV residual 0.6931786 0.09766389 -0.6039453 0.04545674 0.1605899 0.3547491
472 488 490 502 503 508
Predicted 12.40967741 12.3425724 12.3804610 12.3213945 12.7028324 12.7114793
cvpred 12.41927532 12.3465404 12.3908499 12.3279782 12.7072937 12.7184198
log(Price) 12.32385568 13.2447580 12.2060726 12.5425449 12.8739020 12.8344146
CV residual -0.09541963 0.8982176 -0.1847772 0.2145667 0.1666083 0.1159948
512 517 523 525 527 541
Predicted 12.7672056 11.983939 12.7981865 12.752205 12.4935575 12.7784650
cvpred 12.7812959 11.986454 12.8164379 12.762846 12.4987704 12.7893065
log(Price) 12.6115378 10.714418 12.6912727 13.081541 13.0167806 12.6760763
CV residual -0.1697582 -1.272036 -0.1251652 0.318695 0.5180102 -0.1132302
546 548 549 560 564 571
Predicted 12.600105 12.6382499 11.99693694 12.4965075 12.5790032 12.78263442
cvpred 12.619231 12.6354864 11.99484910 12.5147806 12.5899239 12.79723282
log(Price) 11.594505 13.2356921 11.91839057 12.7218858 12.7068479 12.84792653
CV residual -1.024725 0.6002057 -0.07645853 0.2071053 0.1169241 0.05069371
576 580 582 583 584 586
Predicted 12.3435086 12.669841 12.7331441 13.635054 12.743138 12.5903335
cvpred 12.3448007 12.673676 12.7430487 13.652402 12.754453 12.6036998
log(Price) 11.7791285 11.225243 12.4950039 13.246349 12.468437 12.4684369
CV residual -0.5656722 -1.448433 -0.2480448 -0.406053 -0.286016 -0.1352629
598 601 606 617 619 622
Predicted 12.398152 12.3623592 12.6099726 12.78848406 12.4837786 12.8010590
cvpred 12.413268 12.3696573 12.6233615 12.80312324 12.4998151 12.8143374
log(Price) 10.571317 12.0435537 12.0317193 12.84792653 12.7367009 13.2085411
CV residual -1.841951 -0.3261036 -0.5916422 0.04480329 0.2368858 0.3942037
624 632 644 648 649 650
Predicted 12.9849033 13.0797640 13.1440511 12.8049580 12.7480617 12.8888684
cvpred 12.9835638 13.0843477 13.1579654 12.8063125 12.7677690 12.9057388
log(Price) 13.0919042 13.2878778 12.7656884 12.0435537 13.1519222 13.1519222
CV residual 0.1083404 0.2035301 -0.3922769 -0.7627588 0.3841531 0.2461834
654 655 656 659 660 673
Predicted 12.63560276 12.8821481 12.8290301 12.4795140 13.16163443 12.7067183
cvpred 12.64639513 12.9087432 12.8438432 12.4867905 13.17362293 12.7060380
log(Price) 12.62806706 12.6770289 12.4490188 13.3534751 13.21767356 13.0069525
CV residual -0.01832807 -0.2317142 -0.3948244 0.8666846 0.04405063 0.3009145
685 709 712 714 716 720
Predicted 13.2280853 12.9758921 12.7191382 13.1601881 13.0488250 12.9024616
cvpred 13.2485841 12.9829884 12.7218688 13.1773900 13.0504413 12.9213120
log(Price) 12.2499938 12.6760763 12.8866410 13.3326243 13.3931536 13.6802634
CV residual -0.9985902 -0.3069121 0.1647722 0.1552343 0.3427123 0.7589514
724 731 740 743 750 751
Predicted 12.3640649 12.5552390 12.88976726 13.16579980 13.0260722 12.9413793
cvpred 12.3608816 12.5571327 12.90742787 13.17591097 13.0398717 12.9519043
log(Price) 12.1547794 11.8235596 12.96453929 13.16158409 12.8452915 13.5278285
CV residual -0.2061022 -0.7335731 0.05711142 -0.01432688 -0.1945802 0.5759242
752 755 761 763 766 768
Predicted 13.1781938 13.389308 12.8688457 13.1661043 12.8962660 12.85334821
cvpred 13.1889581 13.386381 12.8827776 13.1713294 12.9111614 12.86097250
log(Price) 13.3582257 13.710150 12.4490188 13.6452855 13.7101500 12.89921983
CV residual 0.1692676 0.323769 -0.4337588 0.4739562 0.7989886 0.03824733
769 779 784 804 815 824
Predicted 12.8357723 13.20886684 12.9002285 12.8032848 13.193067 13.53185224
cvpred 12.8389775 13.22151096 12.9124199 12.7993927 13.200333 13.54928242
log(Price) 13.1478362 13.31298374 13.4730202 11.9511804 14.221042 13.58231667
CV residual 0.3088586 0.09147278 0.5606003 -0.8482123 1.020709 0.03303425
825 827 828 834 840 846
Predicted 13.2638036 13.00099416 13.2944202 13.2526376 13.289377370 13.682957
cvpred 13.2726919 13.02269397 13.3097784 13.2577241 13.299263252 13.689851
log(Price) 13.0389818 13.08720241 13.0710701 13.4588356 13.304601597 13.582948
CV residual -0.2337102 0.06450844 -0.2387083 0.2011115 0.005338346 -0.106903
853 854 858 862 875 876
Predicted 13.6428714 13.1157313 13.1723709 13.7683733 13.787382 14.1474270
cvpred 13.6480745 13.1290969 13.1818120 13.7761287 13.792539 14.1585405
log(Price) 13.4444469 13.3923905 14.1519828 14.1156152 13.539757 14.6039679
CV residual -0.2036277 0.2632937 0.9701708 0.3394865 -0.252782 0.4454274
877 878 881 882 883 887
Predicted 13.3116388 13.3929365 13.74097647 14.1905598 13.8838720 13.8749039
cvpred 13.3289396 13.3952618 13.75183515 14.1983691 13.8888819 13.8832203
log(Price) 13.0879790 14.1696824 13.74508809 13.3876465 13.4588356 13.5922420
CV residual -0.2409606 0.7744206 -0.00674706 -0.8107227 -0.4300463 -0.2909783
895 899 909
Predicted 13.9611228 14.2940499 14.5989154
cvpred 13.9678559 14.2895023 14.5859808
log(Price) 14.0931423 13.8155106 13.8402032
CV residual 0.1252864 -0.4739917 -0.7457776
Sum of squares = 42.02 Mean square = 0.23 n = 182
fold 4
Observations in test set: 182
2 6 7 15 16
Predicted 11.8525010 11.8866348 11.95773812 11.9054115 11.864687204
cvpred 11.8556086 11.8900242 11.96096165 11.9076029 11.858276489
log(Price) 12.0317193 12.3779229 11.86358234 12.5515223 11.849397702
CV residual 0.1761107 0.4878988 -0.09737931 0.6439194 -0.008878787
19 30 33 35 41 51
Predicted 11.8410937 11.9606361 11.963486 11.9397037 12.1936376 11.97520476
cvpred 11.8716335 11.9352782 11.963050 11.9420114 12.2228622 11.94988773
log(Price) 12.0725413 11.9569701 11.308358 11.5898865 12.3673408 11.99535161
CV residual 0.2009077 0.0216919 -0.654692 -0.3521249 0.1444786 0.04546389
55 63 64 70 79 83
Predicted 12.2464011 11.93652485 11.9439953 11.9818675 11.9769161 11.9669294
cvpred 12.2478697 11.93903626 11.9328134 11.9439894 11.9521592 11.9545465
log(Price) 12.0137008 11.98604922 11.6036798 12.2307653 11.4075649 12.2428866
CV residual -0.2341689 0.04701296 -0.3291336 0.2867759 -0.5445942 0.2883401
84 93 95 100 103 106
Predicted 11.9212569 12.204893 12.2118937 12.5958138 12.27658756 12.2618763
cvpred 11.9242150 12.246400 12.2523283 12.6215871 12.26449528 12.2632484
log(Price) 11.6587559 12.100712 11.9823039 12.2524790 12.17561344 12.6760763
CV residual -0.2654591 -0.145688 -0.2700244 -0.3691081 -0.08888184 0.4128279
118 120 135 141 144 149
Predicted 12.0020697 12.2988533 12.28811873 12.0483519 12.2250758 11.912466
cvpred 12.0322312 12.3277510 12.28830922 12.0382555 12.2259180 11.928351
log(Price) 12.3013828 11.9183906 12.19349386 12.2922503 12.7938593 11.418615
CV residual 0.2691516 -0.4093604 -0.09481536 0.2539948 0.5679413 -0.509736
163 164 174 178 179 184
Predicted 12.0095866 12.0120345 12.55988105 12.2404698 12.53240637 12.064515
cvpred 11.9573288 11.9597865 12.49511461 12.2546837 12.49509938 12.019246
log(Price) 12.0725413 12.1415341 12.53896706 12.4490188 12.56024446 13.073173
CV residual 0.1152124 0.1817476 0.04385245 0.1943351 0.06514508 1.053927
189 191 194 198 210 221
Predicted 12.46429945 11.9664922 12.2706154 12.29104806 12.3179569 12.2219888
cvpred 12.49362624 11.9409977 12.2720888 12.26524780 12.3178804 12.2372477
log(Price) 12.57763620 11.4668815 12.8479265 12.27839331 12.2010601 12.1117620
CV residual 0.08400996 -0.4741162 0.5758378 0.01314551 -0.1168203 -0.1254858
222 226 227 228 230 237
Predicted 12.3357983 12.3269263 12.3060546 12.3060546 12.3042556 12.3257885
cvpred 12.3070844 12.3140110 12.3065108 12.3065108 12.2919933 12.3119242
log(Price) 12.4874851 12.6726329 12.1495023 12.1495023 12.8452915 12.7218858
CV residual 0.1804007 0.3586218 -0.1570085 -0.1570085 0.5532982 0.4099616
239 240 246 252 261 275
Predicted 12.4106841 12.523255 12.6439290 12.6919338 12.3477289 12.33375220
cvpred 12.3929194 12.564269 12.6292381 12.7032236 12.3352337 12.36285291
log(Price) 12.5772913 12.296827 12.3673408 12.5281561 12.5061772 12.33270530
CV residual 0.1843719 -0.267442 -0.2618973 -0.1750675 0.1709435 -0.03014761
279 282 283 299 303 314
Predicted 12.3141724 12.3499004 12.3146397 11.9990033 12.3022684 12.2277370
cvpred 12.3131359 12.3369811 12.2775983 11.9626822 12.3033201 12.2431949
log(Price) 11.7597855 11.8810348 12.5245264 11.7752897 12.1547794 12.3983198
CV residual -0.5533503 -0.4559463 0.2469281 -0.1873925 -0.1485408 0.1551249
317 320 321 323 329 348
Predicted 12.3320225 12.3291340 12.3090629 12.3516109 12.3124189 12.36797181
cvpred 12.3570442 12.3290241 12.3099170 12.3248981 12.3129724 12.35520061
log(Price) 12.0045683 12.4680522 13.1223634 11.4075649 12.4645833 12.42921620
CV residual -0.3524759 0.1390281 0.8124463 -0.9173332 0.1516109 0.07401558
352 357 360 365 372 380
Predicted 12.4135144 12.39502606 12.3885659 12.5310165 12.28437783 12.6986948
cvpred 12.3743779 12.38190832 12.3613430 12.5300729 12.29837959 12.6967663
log(Price) 12.1807548 12.31716669 12.1807548 12.5496623 12.31043266 12.4874851
CV residual -0.1936231 -0.06474163 -0.1805882 0.0195894 0.01205307 -0.2092812
391 393 396 407 413 415
Predicted 12.57231618 12.4980855 12.025558 12.3435577 12.3152161 12.6752811
cvpred 12.57182825 12.4700904 12.025680 12.3443918 12.3160050 12.6606093
log(Price) 12.52452638 12.7656884 10.819778 12.8583978 12.1415341 12.8866410
CV residual -0.04730187 0.2955981 -1.205902 0.5140061 -0.1744709 0.2260318
418 421 430 433 453 458
Predicted 12.5067044 12.9242887 12.0625542 12.7486898 12.7364756 12.3276883
cvpred 12.4803260 12.9219318 12.0248890 12.7338646 12.7076618 12.3281608
log(Price) 12.2548628 13.2085411 12.4288161 12.5602445 12.7367009 12.1871446
CV residual -0.2254632 0.2866093 0.4039271 -0.1736201 0.0290391 -0.1410162
461 466 489 494 501 505
Predicted 12.51688961 12.7277496 12.5819455 12.6469758 12.1063519 12.3875599
cvpred 12.51750825 12.7113532 12.5540535 12.6734804 12.1367022 12.3751908
log(Price) 12.55989352 13.1223634 12.6915805 12.4684369 11.9829291 11.9640011
CV residual 0.04238528 0.4110101 0.1375269 -0.2050435 -0.1537731 -0.4111897
507 520 522 524 534 536
Predicted 12.7528510 12.3120719 12.04773310 12.5140343 12.3767642 12.4041267
