| Term | EDF | Ref.df | F | p_value |
|---|---|---|---|---|
| s(sq_ft_total) | 1.000 | 1.000 | 174.230 | < 1e-04 |
| s(lot_size) | 1.912 | 1.985 | 7.380 | 0.000885 |
| s(age) | 2.599 | 2.859 | 9.568 | < 1e-04 |
| s(baths_total) | 3.705 | 3.848 | 10.433 | < 1e-04 |
| s(beds_total) | 1.000 | 1.000 | 0.691 | 0.406118 |
| s(garage_spaces) | 1.831 | 1.952 | 3.862 | 0.024498 |
| s(hoa_fee) | 5.492 | 6.042 | 15.491 | < 1e-04 |
| s(latitude) | 