cvpred 12.7645752 12.2872393 11.99664160 12.5134455 12.3891869 12.3632306
log(Price) 12.6115378 12.0137008 11.91170158 13.0497927 12.1281111 13.0269532
CV residual -0.1530375 -0.2735385 -0.08494002 0.5363472 -0.2610758 0.6637226
542 544 545 551 553 568
Predicted 13.054393 13.12495420 12.7613378 12.6455368 12.3785545 12.941220847
cvpred 13.063734 13.15539223 12.7745970 12.6175264 12.3652975 12.936606200
log(Price) 13.296317 13.08984019 12.5425449 12.7882883 12.7938593 12.933621253
CV residual 0.232583 -0.06555205 -0.2320521 0.1707619 0.4285618 -0.002984948
569 574 578 587 591 592
Predicted 12.62675313 12.3429526 12.78276955 12.8747055 12.7985740 12.7800638
cvpred 12.61310311 12.3300249 12.80370550 12.8479410 12.7822533 12.7935111
log(Price) 12.63947712 12.6443276 12.71138309 13.0497927 13.2085411 13.2912619
CV residual 0.02637401 0.3143026 -0.09232241 0.2018517 0.4262878 0.4977508
596 600 602 603 607 615
Predicted 12.7753300 12.3191761 12.65602122 12.6740780 12.6638185 12.7084717
cvpred 12.7668874 12.3074826 12.66992652 12.6884734 12.6358480 12.7063600
log(Price) 12.5602445 12.7656884 12.76568843 11.9829291 12.8076526 13.0540845
CV residual -0.2066429 0.4582058 0.09576192 -0.7055443 0.1718047 0.3477246
618 621 634 637 639 642
Predicted 12.9377167 12.78285142 13.1502142 12.1250889 12.7041443 12.618382
cvpred 12.9634266 12.76507252 13.1512863 12.0589994 12.7182213 12.659536
log(Price) 13.0972507 12.69158046 12.9515751 12.2060726 13.4588356 10.657259
CV residual 0.1338241 -0.07349206 -0.1997112 0.1470733 0.7406143 -2.002276
643 645 647 651 677 678
Predicted 12.7938014 12.4381094 13.0018745 12.70671 12.8662952 12.8411978
cvpred 12.7782179 12.4252928 13.0399921 12.69420 12.8400618 12.8210192
log(Price) 12.5776362 12.9831013 12.4684369 12.87133 13.7642173 12.4490188
CV residual -0.2005817 0.5578085 -0.5715552 0.17713 0.9241554 -0.3720004
680 681 683 697 698 702
Predicted 12.4846215 12.817479 12.827543 12.8498214 12.6012139 12.8605363
cvpred 12.4699502 12.799157 12.784093 12.8345818 12.5461339 12.8452372
log(Price) 12.6014874 12.487485 12.994530 12.7798731 13.0867362 13.2332784
CV residual 0.1315372 -0.311672 0.210437 -0.0547087 0.5406023 0.3880413
703 705 706 707 708 713
Predicted 12.8108951 12.8205405 12.7990890 12.79775217 12.629617 12.7907409
cvpred 12.8196703 12.8324725 12.8116330 12.81880259 12.601821 12.8000348
log(Price) 12.6587394 12.6115378 12.5425449 12.80765263 12.428816 12.6823068
CV residual -0.1609309 -0.2209347 -0.2690882 -0.01114996 -0.173005 -0.1177279
719 725 728 729 730 734
Predicted 12.8787131 12.7327134 12.730803979 12.8206132 12.7945634 13.1675487
cvpred 12.8598382 12.7587492 12.716038227 12.8322213 12.7922798 13.1784715
log(Price) 13.6802634 12.9945300 12.717398144 12.7218858 12.5776362 12.8531759
CV residual 0.8204252 0.2357808 0.001359917 -0.1103355 -0.2146436 -0.3252956
735 738 739 745 746
Predicted 12.8714222 12.76039653 13.2071430 13.0483995 13.19980393
cvpred 12.8571229 12.74731148 13.1838304 13.0603726 13.17957235
log(Price) 13.2356921 12.71844707 13.4224680 13.2621253 13.08154138
CV residual 0.3785691 -0.02886441 0.2386376 0.2017528 -0.09803097
748 754 759 767 773 774
Predicted 13.50363948 12.0560018 12.9400349 12.8962666 12.8245156 12.8115168
cvpred 13.53825761 12.0208958 12.9748586 12.8791988 12.7559572 12.7978068
log(Price) 13.47812410 12.7656884 12.8479265 13.7101500 13.6109434 11.7981044
CV residual -0.06013351 0.7447927 -0.1269321 0.8309513 0.8549862 -0.9997024
776 782 791 801 806 808
Predicted 12.7726623 12.8939632 12.9982420 13.0823299 12.93663540 12.9213146
cvpred 12.7583558 12.8967576 12.9694282 13.0546802 12.92246407 12.9033809
log(Price) 13.1843988 12.0435537 13.2577680 12.4130868 13.01922262 13.0047053
CV residual 0.4260429 -0.8532039 0.2883399 -0.6415934 0.09675855 0.1013245
810 814 820 821 822 823
Predicted 12.957939 12.8068136 13.51260596 13.1207394 12.9348877 12.6763883
cvpred 12.939965 12.7785458 13.51861264 13.1154953 12.9460246 12.6214376
log(Price) 13.122363 12.8967167 13.59236701 13.0710701 13.1615841 13.0158911
CV residual 0.182398 0.1181709 0.07375437 -0.0444252 0.2155595 0.3944535
836 845 850 851 852 856
Predicted 13.5412162 12.9978312 13.5557242 13.2311264 13.6615324 14.0005342
cvpred 13.5473777 12.9689291 13.5754968 13.1907104 13.6702551 14.0120499
log(Price) 13.7536352 13.4135393 14.0817136 13.8402032 14.1749317 13.7642173
CV residual 0.2062575 0.4446103 0.5062168 0.6494927 0.5046766 -0.2478326
857 861 864 870 871 884
Predicted 13.3251740 13.6331927 13.690033 13.39340015 13.7383749 14.34121217
cvpred 13.3028181 13.6704536 13.697249 13.39876349 13.7424343 14.31192506
log(Price) 14.1519828 13.0389818 13.244581 13.30468493 13.3847276 14.29174474
CV residual 0.8491647 -0.6314718 -0.452668 -0.09407856 -0.3577066 -0.02018033
885 892 898 910
Predicted 13.5027619 14.1055244 14.5291831 15.1411542
cvpred 13.4955358 14.1043054 14.5318094 15.1855827
log(Price) 13.7901927 14.7297993 13.9552725 14.8087623
CV residual 0.2946569 0.6254939 -0.5765369 -0.3768203
Sum of squares = 30.46 Mean square = 0.17 n = 182
fold 5
Observations in test set: 182
3 8 9 10 11 12
Predicted 11.81452155 11.8750212 12.0971445 11.8822228 11.8858821 12.0792761
cvpred 11.81396849 11.8876499 12.0849020 11.8947194 11.8913791 12.0752870
log(Price) 11.78295260 11.6952470 12.3327053 11.0186291 11.5627722 11.4403548
CV residual -0.03101589 -0.1924028 0.2478033 -0.8760903 -0.3286069 -0.6349322
17 20 24 34 36 42
Predicted 11.920216 11.8032669 11.8550441 11.9324591 12.2439834 12.18757
cvpred 11.930241 11.8254924 11.8725408 11.9436517 12.2293831 12.17839
log(Price) 12.100712 11.6952470 11.4075649 12.1007121 11.8122890 12.34583
CV residual 0.170471 -0.1302454 -0.4649758 0.1570604 -0.4170941 0.16744
45 56 67 71 72 74
Predicted 12.24107608 11.9192525 11.9790110 12.3385642 12.2611274 11.9701222
cvpred 12.23839458 11.9387381 11.9956572 12.3241130 12.2531010 11.9757816
log(Price) 12.21602298 11.5129255 11.8705999 11.9766595 11.6217799 11.3504065
CV residual -0.02237161 -0.4258126 -0.1250573 -0.3474535 -0.6313211 -0.6253751
77 80 82 85 88 94
Predicted 12.1826463 12.282161 12.2386141 11.92303795 12.355766251 11.89569
cvpred 12.1779002 12.273230 12.2362187 11.94450389 12.348169569 11.92251
log(Price) 12.0137008 11.171139 12.3488734 11.99535161 12.345834588 11.47210
CV residual -0.1641994 -1.102091 0.1126547 0.05084772 -0.002334981 -0.45041
105 117 121 125 136 137
Predicted 12.1449290 12.34030072 11.950520 12.0459535 12.259310 12.0761016
cvpred 12.1500113 12.32755857 11.972779 12.0734677 12.256504 12.0844786
log(Price) 11.7519424 12.36734079 11.849398 11.6952470 12.100712 12.4411448
CV residual -0.3980689 0.03978222 -0.123381 -0.3782207 -0.155792 0.3566661
143 152 154 157 159 161
Predicted 12.0869192 12.2476566 12.3221264 12.9828953 12.6146488 11.93258148
cvpred 12.0949239 12.2410227 12.3130902 12.9111421 12.5705165 11.95534570
log(Price) 12.2307653 12.4126802 12.2783933 13.8729886 12.1547794 11.89136190
CV residual 0.1358414 0.1716576 -0.0346969 0.9618465 -0.4157371 -0.06398379
162 170 177 193 196 200
Predicted 12.2725373 12.6722220 11.967106921 12.3255094 12.0207209 11.9135079
cvpred 12.2720740 12.6410811 11.983117787 12.3157100 12.0423540 11.9457928
log(Price) 12.4490188 12.2783933 11.976659481 12.0435537 12.4874851 11.9640011
CV residual 0.1769449 -0.3626878 -0.006458306 -0.2721563 0.4451311 0.0182083
202 205 206 211 216 220
Predicted 11.9705637 12.630357 12.1434321 12.2772796 12.331961056 12.187050
cvpred 11.9907885 12.601002 12.1560621 12.2779409 12.329535149 12.191168
log(Price) 12.2060726 12.449019 12.3883942 12.1704455 12.323855681 11.599103
CV residual 0.2152842 -0.151983 0.2323321 -0.1074955 -0.005679468 -0.592065
224 225 241 244 247 254
Predicted 12.370940 12.6995939 11.9733653 12.2892834 11.973765 11.98449
cvpred 12.362411 12.6588996 12.0015762 12.2847394 12.002433 12.01208
log(Price) 12.577636 12.7938593 12.7218858 11.8837991 13.033532 10.81978
CV residual 0.215225 0.1349597 0.7203096 -0.4009403 1.031099 -1.19230
256 259 262 264 265 273
Predicted 12.2467254 12.253769 12.3574442 12.3075579 12.00297 12.3417068
cvpred 12.2426607 12.262592 12.3595483 12.3086968 12.03698 12.3281103
log(Price) 11.9015835 9.210340 12.7218858 12.8531759 12.42118 12.3458346
CV residual -0.3410772 -3.052251 0.3623375 0.5444791 0.38420 0.0177243
284 298 305 310 315 319
Predicted 12.2853975 12.4039815 12.35906326 11.979342 12.4172596 12.3090629
cvpred 12.2892713 12.4041358 12.35614693 12.017051 12.4048372 12.3127591
log(Price) 12.4292162 11.8844890 12.31492705 11.818938 12.9099743 13.1223634
CV residual 0.1399449 -0.5196467 -0.04121988 -0.198112 0.5051371 0.8096043
322 324 327 331 339 342
Predicted 12.3292533 12.684943 12.2903069 12.3750577 12.95793858 12.3577791
cvpred 12.3318684 12.651791 12.2961319 12.3714506 12.88151778 12.3630812
log(Price) 12.4680522 12.513557 13.0540845 12.4292162 12.97154049 11.3963916
CV residual 0.1361839 -0.138234 0.7579527 0.0577656 0.09002271 -0.9666896
345 346 347 349 351
Predicted 12.339521364 12.3381829 12.4264399 11.9356102 12.60094201
cvpred 12.342313359 12.3411268 12.4158943 11.9815131 12.58233738
log(Price) 12.345834588 12.1858699 12.7367009 11.6526874 12.61120436
CV residual 0.003521229 -0.1552569 0.3208066 -0.3288257 0.02886699
354 355 364 367 369 381
Predicted 12.69206465 12.7093376 12.6443747 11.9635689 12.37232787 12.6986948
cvpred 12.66389451 12.6744887 12.6222678 11.9989054 12.37437702 12.6770889
log(Price) 12.63525428 12.5245264 12.8479265 12.2543865 12.34147728 12.4874851
CV residual -0.02864023 -0.1499623 0.2256587 0.2554811 -0.03289974 -0.1896038
383 386 389 394 402 405
Predicted 12.3351559 12.2692184 12.3573627 12.6946036 12.295420 12.0459825
cvpred 12.3404826 12.2852358 12.3632050 12.6696885 12.305336 12.0785251
log(Price) 12.7541941 12.1388639 12.1172414 12.9116423 12.111212 11.7752897
CV residual 0.4137114 -0.1463719 -0.2459636 0.2419539 -0.194124 -0.3032354
410 422 423 425 426
Predicted 12.233440756 12.3585263 12.6197656 12.6325158 12.5344789
cvpred 12.253242190 12.3691950 12.6041592 12.6154135 12.5226990
log(Price) 12.245293359 13.1223634 13.0058296 13.2445810 13.2176372
CV residual -0.007948831 0.7531684 0.4016704 0.6291675 0.6949382
435 437 446 449 462 464
Predicted 12.32647460 12.331685 12.1785627 12.2720232 12.33902920 12.1961383
cvpred 12.33617340 12.335791 12.1969631 12.2760017 12.34847167 12.2208287
log(Price) 12.30817787 13.392391 12.0610469 12.9598444 12.32385568 12.0610469
CV residual -0.02799553 1.056599 -0.1359163 0.6838428 -0.02461599 -0.1597818
470 474 475 476 477 478
Predicted 12.5265493 12.7247920 12.3478190 12.3205746 12.63941243 12.82103888
cvpred 12.5166337 12.6984385 12.3574145 12.3407527 12.62381530 12.79628126
log(Price) 12.9831013 12.3673408 13.0170029 12.7218858 12.70381303 12.77987307
CV residual 0.4664676 -0.3310977 0.6595883 0.3811332 0.07999773 -0.01640819
491 492 496 498 509 511
Predicted 12.3514635 12.3189057 12.3548308 12.78577590 12.63394566 12.6779959
cvpred 12.3661554 12.3382608 12.3726898 12.76199981 12.63308478 12.6575903
log(Price) 12.6491546 11.8130301 12.0076217 12.80490915 12.69158046 12.4818086
CV residual 0.2829992 -0.5252308 -0.3650681 0.04290933 0.05849568 -0.1757817
514 531 537 539 540 554
Predicted 12.3476753 12.8213162 12.4041289 12.65648155 12.3692626 12.2160066
cvpred 12.3435504 12.7901031 12.4146563 12.63698534 12.3878154 12.2385088
log(Price) 13.2861815 12.5514338 13.0269532 12.57418197 13.2445810 12.4411448
CV residual 0.9426311 -0.2386693 0.6122969 -0.06280338 0.8567656 0.2026359
557 558 559 563 566 573
Predicted 12.6582631 13.1481687 12.62502134 12.2666643 12.7199577 12.81831994
cvpred 12.6542713 13.1112628 12.61467604 12.2958239 12.7204655 12.79538193
log(Price) 13.5144055 12.6014874 12.69158046 11.9829291 12.4130868 12.76540268
CV residual 0.8601341 -0.5097753 0.07690442 -0.3128948 -0.3073787 -0.02997925
593 597 614 620 625 627
Predicted 12.67841 12.76224010 12.81550109 12.3878633 12.9849051 12.85719714
cvpred 12.67168 12.75413192 12.79781506 12.4095650 12.9592744 12.84154894
log(Price) 11.99520 12.83468130 12.85134175 12.0137008 13.0919042 12.86099861
CV residual -0.67648 0.08054938 0.05352669 -0.3958643 0.1326298 0.01944968
629 630 636 657 664 668
Predicted 12.4771189 12.7349490 12.4039889 12.7904328 13.1161191 12.8284538
cvpred 12.4851103 12.7260178 12.4165312 12.7757034 13.0758753 12.8150179
log(Price) 13.0527989 12.8557903 12.5389671 12.9480100 13.2836315 12.5061772
CV residual 0.5676886 0.1297725 0.1224359 0.1723066 0.2077562 -0.3088406
670 674 686 687 688 689
Predicted 12.7342723 12.7733635 12.2708324 12.726934 12.5170141 12.3828877
cvpred 12.7304618 12.7647392 12.3101236 12.714287 12.5269610 12.4059237
log(Price) 12.3544927 12.6443276 12.6539585 12.873902 12.9715405 11.9183906
CV residual -0.3759691 -0.1204116 0.3438349 0.159615 0.4445794 -0.4875332
692 699 701 710 718 721
Predicted 12.4675514 12.7888780 13.0602618 12.45383135 13.13065 12.528063113
cvpred 12.4955032 12.7821157 13.0382832 12.46923844 13.10363 12.538780780
log(Price) 12.0552498 12.5245264 12.8942073 12.37158708 13.55298 12.542544882
CV residual -0.4402534 -0.2575893 -0.1440759 -0.09765136 0.44935 0.003764102
732 742 744 749 758 765
Predicted 13.1779973 13.1624612 13.174572 13.0590448 12.8217515 12.86629102
cvpred 13.1474994 13.1325197 13.145017 13.0505263 12.8257504 12.86996106
log(Price) 13.3689109 13.4224680 13.272506 13.2176736 13.4371741 12.84792653
CV residual 0.2214115 0.2899483 0.127489 0.1671473 0.6114237 -0.02203453
770 780 785 786 792 796
Predicted 13.14468405 12.9254580 12.9002308 13.163111 13.57542374 13.56230966
cvpred 13.11804977 12.9236953 12.9060758 13.143526 13.52446986 13.50909140
log(Price) 13.21767356 13.1661410 13.4730202 12.885374 13.45166712 13.59236701
CV residual 0.09962379 0.2424457 0.5669444 -0.258152 -0.07280274 0.08327561
800 802 812 817 818 826
Predicted 13.0072626 12.4859113 12.82105144 13.1948986 13.1948986 12.9527829
cvpred 13.0104229 12.5372038 12.84670100 13.1891415 13.1891415 12.9687409
log(Price) 13.2176736 12.1281111 12.91164235 13.8878312 13.8878312 13.2085411
CV residual 0.2072506 -0.4090927 0.06494135 0.6986898 0.6986898 0.2398002
831 832 838 848 867 868
Predicted 13.6459127 13.2812527 13.4723509 13.1622352 13.2823327 13.732612
cvpred 13.6080333 13.2630114 13.4545911 13.1737559 13.3068278 13.712582
log(Price) 13.2793671 13.8831692 13.1021607 12.9239124 13.7953079 13.244581
CV residual -0.3286662 0.6201578 -0.3524304 -0.2498435 0.4884801 -0.468001
872 874 880 888 891 897
Predicted 13.4193143 12.5213370 13.3690602 13.8685952 13.9006671 14.0495114
cvpred 13.4369217 12.6138945 13.3986468 13.9004721 13.9291585 14.0819455
log(Price) 14.0778748 13.3046849 13.5923670 14.4769090 14.0961680 13.7483018
CV residual 0.6409531 0.6907904 0.1937202 0.5764369 0.1670095 -0.3336437
901 902 907 911
Predicted 13.2587295 12.9319094 13.725961 13.138802
cvpred 13.3592241 13.0648901 13.800547 13.412083
log(Price) 13.6381765 13.1806323 12.765688 11.609244
CV residual 0.2789524 0.1157421 -1.034859 -1.802839
Sum of squares = 43.45 Mean square = 0.24 n = 182
Overall (Sum over all 182 folds)
ms
0.2256241 #Obtain PRESS, MSPE, and prediction R-squared
PRESS <- function(linear.model) {
pr <- residuals(linear.model)/(1-lm.influence(linear.model)$hat)
PRESS <- sum(pr^2)
return(PRESS)
}
MSPE <- function(linear.model) {
return(PRESS(linear.model)/length(residuals(linear.model)))
}
pred_r_squared <- function(linear.model) {
lm.anova <- anova(linear.model)
tss <- sum(lm.anova$'Sum Sq')
pred.r.squared <- 1-PRESS(linear.model)/(tss)
return(pred.r.squared)
}
PRESS(model3)[1] 206.8873MSPE(model3)[1] 0.2270991pred_r_squared(model3)[1] 0.5198919For model3 (the model with the Numbath variable), PRESS = 206.8873, MSPE = 0.2270991, prediction R-squared = 0.5198919
KCV = cv.lm(data=data_frame, model4, m=5, seed=123)
fold 1
Observations in test set: 182
1 5 13 21 22 29
Predicted 12.1611593 12.0110704 11.8566344 12.2173648 11.9906149 11.9694392
cvpred 12.1865523 12.0327058 11.8802118 12.2380178 12.0122417 11.9870692
log(Price) 12.3458346 12.0810762 11.3850921 12.0137008 11.4616322 12.1547794
CV residual 0.1592823 0.0483704 -0.4951197 -0.2243171 -0.5506096 0.1677102
31 37 39 43 48 52
Predicted 11.9904735 12.0801595 12.085107 12.05679315 11.9384438 12.2500959
cvpred 12.0074400 12.0953174 12.101865 12.07453271 11.9571811 12.2688394
log(Price) 12.5317728 11.3265959 11.002100 12.04941884 12.6915805 11.6952470
CV residual 0.5243328 -0.7687215 -1.099765 -0.02511388 0.7343994 -0.5735924
58 61 75 81 92 97
Predicted 12.1898399 12.2854689 11.910815 12.2553133 12.01865059 12.342454
cvpred 12.2067366 12.3080102 11.926527 12.2702220 12.03236591 12.392061
log(Price) 12.4684369 12.0435537 9.210340 11.3022044 12.10071213 10.596635
CV residual 0.2617003 -0.2644564 -2.716187 -0.9680176 0.06834622 -1.795426
101 102 109 110 115 116
Predicted 12.2745394 12.3053364 12.4480317 12.3966872 12.295159904 12.1830390
cvpred 12.2906690 12.3253936 12.5040853 12.4337236 12.308809373 12.1972992
log(Price) 11.3445068 12.1730328 13.1519222 11.7117763 12.301382825 13.1615841
CV residual -0.9461622 -0.1523608 0.6478368 -0.7219473 -0.007426548 0.9642849
127 129 131 133 140 142
Predicted 12.0790039 12.3809594 12.13636024 12.4925794 12.3232548 12.1441692
cvpred 12.0919443 12.3927317 12.15271632 12.5124641 12.3441890 12.1537447
log(Price) 11.2897819 11.5607628 12.07254125 12.6776376 12.0725413 12.4411448
CV residual -0.8021624 -0.8319689 -0.08017506 0.1651734 -0.2716477 0.2874001
146 148 151 155 171 172
Predicted 12.188785 12.08646563 12.1305902 12.5483475 12.3528633 12.28902574
cvpred 12.203924 12.09978584 12.1417719 12.5889807 12.3711333 12.30230075
log(Price) 12.100712 12.18024189 12.5947306 12.7218858 12.2452934 12.35664550
CV residual -0.103212 0.08045605 0.4529588 0.1329051 -0.1258399 0.05434475
176 181 182 185 186 187
Predicted 12.8374751 12.7145292 12.069587 12.54428868 12.35999336 12.4587159
cvpred 12.9111478 12.7834544 12.078308 12.55641599 12.36924681 12.4933709
log(Price) 12.6760763 12.4490188 10.915088 12.57068104 12.30138283 12.6760763
CV residual -0.2350715 -0.3344356 -1.163219 0.01426505 -0.06786399 0.1827054
195 197 201 203 207 217
Predicted 12.3859127 12.40171432 12.276483 12.5372654 12.3246236 12.35215484
cvpred 12.4019403 12.41185907 12.287415 12.5530152 12.3350000 12.36430031
log(Price) 12.1750978 12.37792290 12.128111 12.0698405 12.5845091 12.32385568
CV residual -0.2268425 -0.03393617 -0.159304 -0.4831748 0.2495091 -0.04044463
229 235 236 243 248 249
Predicted 12.338358 12.4049224 12.3707067 12.2787973 12.211350 12.3623421
cvpred 12.344396 12.4273314 12.3884851 12.2904344 12.230219 12.3748749
log(Price) 12.611538 12.2060726 12.4946293 12.8479265 11.482466 11.8844890
CV residual 0.267142 -0.2212588 0.1061443 0.5574922 -0.747753 -0.4903858
250 258 267 268 271 272
Predicted 12.1851539 12.3653810 1.243683e+01 12.113792 12.39405695 12.5543183
cvpred 12.1902138 12.3736569 1.245253e+01 12.120302 12.40270607 12.5624728
log(Price) 11.9511804 12.1275704 1.245293e+01 12.683548 12.46843691 12.3925522
CV residual -0.2390334 -0.2460865 3.977817e-04 0.563246 0.06573084 -0.1699206
277 280 281 285 286 291
Predicted 12.34631681 12.4261934 12.56660052 12.2864477 12.327552 12.5241570
cvpred 12.34860542 12.4383230 12.59790674 12.2926009 12.335931 12.5421667
log(Price) 12.31492705 12.3238557 12.64432758 12.7337554 11.289782 12.3800260
CV residual -0.03367837 -0.1144673 0.04642083 0.4411545 -1.046149 -0.1621408
295 296 302 306 308 311
Predicted 12.51781780 12.6260721 12.49863138 12.322613 12.3787314 12.2740216
cvpred 12.52523952 12.6466296 12.50854646 12.328093 12.3840332 12.2813049
log(Price) 12.46843691 12.4081968 12.54254488 11.856515 11.7597855 11.8130301
CV residual -0.05680261 -0.2384328 0.03399842 -0.471578 -0.6242476 -0.4682748
313 336 341 353 359 362
Predicted 12.2732878 12.50363324 12.3155470 12.39555647 12.3185245 12.1623974
cvpred 12.2815036 12.52030779 12.3220437 12.39953726 12.3211598 12.1619511
log(Price) 13.1441249 12.49874226 12.1547794 12.46843691 12.8266491 12.2737313
CV residual 0.8626213 -0.02156553 -0.1672643 0.06889965 0.5054893 0.1117802
368 370 375 387 388 390
Predicted 12.2935150 12.4476798 12.4200867 12.7354500 12.1812538 12.5013343
cvpred 12.3161958 12.4517710 12.4286066 12.7789186 12.1815099 12.5188206
log(Price) 12.5281561 12.3414773 12.3194013 13.0170029 12.6603279 12.2404741
CV residual 0.2119604 -0.1102937 -0.1092053 0.2380842 0.4788181 -0.2783465
392 395 397 406 409 412
Predicted 12.5975615 12.4302728 12.346964 12.3657032 12.4251184 12.5593167
cvpred 12.6123347 12.4317554 12.355089 12.3665341 12.4308031 12.5631546
log(Price) 12.1415341 12.0719697 13.444447 12.8346813 12.7685415 12.0051797
CV residual -0.4708006 -0.3597857 1.089358 0.4681472 0.3377384 -0.5579749
434 438 440 441 465 468
Predicted 12.5817564 12.51721513 12.2158680 12.331013 12.530180381 12.5340190
cvpred 12.5827602 12.52112977 12.2163558 12.332962 12.535424911 12.5349411
log(Price) 13.1421660 12.46843691 12.3453997 12.660328 12.542187676 12.3764903
CV residual 0.5594058 -0.05269286 0.1290439 0.327366 0.006762765 -0.1584508
471 479 480 484 485
Predicted 12.64704640 12.599981 12.75592692 12.5234455 12.507823145
cvpred 12.65648679 12.608618 12.75988448 12.5294072 12.512327767
log(Price) 12.67607627 11.918391 12.69158046 12.1807548 12.506177238
CV residual 0.01958948 -0.690227 -0.06830402 -0.3486524 -0.006150529
486 487 497 499 510 516
Predicted 12.39613267 12.4283455 12.657776 12.429703 12.914026 12.4730180
cvpred 12.39459627 12.4324076 12.661566 12.439589 12.960341 12.4750119
log(Price) 12.47800636 12.7068479 13.005830 12.165251 12.765403 12.2783933
CV residual 0.08341009 0.2744403 0.344264 -0.274338 -0.194938 -0.1966186
521 533 535 543 552 555
Predicted 12.77574671 12.4286213 12.602115 12.7106889 12.6566778 12.3865890
cvpred 12.77538934 12.4307639 12.609817 12.7037881 12.6609812 12.3817361
log(Price) 12.72783821 12.5947306 13.026953 12.6729464 13.4828311 13.2445810
CV residual -0.04755113 0.1639667 0.417136 -0.0308417 0.8218499 0.8628449
562 567 570 575 577 579
Predicted 12.29058027 12.4881859 12.80269764 12.4416839 12.6099083 12.4862544
cvpred 12.27877636 12.4865681 12.79830160 12.4401921 12.6123926 12.4878929
log(Price) 12.34147728 12.8609986 12.78549106 11.7791285 13.0389818 13.3533164
CV residual 0.06270092 0.3744305 -0.01281054 -0.6610636 0.4265891 0.8654235
585 589 590 594 595 605
Predicted 12.64694122 12.6589864 12.713993 12.57835720 12.7547537 12.8250694
cvpred 12.64018214 12.6626971 12.712542 12.58739766 12.7582790 12.8273146
log(Price) 12.54254488 11.9316358 12.506177 12.50580680 12.8992198 12.7068479
CV residual -0.09763726 -0.7310613 -0.206365 -0.08159086 0.1409409 -0.1204667
609 610 613 623 631 633
Predicted 12.8291354 12.8607532 12.8148257 12.97028075 12.663623 12.7037104
cvpred 12.8339126 12.8574676 12.8089967 12.98886270 12.662874 12.6893141
log(Price) 12.4529327 12.7570801 12.3458346 13.01811336 12.855790 13.2878778
CV residual -0.3809799 -0.1003876 -0.4631621 0.02925066 0.192916 0.5985637
638 658 661 666 667 671
Predicted 12.525664 12.6520431 12.5248774 12.7074013 12.7074013 12.6248469
cvpred 12.518521 12.6502700 12.5190764 12.7066664 12.7066664 12.6230226
log(Price) 13.458836 12.3238557 13.2655975 12.8346813 12.8346813 13.0147782
CV residual 0.940315 -0.3264143 0.7465212 0.1280149 0.1280149 0.3917556
672 675 676 684 690 691
Predicted 12.5778850 12.8819580 12.6748486 12.901366 12.9700994 13.18860765
cvpred 12.5619021 12.8745209 12.6669873 12.924635 12.9697564 13.23068086
log(Price) 12.3544927 12.9945300 12.4450895 12.524526 13.0389818 13.25339164
CV residual -0.2074095 0.1200091 -0.2218977 -0.400109 0.0692254 0.02271078
693 694 695 704 722 737
Predicted 12.9823277 12.9823306 12.6903646 12.8707866 12.7979183 12.9993309
cvpred 12.9848408 12.9848443 12.6879533 12.8691652 12.8094755 13.0284132
log(Price) 13.4758332 13.4758332 13.3179302 13.1470560 13.1711535 12.8942073
CV residual 0.4909924 0.4909889 0.6299768 0.2778908 0.3616781 -0.1342059
747 760 771 772 778 781
Predicted 12.925156 12.9948904 13.1859005 12.970239 13.0371504 13.1529353
cvpred 12.909964 12.9750926 13.1617114 12.958806 13.0320582 13.1538827
log(Price) 14.066269 12.7938593 14.0306219 12.765403 13.7991271 12.9189612
CV residual 1.156306 -0.1812333 0.8689106 -0.193403 0.7670689 -0.2349216
783 790 793 794 795 798
Predicted 12.8623930 13.1348167 12.9860181 13.0719727 13.0983210 12.972006
cvpred 12.8357236 13.1150373 12.9647118 13.0507757 13.0817920 12.964613
log(Price) 13.4730202 12.9480100 12.7656884 13.1709630 13.4980563 10.558414
CV residual 0.6372966 -0.1670273 -0.1990233 0.1201874 0.4162643 -2.406199
799 805 809 816 819
Predicted 13.02315866 13.11497521 12.97029439 13.070105 12.9684942
cvpred 12.99695649 13.08807584 12.94459930 13.046869 12.9526913
log(Price) 13.09601940 13.12036137 13.01700286 14.221042 13.9332936
CV residual 0.09906291 0.03228554 0.07240356 1.174174 0.9806023
833 837 842 844 855 859
Predicted 13.08275126 13.0596274 13.0005598 13.4224207 13.3961383 13.225075
cvpred 13.04526274 13.0365569 12.9641472 13.3901103 13.3533354 13.190857
log(Price) 13.05622357 13.8145101 12.6729464 13.1711535 13.1806323 14.457364
CV residual 0.01096084 0.7779532 -0.2912008 -0.2189568 -0.1727031 1.266507
863 865 866 869 873 889
Predicted 13.4368506 13.1008197 13.1008197 13.2551811 13.9422191 13.8587811
cvpred 13.4185747 13.0500433 13.0500433 13.2043891 13.9234554 13.8014216
log(Price) 13.0604880 13.5276951 13.5276951 13.7642173 13.3692235 14.4032972
CV residual -0.3580867 0.4776518 0.4776518 0.5598282 -0.5542319 0.6018757
893 894 903 904
Predicted 13.959821 14.1625681 14.4268589 14.1048631
cvpred 13.855493 14.0780837 14.3473311 13.9999342
log(Price) 14.922422 13.8254609 14.8451300 13.3195735
CV residual 1.066929 -0.2526228 0.4977989 -0.6803606
Sum of squares = 55.91 Mean square = 0.31 n = 182
fold 2
Observations in test set: 183
4 18 23 25 27 28
Predicted 12.02253325 12.0501330 12.0759971 12.115103 12.336490 11.99164751
cvpred 11.98840070 12.0169194 12.0436598 12.070948 12.343559 11.95155964
log(Price) 12.08107616 12.1007121 11.4131051 12.577636 10.373491 11.97035031
CV residual 0.09267545 0.0837927 -0.6305547 0.506688 -1.970067 0.01879067
32 38 44 46 49 53
Predicted 12.10365311 12.0894166 12.2290515 12.262810 12.1073011 12.2824435
cvpred 12.07179232 12.0565367 12.2188999 12.260654 12.0751938 12.2793236
log(Price) 12.06104687 11.6656466 12.0662357 12.072541 11.6868788 11.6868788
CV residual -0.01074545 -0.3908901 -0.1526642 -0.188113 -0.3883151 -0.5924448
59 60 62 65 66 69
Predicted 11.895848 12.24149549 12.14200706 12.3099624 11.9524923 12.2582333
cvpred 11.844501 12.23344098 12.12616049 12.3080913 11.9030702 12.2515288
log(Price) 10.235880 12.20106010 12.11450545 11.9177237 12.7585199 11.9009053
CV residual -1.608621 -0.03238087 -0.01165504 -0.3903676 0.8554498 -0.3506235
76 78 87 89 90 91
Predicted 11.9474426 12.2593007 11.8735580 12.2551941 12.5264856 12.02178487
cvpred 11.8997045 12.2516169 11.8159703 12.2466386 12.5574093 11.97945357
log(Price) 12.0137008 11.8130301 12.4292162 12.4968748 12.0725413 12.07254125
CV residual 0.1139962 -0.4385868 0.6132459 0.2502362 -0.4848681 0.09308769
98 104 108 111 114 122
Predicted 12.0372852 12.3970161 12.3363166 12.2229023 12.4106401 12.076825
cvpred 11.9966304 12.3957641 12.3281080 12.1998585 12.4172915 12.038412
log(Price) 12.1542529 12.5425449 12.2160230 11.7117763 12.5245264 12.367341
CV residual 0.1576225 0.1467808 -0.1120851 -0.4880821 0.1072349 0.328929
123 124 128 132 138 145
Predicted 12.30192745 12.2477655 12.3694474 12.1840929 12.3056748 12.2665084
cvpred 12.29582305 12.2371993 12.3684270 12.1679735 12.2975560 12.2562970
log(Price) 12.20557252 11.5617156 12.2548628 12.6915805 12.1007121 12.7938593
CV residual -0.09025053 -0.6754836 -0.1135642 0.5236069 -0.1968439 0.5375623
147 150 153 168 169 180
Predicted 12.1537539 12.2878244 12.28168923 12.1700290 12.13337909 12.3642145
cvpred 12.1330581 12.2625449 12.27217475 12.1522602 12.11407520 12.3541608
log(Price) 12.7158978 11.8130301 12.25486281 11.6952470 12.13618652 12.7742233
CV residual 0.5828397 -0.4495148 -0.01731194 -0.4570132 0.02211132 0.4200625
188 204 208 218 234
Predicted 12.4086644 12.03423827 12.1768922 12.31937256 12.493614071
cvpred 12.4199525 11.99035603 12.1534370 12.31229375 12.484992446
log(Price) 12.1007121 12.00456827 12.5567295 12.32385568 12.487485105
CV residual -0.3192403 0.01421224 0.4032925 0.01156193 0.002492659
253 260 263 266 269 276
Predicted 12.3150544 12.232200 12.3054508 12.3981008 12.3848043 12.35204917
cvpred 12.3045646 12.214580 12.2932172 12.3937067 12.3791721 12.33601169
log(Price) 12.7798731 12.983101 12.8531759 11.8130301 11.7440372 12.38971000
CV residual 0.4753085 0.768521 0.5599587 -0.5806766 -0.6351349 0.05369831
287 289 293 300 301 304
Predicted 12.4994931 12.4145051 12.25552988 12.2872341 12.2148190 12.5170477
cvpred 12.5166660 12.4015818 12.23751952 12.2725281 12.1934025 12.5374367
log(Price) 12.3013828 12.5245264 12.33270530 12.9360338 13.1123130 12.3149271
CV residual -0.2152832 0.1229445 0.09518577 0.6635057 0.9189105 -0.2225097
316 325 326 328 330 332
Predicted 12.2639077 12.3559700 12.2380622 12.545859 12.3043091 12.29833327
cvpred 12.2575465 12.3451686 12.2190891 12.557793 12.2925311 12.26261206
log(Price) 12.0317193 12.8615180 11.6526874 12.201060 12.1579323 12.31940133
CV residual -0.2258272 0.5163494 -0.5664017 -0.356733 -0.1345988 0.05678927
333 335 337 356 358
Predicted 12.2620937 12.65233224 12.2652149 12.54938693 12.39726598
cvpred 12.2466073 12.67820813 12.2461442 12.55859892 12.38869269
log(Price) 12.9480100 12.64432758 11.7360690 12.52452638 12.30138283
CV residual 0.7014027 -0.03388055 -0.5100751 -0.03407254 -0.08730986
361 363 373 374 385 398
Predicted 12.2719259 12.1616761 12.4504940 12.54263160 12.3662738 12.5703450
cvpred 12.2524862 12.1314741 12.4473430 12.54524048 12.3680313 12.5777668
log(Price) 13.1470560 12.2737313 13.0919042 12.48748510 11.9835539 12.8674711
CV residual 0.8945698 0.1422572 0.6445612 -0.05775538 -0.3844774 0.2897043
403 417 419 424 427 428
Predicted 12.2524611 12.3496671 12.7021367 12.2730312 12.4317658 12.4317658
cvpred 12.2299867 12.3379506 12.7348930 12.2518455 12.4197868 12.4197868
log(Price) 12.3673408 12.8992198 12.5061772 12.8212583 12.1172414 12.1172414
CV residual 0.1373541 0.5612692 -0.2287157 0.5694128 -0.3025454 -0.3025454
429 439 442 443 444 445
Predicted 12.387673 12.73817966 12.3310156 12.4988074 12.4019630 12.4284439
cvpred 12.379165 12.77497993 12.3132800 12.5200882 12.3931865 12.4188879
log(Price) 11.112448 12.69158046 12.5947306 11.8844890 12.6443276 11.6952470
CV residual -1.266717 -0.08339947 0.2814507 -0.6355991 0.2511411 -0.7236409
452 454 456 457 460 473
Predicted 12.7252598 12.3594470 12.5749239 12.5135250 12.610176 12.399989
cvpred 12.7586283 12.3450115 12.5806971 12.5279599 12.645798 12.378114
log(Price) 12.5425449 12.4780064 12.7454857 12.8609986 10.820038 13.527828
CV residual -0.2160834 0.1329949 0.1647887 0.3330388 -1.825759 1.149714
481 482 483 493 495 500
Predicted 12.5023649 12.3980996 12.4624665 12.6900535 12.41088298 12.4290644
cvpred 12.5128713 12.3958535 12.4695456 12.6753213 12.38567546 12.4294303
log(Price) 13.3999951 12.2060726 13.0170029 12.9945300 12.46843691 11.6082356
CV residual 0.8871238 -0.1897808 0.5474573 0.3192087 0.08276145 -0.8211946
504 506 513 515 518 519
Predicted 12.2125438 12.7856459 12.4382099 12.4274295 12.393616 12.351758
cvpred 12.1677988 12.7908360 12.4333971 12.4142631 12.366226 12.332841
log(Price) 12.4292162 12.5686303 13.2861815 12.9715405 12.194759 13.384574
CV residual 0.2614174 -0.2222058 0.8527844 0.5572774 -0.171467 1.051733
526 528 529 530 532
Predicted 12.5168228 12.4224586 12.2430069 12.494733801 12.73765886
cvpred 12.5246860 12.4061516 12.2098114 12.489336707 12.76650835
log(Price) 13.2267234 12.2922503 12.4292162 12.491251588 12.70987365
CV residual 0.7020374 -0.1139013 0.2194048 0.001914881 -0.05663469
538 547 550 556 561 565
Predicted 12.4081312 12.69824243 12.81122362 12.6682783 13.0300819 12.4805658
cvpred 12.3808656 12.72142687 12.81709114 12.7031500 13.0613206 12.4685453
log(Price) 12.5591913 12.62806706 12.78828827 12.1388639 12.5425449 12.8825822
CV residual 0.1783257 -0.09335981 -0.02880287 -0.5642861 -0.5187757 0.4140369
572 581 588 599 604 608
Predicted 12.4432749 12.7910910 12.5931852 12.6162584 12.8175832 12.611000
cvpred 12.4313119 12.8154738 12.6017543 12.6272963 12.8166950 12.608900
log(Price) 12.8103886 12.6915805 12.4371844 13.2339048 12.9633676 12.264214
CV residual 0.3790767 -0.1238933 -0.1645699 0.6066085 0.1466726 -0.344686
611 612 616 626 628
Predicted 12.7550624 12.56819305 12.85026114 12.6847869 12.6219111
cvpred 12.7797342 12.58360859 12.84247216 12.7129265 12.6305001
log(Price) 12.9116423 12.52815614 12.76568843 13.2533916 12.1547794
CV residual 0.1319081 -0.05545245 -0.07678373 0.5404652 -0.4757208
635 640 641 646 652 653
Predicted 12.95515442 12.5518171 12.6973204 12.95876297 12.5346850 12.717400
cvpred 12.97906867 12.5396461 12.7045264 13.00040233 12.5057795 12.734914
log(Price) 13.04979268 12.7868906 12.3059180 12.92391244 12.0435537 13.458836
CV residual 0.07072401 0.2472446 -0.3986084 -0.07648989 -0.4622258 0.723922
662 663 665 669 679 682
Predicted 12.90133135 12.810843 12.5053426 12.6248469 12.8336802 12.979862724
cvpred 12.93253200 12.849342 12.5008089 12.6322140 12.8607821 13.015770852
log(Price) 12.91164235 11.736069 13.0389818 13.0147782 12.6587394 13.016780615
CV residual -0.02088966 -1.113273 0.5381728 0.3825642 -0.2020427 0.001009763
696 700 711 715 717 723
Predicted 13.2444766 12.9022234 12.5700760 12.8535757 12.8911463 12.9636976
cvpred 13.2895262 12.9309965 12.5696507 12.8742420 12.9147004 12.9874698
log(Price) 12.9831013 13.1221634 11.6952470 12.6115378 13.0919042 13.1519222
CV residual -0.3064249 0.1911669 -0.8744036 -0.2627042 0.1772038 0.1644524
726 727 733 736 741 753
Predicted 12.5615807 12.9891918 12.7314653 12.9993280 12.73979387 12.7837777
cvpred 12.5427105 12.9855983 12.7305114 13.0108905 12.75126592 12.7854511
log(Price) 12.9945300 13.3228522 13.2360491 12.8942073 12.70654486 13.3645249
CV residual 0.4518195 0.3372539 0.5055378 -0.1166832 -0.04472106 0.5790739
756 757 762 764 775
Predicted 13.219571 13.21618250 13.12688354 13.0113093 12.91146346
cvpred 13.286438 13.23659417 13.15101501 13.0389910 12.92034742
log(Price) 13.028053 13.30468493 13.17685156 12.9360338 12.93603380
CV residual -0.258385 0.06809077 0.02583656 -0.1029572 0.01568638
777 787 788 789 797 803
Predicted 13.01417494 12.8833992 12.78481919 13.0790460 12.8071711 13.0299202
cvpred 13.04280424 12.8921684 12.79277353 13.1133560 12.8067604 13.0604618
log(Price) 12.97386337 12.6931177 12.87390202 12.8891695 13.2176736 13.9978321
CV residual -0.06894087 -0.1990507 0.08112849 -0.2241865 0.4109132 0.9373703
807 811 813 829 830 835
Predicted 12.572986 13.17270012 13.0831064 13.0136093 13.26190856 13.18669654
cvpred 12.535569 13.20372594 13.1033184 13.0137820 13.29181695 13.21153439
log(Price) 13.864301 13.27936713 13.2878778 13.8726052 13.33747476 13.23569206
CV residual 1.328732 0.07564119 0.1845594 0.8588232 0.04565781 0.02415767
839 841 843 847 849 860
Predicted 13.4368609 12.71303130 13.2312664 13.5273801 13.1666669 13.59142
cvpred 13.4961817 12.66998487 13.2564332 13.5783265 13.1914380 13.65127
log(Price) 13.6631749 12.61153775 13.1223634 13.3813373 14.0824796 13.17115
CV residual 0.1669932 -0.05844712 -0.1340698 -0.1969892 0.8910416 -0.48012
879 886 890 896 900 905
Predicted 13.8410251 14.158412 14.0283330 14.175024 13.9532632 13.854246
cvpred 13.8958736 14.234473 14.0821364 14.250186 13.9902296 13.846376
log(Price) 13.5144055 14.077875 13.8145101 13.158763 13.7953079 12.278393
CV residual -0.3814681 -0.156598 -0.2676263 -1.091423 -0.1949218 -1.567983
906 908
Predicted 14.3501720 14.610421
cvpred 14.3942129 14.687615
log(Price) 14.2222815 13.455401
CV residual -0.1719314 -1.232213
Sum of squares = 48.96 Mean square = 0.27 n = 183
fold 3
Observations in test set: 182
14 26 40 47 50 54
Predicted 11.8566357 12.1744819 12.0199565 11.8683917 12.2480701 12.034244
cvpred 11.8596290 12.1894391 12.0217207 11.8586061 12.2603872 12.030507
log(Price) 11.3850921 12.6765449 12.2783933 12.2307653 11.7675677 12.524526
CV residual -0.4745369 0.4871058 0.2566726 0.3721592 -0.4928195 0.494019
57 68 73 86 96 99
Predicted 12.12214 12.2580991 12.010909 12.3001732 12.2687839 12.45077673
cvpred 12.12534 12.2699464 12.007553 12.3135999 12.2794946 12.46635640
log(Price) 11.12726 11.8705999 10.596635 11.9183906 11.8844890 12.41268023
CV residual -0.99808 -0.3993465 -1.410918 -0.3952093 -0.3950056 -0.05367617
107 112 113 119 126 130
Predicted 11.96798 12.2229023 12.308826 12.2226334 12.23557863 12.276179
cvpred 11.96418 12.2141687 12.309149 12.2139051 12.22609449 12.286279
log(Price) 12.76569 11.7117763 12.429216 11.8670973 12.15477935 10.915088
CV residual 0.80151 -0.5023924 0.120067 -0.3468078 -0.07131514 -1.371191
134 139 156 158 160 165
Predicted 11.706123 12.2883007 12.402385 12.23122995 12.4283712 12.1873379
cvpred 11.683659 12.2970951 12.416149 12.24093387 12.4541619 12.1873076
log(Price) 12.144197 11.5617156 11.849398 12.19095901 11.9447079 12.0725413
CV residual 0.460538 -0.7353795 -0.566751 -0.04997486 -0.5094541 -0.1147663
166 167 173 175 183 190
Predicted 12.0643790 12.1989100 12.27266807 12.2344763 12.1968693 12.2690017
cvpred 12.0639328 12.2080719 12.28776452 12.2577933 12.2058387 12.2755972
log(Price) 11.3621026 12.8212583 12.20607265 11.8947807 12.3327053 12.3800260
CV residual -0.7018302 0.6131864 -0.08169187 -0.3630126 0.1268666 0.1044288
192 199 209 212 213 214
Predicted 12.2782694 12.3639664 12.2718530 12.4609215 12.243416 12.1981457
cvpred 12.2985907 12.3769760 12.2866383 12.4704041 12.252246 12.2001659
log(Price) 12.7038130 12.2160230 11.8493977 12.9384405 12.703813 12.1001564
CV residual 0.4052223 -0.1609531 -0.4372406 0.4680365 0.451567 -0.1000094
215 219 223 231 232 233
Predicted 12.1390653 12.2623595 12.3356568 12.7789603 12.5119226 12.41681861
cvpred 12.1470037 12.2690619 12.3417753 12.8444699 12.5226623 12.43266366
log(Price) 11.3504065 12.8479265 11.7076695 12.5776362 12.6603279 12.45097769
CV residual -0.7965971 0.5788647 -0.6341057 -0.2668337 0.1376656 0.01831403
238 242 245 251 255 257
Predicted 12.50158160 12.4140148 12.24294101 12.49205 12.4978190 12.4995838
cvpred 12.51131089 12.4090754 12.25013621 12.49638 12.5138472 12.5228998
log(Price) 12.45293272 12.2548628 12.34583459 12.20607 12.3238557 12.2783933
CV residual -0.05837817 -0.1542126 0.09569838 -0.29031 -0.1899915 -0.2445065
270 274 278 288 290 292
Predicted 12.3865582 12.33771828 12.5029454 12.2959394 12.5239293 12.6260706
cvpred 12.3914199 12.32945248 12.5159590 12.3072587 12.5429910 12.6361924
log(Price) 11.8493977 12.38797745 12.4090135 13.1342919 12.3458346 12.4081968
CV residual -0.5420222 0.05852496 -0.1069455 0.8270332 -0.1971564 -0.2279956
294 297 307 309 312 318
Predicted 12.5105429 12.486108296 12.5226029 12.3121106 12.35484999 12.446225
cvpred 12.5193481 12.499526100 12.5424449 12.3227739 12.36449109 12.461389
log(Price) 12.4086052 12.491251588 12.5245264 11.8130301 12.45683136 11.288531
CV residual -0.1107429 -0.008274512 -0.0179185 -0.5097439 0.09234027 -1.172858
334 338 340 343 344 350
Predicted 12.3219910 12.3927462 12.43677486 12.6209872 12.4732208 12.41220857
cvpred 12.3325846 12.4012319 12.44539197 12.6470332 12.4822000 12.41467814
log(Price) 13.1421660 12.0940231 12.47990931 12.3966930 12.3282903 12.47609978
CV residual 0.8095814 -0.3072088 0.03451734 -0.2503402 -0.1539098 0.06142164
366 371 376 377 378 379
Predicted 12.47720251 12.57265679 12.4251303 12.4958679 12.3217611 11.979712
cvpred 12.48560509 12.58259582 12.4431628 12.5086835 12.3240751 11.962098
log(Price) 12.54966235 12.63785506 12.5496623 12.6297051 13.2621253 12.936034
CV residual 0.06405726 0.05525924 0.1064996 0.1210215 0.9380502 0.973936
382 384 399 400 401 404
Predicted 12.3606195 12.5754106 12.5703413 12.64320717 12.2977636 12.2143689
cvpred 12.3713716 12.5925830 12.5934450 12.66533321 12.2930317 12.2102173
log(Price) 11.7745202 12.3673408 12.8674711 12.61818230 12.1164214 12.3673408
CV residual -0.5968514 -0.2252422 0.2740262 -0.04715091 -0.1766103 0.1571235
408 411 414 416 420 431
Predicted 12.3464717 12.460358 12.3561950 12.5351772 12.5683634 12.4645148
cvpred 12.3537186 12.448002 12.3641559 12.5583215 12.6061575 12.4821237
log(Price) 13.1203614 12.860999 12.5637471 12.8866410 12.3925522 12.2783933
CV residual 0.7666428 0.412997 0.1995912 0.3283195 -0.2136053 -0.2037303
432 436 447 448 450 451
Predicted 12.5166584 12.466111 12.500366 12.78195557 12.1690140 12.1690172
cvpred 12.5224657 12.472223 12.532832 12.80008213 12.1586099 12.1586134
log(Price) 12.2060726 12.154779 11.849398 12.81967595 12.9598444 12.9598444
CV residual -0.3163931 -0.317444 -0.683434 0.01959382 0.8012346 0.8012311
455 459 463 467 469 472
Predicted 12.38877344 12.4507583 12.48941246 12.5795687 12.4113792 12.5396943
cvpred 12.38834396 12.4490171 12.49760424 12.5803433 12.4262374 12.5532028
log(Price) 12.44901882 11.7752897 12.44901882 13.1900220 12.9831013 12.3238557
CV residual 0.06067487 -0.6737274 -0.04858541 0.6096788 0.5568639 -0.2293471
488 490 502 503 508 512
Predicted 12.3779137 12.5154738 12.4176450 12.5120612 12.560948 12.7215929
cvpred 12.3766009 12.5332694 12.4310811 12.5162018 12.560689 12.7426135
log(Price) 13.2447580 12.2060726 12.5425449 12.8739020 12.834415 12.6115378
CV residual 0.8681571 -0.3271968 0.1114638 0.3577002 0.273726 -0.1310757
517 523 525 527 541 546
Predicted 12.248766 12.815173 12.6551453 12.4373894 12.684791565 12.847366
cvpred 12.240094 12.832057 12.6534131 12.4445242 12.685994034 12.890563
log(Price) 10.714418 12.691273 13.0815414 13.0167806 12.676076275 11.594505
CV residual -1.525676 -0.140784 0.4281282 0.5722564 -0.009917759 -1.296057
548 549 560 564 571 576
Predicted 12.356051 12.1957939 12.77441499 12.64032317 12.77308806 12.3655041
cvpred 12.352404 12.1696343 12.79606448 12.65965142 12.78873620 12.3538277
log(Price) 13.235692 11.9183906 12.72188581 12.70684793 12.84792653 11.7791285
CV residual 0.883288 -0.2512437 -0.07417867 0.04719652 0.05919033 -0.5746991
580 582 583 584 586 598
Predicted 12.523079 12.6526968 13.12089404 12.6972895 12.6972895 12.678950
cvpred 12.539638 12.6614933 13.15945779 12.7113073 12.7113073 12.710174
log(Price) 11.225243 12.4950039 13.24634936 12.4684369 12.4684369 10.571317
CV residual -1.314395 -0.1664894 0.08689156 -0.2428704 -0.2428704 -2.138857
601 606 617 619 622 624
Predicted 12.5096900 12.7244043 12.80341254 12.76119063 12.7931078 12.5277757
cvpred 12.5179930 12.7393275 12.81438419 12.77813146 12.8089230 12.5354200
log(Price) 12.0435537 12.0317193 12.84792653 12.73670090 13.2085411 13.0919042
CV residual -0.4744393 -0.7076083 0.03354234 -0.04143056 0.3996181 0.5564841
632 644 648 649 650 654
Predicted 12.7037080 12.9125643 12.5969308 12.952479 12.9314471 12.72751392
cvpred 12.6960852 12.9215200 12.5766521 12.974088 12.9524128 12.71967627
log(Price) 13.2878778 12.7656884 12.0435537 13.151922 13.1519222 12.62806706
CV residual 0.5917926 -0.1558316 -0.5330984 0.177834 0.1995093 -0.09160921
655 656 659 660 673 685
Predicted 13.107844 12.8606145 12.6382043 12.9053353 12.5147047 13.1870130
cvpred 13.137760 12.8733613 12.6413705 12.9194193 12.5026576 13.2316211
log(Price) 12.677029 12.4490188 13.3534751 13.2176736 13.0069525 12.2499938
CV residual -0.460731 -0.4243425 0.7121046 0.2982543 0.5042949 -0.9816273
709 712 714 716 720 724
Predicted 12.7948639 12.6402289 13.0281288 12.6940400 13.0268740 12.4261393
cvpred 12.7847733 12.6560906 13.0489859 12.7008925 13.0340385 12.4114941
log(Price) 12.6760763 12.8866410 13.3326243 13.3931536 13.6802634 12.1547794
CV residual -0.1086971 0.2305504 0.2836384 0.6922611 0.6462249 -0.2567147
731 740 743 750 751 752
Predicted 12.5644687 13.01547636 12.9411822 12.9862611 12.9711884 12.972370
cvpred 12.5602379 13.01901605 12.9460377 12.9879494 12.9847757 12.975542
log(Price) 11.8235596 12.96453929 13.1615841 12.8452915 13.5278285 13.358226
CV residual -0.7366783 -0.05447676 0.2155464 -0.1426579 0.5430528 0.382684
755 761 763 766 768 769
Predicted 12.7520864 12.9766828 12.8930458 13.0194556 12.86764640 12.7835935
cvpred 12.7576434 12.9762377 12.8744274 13.0204907 12.84978580 12.7721167
log(Price) 13.7101500 12.4490188 13.6452855 13.7101500 12.89921983 13.1478362
CV residual 0.9525067 -0.5272189 0.7708582 0.6896593 0.04943403 0.3757195
779 784 804 815 824 825
Predicted 13.0621636 12.9929441 12.7164383 13.070105 13.4298278 13.1631032
cvpred 13.0587098 12.9975071 12.6887827 13.079127 13.4509958 13.1511434
log(Price) 13.3129837 13.4730202 11.9511804 14.221042 13.5823167 13.0389818
CV residual 0.2542739 0.4755131 -0.7376023 1.141916 0.1313209 -0.1121616
827 828 834 840 846 853
Predicted 13.3571895 13.2984823 13.1286275 13.23651612 13.352201 13.3332843
cvpred 13.3663217 13.3036126 13.1247607 13.21855203 13.350710 13.3194395
log(Price) 13.0872024 13.0710701 13.4588356 13.30460160 13.582948 13.4444469
CV residual -0.2791193 -0.2325425 0.3340749 0.08604956 0.232238 0.1250073
854 858 862 875 876 877
Predicted 13.30252998 13.3195360 13.5340237 13.58406521 13.7905952 13.6655631
cvpred 13.30963115 13.3195599 13.5232084 13.56507530 13.7862451 13.6483937
log(Price) 13.39239051 14.1519828 14.1156152 13.53975706 14.6039679 13.0879790
CV residual 0.08275936 0.8324229 0.5924068 -0.02531824 0.8177228 -0.5604148
878 881 882 883 887
Predicted 13.4390232 13.7618474833 13.930273 13.7747339 13.9313889
cvpred 13.4112918 13.7458244955 13.934255 13.7469303 13.8973918
log(Price) 14.1696824 13.7450880937 13.387646 13.4588356 13.5922420
CV residual 0.7583906 -0.0007364018 -0.546609 -0.2880947 -0.3051498
895 899 909
Predicted 14.11845644 14.0696241 14.115175
cvpred 14.08047414 14.0049599 14.051734
log(Price) 14.09314229 13.8155106 13.840203
CV residual 0.01266815 -0.1894493 -0.211531
Sum of squares = 50.16 Mean square = 0.28 n = 182
fold 4
Observations in test set: 182
2 6 7 15 16 19
Predicted 11.8915902 11.9759559 12.1516293 12.0086106 11.90046871 11.7827223
cvpred 11.9057894 11.9966694 12.1895857 12.0286993 11.92397923 11.8140251
log(Price) 12.0317193 12.3779229 11.8635823 12.5515223 11.84939770 12.0725413
CV residual 0.1259299 0.3812535 -0.3260034 0.5228231 -0.07458153 0.2585161
30 33 35 41 51 55
Predicted 12.2152320 12.1244871 12.0917943 11.9776580 12.2485408 12.1767679
cvpred 12.2205875 12.1491020 12.1180051 11.9945892 12.2549291 12.1782858
log(Price) 11.9569701 11.3083583 11.5898865 12.3673408 11.9953516 12.0137008
CV residual -0.2636174 -0.8407437 -0.5281186 0.3727516 -0.2595775 -0.1645851
63 64 70 79 83 84
Predicted 12.0815410 12.1060131 12.28028388 12.255793 12.21185693 12.0460701
cvpred 12.1041070 12.1217595 12.28140947 12.262202 12.22053090 12.0646840
log(Price) 11.9860492 11.6036798 12.23076526 11.407565 12.24288662 11.6587559
CV residual -0.1180578 -0.5180797 -0.05064421 -0.854637 0.02235572 -0.4059281
93 95 100 103 106
Predicted 11.9805585 11.98748091 12.27325187 12.25541227 12.2103415
cvpred 12.0006356 12.00626004 12.28042938 12.25315419 12.2122161
log(Price) 12.1007121 11.98230390 12.25247902 12.17561344 12.6760763
CV residual 0.1000765 -0.02395614 -0.02795036 -0.07754075 0.4638601
118 120 135 141 144 149
Predicted 11.8661893 12.2297616 12.26259634 12.005893 12.1103548 12.006003
cvpred 11.8756003 12.2663870 12.26640456 12.002085 12.0991657 12.025150
log(Price) 12.3013828 11.9183906 12.19349386 12.292250 12.7938593 11.418615
CV residual 0.4257825 -0.3479965 -0.07291069 0.290165 0.6946936 -0.606535
163 164 174 178 179 184
Predicted 12.4035885 12.4096949 12.785447 12.1375710 12.64382021 12.4061186
cvpred 12.3873561 12.3940259 12.755141 12.1362667 12.63227278 12.4007824
log(Price) 12.0725413 12.1415341 12.538967 12.4490188 12.56024446 13.0731731
CV residual -0.3148148 -0.2524918 -0.216174 0.3127521 -0.07202832 0.6723908
189 191 194 198 210 221
Predicted 12.2761454 12.2136840 12.2262861 12.35175069 12.3286620 12.09821878
cvpred 12.3070635 12.2083690 12.2252007 12.33034012 12.3346137 12.09247545
log(Price) 12.5776362 11.4668815 12.8479265 12.27839331 12.2010601 12.11176197
CV residual 0.2705727 -0.7414875 0.6227258 -0.05194682 -0.1335536 0.01928652
222 226 227 228 230 237
Predicted 12.43382021 12.3641968 12.3029243 12.3029243 12.3137690 12.4130377
cvpred 12.41457419 12.3652806 12.3063997 12.3063997 12.3108123 12.4022017
log(Price) 12.48748510 12.6726329 12.1495023 12.1495023 12.8452915 12.7218858
CV residual 0.07291092 0.3073523 -0.1568974 -0.1568974 0.5344792 0.3196841
239 240 246 252 261
Predicted 12.52568525 12.09062 12.46788951 12.50076003 12.41808023
cvpred 12.53407988 12.08404 12.44595046 12.51282689 12.42386102
log(Price) 12.57729131 12.29683 12.36734079 12.52815614 12.50617724
CV residual 0.04321144 0.21279 -0.07860966 0.01532925 0.08231621
275 279 282 283 299 303
Predicted 12.30822782 12.3056439 12.4183430 12.3736531 12.3223746 12.2944633
cvpred 12.34575779 12.3046366 12.4226790 12.3606992 12.3195561 12.2948251
log(Price) 12.33270530 11.7597855 11.8810348 12.5245264 11.7752897 12.1547794
CV residual -0.01305249 -0.5448511 -0.5416442 0.1638272 -0.5442663 -0.1400458
314 317 320 321 323 329
Predicted 12.1087380 12.2615891 12.3496821 12.3089015 12.486843 12.3136985
cvpred 12.1004179 12.2853188 12.3531518 12.3099482 12.472409 12.3142377
log(Price) 12.3983198 12.0045683 12.4680522 13.1223634 11.407565 12.4645833
CV residual 0.2979019 -0.2807505 0.1149004 0.8124152 -1.064844 0.1503457
348 352 357 360 365
Predicted 12.46072343 12.5959796 12.5242606 12.5714139 12.47720251
cvpred 12.46670187 12.5988186 12.5355821 12.5627014 12.48258493
log(Price) 12.42921620 12.1807548 12.3171667 12.1807548 12.54966235
CV residual -0.03748567 -0.4180638 -0.2184154 -0.3819466 0.06707742
372 380 391 393 396 407
Predicted 12.23227541 12.58126745 12.58272550 12.6338519 12.257267 12.3882518
cvpred 12.23123774 12.57251055 12.59815446 12.6276173 12.277142 12.3927065
log(Price) 12.31043266 12.48748510 12.52452638 12.7656884 10.819778 12.8583978
CV residual 0.07919492 -0.08502544 -0.07362809 0.1380711 -1.457363 0.4656914
413 415 418 421 430 433
Predicted 12.316608 12.5351772 12.5046148 12.7721848 12.45870854 12.7159295
cvpred 12.313455 12.5123186 12.4801462 12.7726280 12.46082371 12.7102957
log(Price) 12.141534 12.8866410 12.2548628 13.2085411 12.42881612 12.5602445
CV residual -0.171921 0.3743224 -0.2252834 0.4359131 -0.03200759 -0.1500512
453 458 461 466 489
Predicted 12.68723072 12.3417729 12.4497874 12.6448532 12.67245344
cvpred 12.66809535 12.3385872 12.4501121 12.6268252 12.65853614
log(Price) 12.73670090 12.1871446 12.5598935 13.1223634 12.69158046
CV residual 0.06860555 -0.1514426 0.1097814 0.4955382 0.03304432
494 501 505 507 520 522
Predicted 12.37956481 12.1010707 12.5011575 12.63866003 12.3907659 12.4843894
cvpred 12.37900953 12.1155818 12.5033573 12.65265067 12.3591719 12.4605333
log(Price) 12.46843691 11.9829291 11.9640011 12.61153775 12.0137008 11.9117016
CV residual 0.08942738 -0.1326527 -0.5393562 -0.04111292 -0.3454711 -0.5488318
524 534 536 542 544 545
Predicted 12.4255770 12.434571 12.6021151 12.6961451 12.7374556 12.6714546
cvpred 12.4176164 12.442102 12.5774426 12.6801993 12.7474024 12.6891848
log(Price) 13.0497927 12.128111 13.0269532 13.2963167 13.0898402 12.5425449
CV residual 0.6321763 -0.313991 0.4495106 0.6161173 0.3424378 -0.1466399
551 553 568 569 574 578
Predicted 12.8244475 12.4654943 12.7794257 12.71445845 12.4390536 12.65681999
cvpred 12.8217446 12.4593737 12.7675267 12.72432584 12.4145501 12.66900673
log(Price) 12.7882883 12.7938593 12.9336213 12.63947712 12.6443276 12.71138309
CV residual -0.0334563 0.3344856 0.1660946 -0.08484871 0.2297775 0.04237636
587 591 592 596 600 602
Predicted 12.900931 12.8120231 12.7155320 12.62899653 12.3888183 12.4080890
cvpred 12.883322 12.8037829 12.7349210 12.61520862 12.3594616 12.3957903
log(Price) 13.049793 13.2085411 13.2912619 12.56024446 12.7656884 12.7656884
CV residual 0.166471 0.4047582 0.5563409 -0.05496416 0.4062269 0.3698982
603 607 615 618 621 634
Predicted 12.4579908 12.86468343 12.5827210 12.7204259 12.7545096 12.8443675
cvpred 12.4516304 12.86209467 12.5591297 12.7371974 12.7350539 12.8212938
log(Price) 11.9829291 12.80765263 13.0540845 13.0972507 12.6915805 12.9515751
CV residual -0.4687013 -0.05444203 0.4949548 0.3600533 -0.0434734 0.1302812
637 639 642 643 645 647
Predicted 12.6580813 12.5256661 12.295753 12.8002046 12.6078610 12.49253189
cvpred 12.6314156 12.5225857 12.286738 12.7871916 12.6095299 12.48295366
log(Price) 12.2060726 13.4588356 10.657259 12.5776362 12.9831013 12.46843691
CV residual -0.4253429 0.9362499 -1.629478 -0.2095554 0.3735714 -0.01451675
651 677 678 680 681 683
Predicted 12.6117608 12.8738947 12.8699821 12.7018855 12.8282791 12.9488692
cvpred 12.5845792 12.8467531 12.8531377 12.7069118 12.8101657 12.9138631
log(Price) 12.8713346 13.7642173 12.4490188 12.6014874 12.4874851 12.9945300
CV residual 0.2867554 0.9174641 -0.4041189 -0.1054244 -0.3226805 0.0806669
697 698 702 703 705 706
Predicted 12.9371912 12.7727647 12.9629277 12.73304483 12.7877968 12.7400919
cvpred 12.9342883 12.7201674 12.9622101 12.73616854 12.8020403 12.7505497
log(Price) 12.7798731 13.0867362 13.2332784 12.65873936 12.6115378 12.5425449
CV residual -0.1544152 0.3665688 0.2710683 -0.07742918 -0.1905025 -0.2080048
707 708 713 719 725
Predicted 12.6793710 12.7678763 12.686021535 12.9695512 12.5615807
cvpred 12.6829819 12.7467656 12.684120378 12.9603742 12.5595087
log(Price) 12.8076526 12.4288161 12.682306825 13.6802634 12.9945300
CV residual 0.1246708 -0.3179495 -0.001813554 0.7198892 0.4350213
728 729 730 734 735
Predicted 12.70015408 12.77979040 12.7797470 12.9695661 12.9934898
cvpred 12.65531681 12.78916343 12.7644588 12.9670493 12.9932446
log(Price) 12.71739814 12.72188581 12.5776362 12.8531759 13.2356921
CV residual 0.06208134 -0.06727761 -0.1868226 -0.1138734 0.2424475
738 739 745 746 748 754
Predicted 12.72726348 13.0742187 12.6801781 13.08502478 13.0274115 12.4292219
cvpred 12.70177436 13.0362221 12.6489017 13.05302812 13.0259548 12.4066139
log(Price) 12.71844707 13.4224680 13.2621253 13.08154138 13.4781241 12.7656884
CV residual 0.01667271 0.3862459 0.6132236 0.02851326 0.4521693 0.3590745
759 767 773 774 776 782
Predicted 12.6519538 13.0194564 13.0183866 12.839862 12.7364369 12.8648514
cvpred 12.6464108 13.0105719 12.9485180 12.818408 12.7030719 12.8585435
log(Price) 12.8479265 13.7101500 13.6109434 11.798104 13.1843988 12.0435537
CV residual 0.2015158 0.6995782 0.6624254 -1.020304 0.4813269 -0.8149898
791 801 806 808 810 814
Predicted 13.1533816 13.1430611 13.1319128 13.05621319 13.14704223 13.1726241
cvpred 13.1326093 13.1274794 13.1280999 13.03747589 13.13723235 13.1685728
log(Price) 13.2577680 12.4130868 13.0192226 13.00470533 13.12236338 12.8967167
CV residual 0.1251587 -0.7143926 -0.1088772 -0.03277056 -0.01486898 -0.2718561
820 821 822 823 836 845
Predicted 13.0832965 13.16855874 13.0276411 13.226954 13.1470704 13.2617857
cvpred 13.0327821 13.15810530 13.0383969 13.215713 13.0969166 13.2470215
log(Price) 13.5923670 13.07107008 13.1615841 13.015891 13.7536352 13.4135393
CV residual 0.5595849 -0.08703522 0.1231872 -0.199822 0.6567186 0.1665179
850 851 852 856 857 861
Predicted 13.1666669 13.1961869 13.4605423 13.4586282 13.3195346 13.3142576
cvpred 13.1207025 13.1359276 13.4383519 13.4074530 13.2673534 13.3032889
log(Price) 14.0817136 13.8402032 14.1749317 13.7642173 14.1519828 13.0389818
CV residual 0.9610111 0.7042756 0.7365798 0.3567643 0.8846294 -0.2643072
864 870 871 884 885 892
Predicted 13.5010313 13.40908362 13.5854953 14.1383372 13.6571194 14.1850146
cvpred 13.4691546 13.39230016 13.5526763 14.0771780 13.6292449 14.1576370
log(Price) 13.2445810 13.30468493 13.3847276 14.2917447 13.7901927 14.7297993
CV residual -0.2245736 -0.08761523 -0.1679487 0.2145668 0.1609478 0.5721623
898 910
Predicted 14.12289916 14.77374158
cvpred 14.02426311 14.71840056
log(Price) 13.95527250 14.80876233
CV residual -0.06899061 0.09036177
Sum of squares = 31.95 Mean square = 0.18 n = 182
fold 5
Observations in test set: 182
3 8 9 10 11 12
Predicted 11.75992086 11.9376162 12.03888 11.955374 11.9865031 12.0630358
cvpred 11.80026834 11.9462316 12.04311 11.962677 11.9839760 12.0539365
log(Price) 11.78295260 11.6952470 12.33271 11.018629 11.5627722 11.4403548
CV residual -0.01731574 -0.2509846 0.28960 -0.944048 -0.4212038 -0.6135818
17 20 24 34 36 42
Predicted 12.05013517 11.6872875 11.8962825 12.08352943 12.0900404 11.9608394
cvpred 12.04520139 11.7656649 11.9235171 12.08110334 12.0865670 11.9825513
log(Price) 12.10071213 11.6952470 11.4075649 12.10071213 11.8122890 12.3458346
CV residual 0.05551074 -0.0704179 -0.5159521 0.01960879 -0.2742779 0.3632833
45 56 67 71 72 74
Predicted 12.14085594 12.1307072 12.2580991 12.2730231 12.2106680 12.2698332
cvpred 12.12295784 12.1161203 12.2244363 12.2510219 12.1857278 12.2263337
log(Price) 12.21602298 11.5129255 11.8705999 11.9766595 11.6217799 11.3504065
CV residual 0.09306513 -0.6031948 -0.3538364 -0.2743624 -0.5639479 -0.8759272
77 80 82 85 88 94
Predicted 11.9474428 12.255313 12.0528144 12.1363388 12.2438713 11.9733032
cvpred 11.9832446 12.223924 12.0751471 12.1268505 12.2307087 12.0118213
log(Price) 12.0137008 11.171139 12.3488734 11.9953516 12.3458346 11.4721035
CV residual 0.0304562 -1.052785 0.2737263 -0.1314989 0.1151258 -0.5397178
105 117 121 125 136 137
Predicted 12.2862457 12.36121900 12.192450 12.1752262 12.1949759 12.050132
cvpred 12.2548634 12.31455633 12.180303 12.1822185 12.1847533 12.078789
log(Price) 11.7519424 12.36734079 11.849398 11.6952470 12.1007121 12.441145
CV residual -0.5029211 0.05278446 -0.330905 -0.4869715 -0.0840412 0.362356
143 152 154 157 159 161
Predicted 12.0750753 12.1082692 12.43570286 12.495383 12.2706974 12.0673839
cvpred 12.1009810 12.1301557 12.36896459 12.431602 12.2602835 12.0982482
log(Price) 12.2307653 12.4126802 12.27839331 13.872989 12.1547794 11.8913619
CV residual 0.1297843 0.2825246 -0.09057128 1.441387 -0.1055041 -0.2068863
162 170 177 193 196 200
Predicted 12.2099184 12.4401743 12.150662 12.2849483 12.3517786 12.0150510
cvpred 12.2027516 12.3976689 12.165191 12.2851382 12.3269296 12.0678182
log(Price) 12.4490188 12.2783933 11.976659 12.0435537 12.4874851 11.9640011
CV residual 0.2462672 -0.1192756 -0.188531 -0.2415845 0.1605555 -0.1038171
202 205 206 211 216
Predicted 12.2499932 12.3433813 12.2734610 12.23776670 12.352154837
cvpred 12.2392678 12.3216077 12.2642217 12.23574617 12.330865658
log(Price) 12.2060726 12.4490188 12.3883942 12.17044547 12.323855681
CV residual -0.0331952 0.1274111 0.1241725 -0.06530071 -0.007009977
220 224 225 241 244 247
Predicted 11.9552294 12.4303711 12.5253520 12.2424945 12.2811965 12.2411648
cvpred 12.0173347 12.3919239 12.4706080 12.2449105 12.2726529 12.2446127
log(Price) 11.5991032 12.5776362 12.7938593 12.7218858 11.8837991 13.0335322
CV residual -0.4182315 0.1857124 0.3232514 0.4769753 -0.3888538 0.7889195
254 256 259 262 264 265
Predicted 12.27053 12.1030499 12.266058 12.0576746 12.3054508 12.2849462
cvpred 12.26972 12.1416123 12.253690 12.1001589 12.3001078 12.2881446
log(Price) 10.81978 11.9015835 9.210340 12.7218858 12.8531759 12.4211840
CV residual -1.44994 -0.2400289 -3.043349 0.6217269 0.5530681 0.1330394
273 284 298 305 310 315
Predicted 12.343450638 12.2559676 12.1632484 12.5170477 12.2359326 12.5824782
cvpred 12.341593604 12.2625604 12.1925803 12.4631320 12.2547709 12.5315654
log(Price) 12.345834588 12.4292162 11.8844890 12.3149271 11.8189385 12.9099743
CV residual 0.004240984 0.1666558 -0.3080912 -0.1482049 -0.4358324 0.3784089
319 322 324 327 331
Predicted 12.3089015 12.3498395 12.47740564 12.2647517 12.445409688
cvpred 12.3112059 12.3450270 12.44605779 12.2762655 12.422287290
log(Price) 13.1223634 12.4680522 12.51355735 13.0540845 12.429216197
CV residual 0.8111574 0.1230253 0.06749956 0.7778191 0.006928907
339 342 345 346 347 349
Predicted 12.5516742 12.49794 12.37840960 12.3755292 12.596160 12.1133467
cvpred 12.4789264 12.45818 12.37330917 12.3711240 12.548607 12.1608333
log(Price) 12.9715405 11.39639 12.34583459 12.1858699 12.736701 11.6526874
CV residual 0.4926141 -1.06179 -0.02747458 -0.1852541 0.188094 -0.5081459
351 354 355 364 367
Predicted 12.2723027 12.4601693 12.54938693 12.3768478 12.221536125
cvpred 12.2875350 12.4383526 12.51141601 12.3754743 12.247574487
log(Price) 12.6112044 12.6352543 12.52452638 12.8479265 12.254386506
CV residual 0.3236694 0.1969016 0.01311036 0.4724522 0.006812019
369 381 383 386 389 394
Predicted 12.44767983 12.58126745 12.3707733 12.287699 12.4039806 12.5751644
cvpred 12.43452519 12.53394130 12.3744674 12.293215 12.4034276 12.5277878
log(Price) 12.34147728 12.48748510 12.7541941 12.138864 12.1172414 12.9116423
CV residual -0.09304791 -0.04645619 0.3797266 -0.154351 -0.2861861 0.3838546
402 405 410 422 423 425
Predicted 12.2812029 12.3996923 12.4528569 12.4955526 12.3140934 12.3498458
cvpred 12.3052141 12.4032254 12.4483708 12.4716225 12.3355364 12.3656884
log(Price) 12.1112124 11.7752897 12.2452934 13.1223634 13.0058296 13.2445810
CV residual -0.1940017 -0.6279356 -0.2030774 0.6507409 0.6702932 0.8788926
426 435 437 446 449 462
Predicted 12.4651388 12.3487127 12.368810 12.2838549 12.1690140 12.38771971
cvpred 12.4566276 12.3668676 12.379175 12.3278136 12.2296640 12.40464247
log(Price) 13.2176372 12.3081779 13.392391 12.0610469 12.9598444 12.32385568
CV residual 0.7610096 -0.0586897 1.013215 -0.2667667 0.7301804 -0.08078679
464 470 474 475 476 477
Predicted 12.3828100 12.3925596 12.5690778 12.4834784 12.309038 12.80981985
cvpred 12.4011640 12.4248505 12.5527196 12.4686746 12.347592 12.73787701
log(Price) 12.0610469 12.9831013 12.3673408 13.0170029 12.721886 12.70381303
CV residual -0.3401171 0.5582508 -0.1853788 0.5483283 0.374294 -0.03406398
478 491 492 496 498 509
Predicted 12.81809125 12.3781446 12.4010989 12.3960835 12.76782054 12.4114527
cvpred 12.74558013 12.4039864 12.4093545 12.4235518 12.70794422 12.4256473
log(Price) 12.77987307 12.6491546 11.8130301 12.0076217 12.80490915 12.6915805
CV residual 0.03429294 0.2451682 -0.5963244 -0.4159301 0.09696492 0.2659332
511 514 531 537 539
Predicted 12.465356697 12.4382099 12.44058437 12.6021181 12.3281511
cvpred 12.474844253 12.4435734 12.45791899 12.5802479 12.3818764
log(Price) 12.481808647 13.2861815 12.55143383 13.0269532 12.5741820
CV residual 0.006964394 0.8426081 0.09351484 0.4467053 0.1923055
540 554 557 558 559 563
Predicted 12.5163410 12.45662025 12.473256 12.781150 12.68689835 12.2827448
cvpred 12.5145322 12.47830226 12.484073 12.736073 12.67120404 12.3292344
log(Price) 13.2445810 12.44114477 13.514405 12.601487 12.69158046 11.9829291
CV residual 0.7300488 -0.03715749 1.030333 -0.134586 0.02037642 -0.3463053
566 573 593 597 614 620
Predicted 12.6907956 12.86843071 12.4415948 12.7025061 12.84974719 12.6619187
cvpred 12.6572682 12.80991554 12.4805671 12.6837409 12.80610063 12.6399905
log(Price) 12.4130868 12.76540268 11.9951973 12.8346813 12.85134175 12.0137008
CV residual -0.2441813 -0.04451286 -0.4853698 0.1509404 0.04524111 -0.6262897
625 627 629 630 636
Predicted 12.5277780 1.290960e+01 12.7812851 12.6636231 12.44197948
cvpred 12.5499510 1.286092e+01 12.7513730 12.6588276 12.50499644
log(Price) 13.0919042 1.286100e+01 13.0527989 12.8557903 12.53896706
CV residual 0.5419532 7.874104e-05 0.3014259 0.1969626 0.03397062
657 664 668 670 674 686
Predicted 12.7133026 12.7478699 12.8860018 12.5778870 12.7595679 12.1156125
cvpred 12.7219881 12.7536157 12.8544207 12.6186261 12.7510581 12.2598902
log(Price) 12.9480100 13.2836315 12.5061772 12.3544927 12.6443276 12.6539585
CV residual 0.2260219 0.5300158 -0.3482434 -0.2641334 -0.1067305 0.3940683
687 688 689 692 699 701
Predicted 12.581827 12.8018759 12.4757519 12.9090554 12.7923639 12.6815537
cvpred 12.617516 12.8035370 12.5352325 12.8528849 12.7868652 12.7009704
log(Price) 12.873902 12.9715405 11.9183906 12.0552498 12.5245264 12.8942073
CV residual 0.256386 0.1680035 -0.6168419 -0.7976352 -0.2623389 0.1932368
710 718 721 732 742 744
Predicted 12.7164834 12.9367123 12.8954374 12.9465344 12.9280578 12.9464539
cvpred 12.7203514 12.9017251 12.8749536 12.9303983 12.9183879 12.9348325
log(Price) 12.3715871 13.5529763 12.5425449 13.3689109 13.4224680 13.2725060
CV residual -0.3487643 0.6512512 -0.3324088 0.4385126 0.5040801 0.3376735
749 758 765 770 780 785
Predicted 13.0960462 12.8489380 12.93054433 12.8230177 13.09165382 12.9929470
cvpred 13.0528490 12.8689807 12.93998901 12.8677375 13.07907729 13.0018149
log(Price) 13.2176736 13.4371741 12.84792653 13.2176736 13.16614100 13.4730202
CV residual 0.1648245 0.5681934 -0.09206248 0.3499361 0.08706371 0.4712054
786 792 796 800 802 812
Predicted 12.93013512 13.2018425 13.1487723 13.20927329 12.7729801 13.2825883
cvpred 12.95233846 13.1630168 13.1432473 13.19875621 12.8529259 13.2676937
log(Price) 12.88537442 13.4516671 13.5923670 13.21767356 12.1281111 12.9116423
CV residual -0.06696404 0.2886503 0.4491197 0.01891734 -0.7248147 -0.3560513
817 818 826 831 832 838
Predicted 12.9834915 12.9834915 13.15651363 13.27015568 13.2423841 13.2451844
cvpred 13.0407366 13.0407366 13.19470445 13.28937683 13.2658787 13.2834762
log(Price) 13.8878312 13.8878312 13.20854107 13.27936713 13.8831692 13.1021607
CV residual 0.8470946 0.8470946 0.01383662 -0.01000971 0.6172905 -0.1813155
848 867 868 872 874 880
Predicted 13.2803617 13.2569866 13.5015472 13.4205893 13.02594807 13.46711636
cvpred 13.3356553 13.3539386 13.5673049 13.5141937 13.24055689 13.57737149
log(Price) 12.9239124 13.7953079 13.2445810 14.0778748 13.30468493 13.59236701
CV residual -0.4117428 0.4413692 -0.3227239 0.5636811 0.06412805 0.01499552
888 891 897 901 902 907
Predicted 13.8258146 13.88218167 14.2628411 13.7862772 13.6196507 14.368618
cvpred 13.9821137 14.06236608 14.4058796 14.0558528 13.9695660 14.552129
log(Price) 14.4769090 14.09616802 13.7483018 13.6381765 13.1806323 12.765688
CV residual 0.4947953 0.03380194 -0.6575778 -0.4176763 -0.7889337 -1.786441
911
Predicted 14.812955
cvpred 15.389573
log(Price) 11.609244
CV residual -3.780329
Sum of squares = 62.25 Mean square = 0.34 n = 182
Overall (Sum over all 182 folds)
ms
0.2735833 PRESS(model4)[1] 248.3408MSPE(model4)[1] 0.2726024pred_r_squared(model4)[1] 0.4236938For model4 (the model without the Numbath variable), PRESS = 248.3408, MSPE = 0.2726024, prediction R-squared = 0.4236938
Based on the provided PRESS, MSPE and prediction R-squared values for the two models, it appears that model3 performs better than model4 in terms of predictive ability:
Model3 has a lower PRESS value than model4. PRESS measures the prediction error sum of squares, so a lower value indicates better out-of-sample predictive performance.
Similarly, model3 has a lower MSPE (mean squared prediction error) than model4. Again, lower MSPE signals better predictions.
Model3 has a higher prediction R-squared value than model4. The prediction R-squared assesses how much variance in the new observations the model can explain. Higher is better, so model3 again demonstrates superior predictive capacity.
Overall, the cross-validation metrics consistently show that model3, which includes the Numbath variable, achieves lower prediction error and higher predictive power compared to model4 without Numbath. This provides an insight that including Numbath improves the model’s ability to make accurate predictions on new data.
However, as model4 provides more natural interpretation of the housing data, we recommend using model4 as the final model.
Conclusion
This study developed a multiple regression model to examine the relationships between key housing characteristics (Numbed, Numbath, Age, Sqft, Lotsize, Numparking) and sale Price. The statistically significant model confirms several housing attributes are useful predictors of Price.
Regarding research question 1, all included variables except for the Numbath, showed significant associations with Price, indicating number of bedrooms, age, square footage, lot size, and parking spots relate to and influence home values. The positive coefficients signify higher values on these features tend to increase sale Price.
For research question 2, square footage, number of bedrooms, and lot size demonstrated the highest standardized coefficients, meaning these factors have the strongest correlations with Price after accounting for differences in measurement scales. This aligns with expectations, as size and capacity features directly influence home appraisals.
In total, the predictors accounted for 43.7% of the variance in Price based on the adjusted R-squared value. This confirms these core housing characteristics substantially explain pricing. However, there are likely additional aesthetic and qualitative factors that contribute to values. First, the sampling process seemed to have been biased. As there were no specific rules in selecting samples from Zillow.com, many contributors selected samples that were sold recently. Further process should address the issue of sample selection. Also, models could expand to include other architectural, neighborhood, and market predictors. But overall, the findings provide data-driven insights into the predominant drivers of residential real estate pricing.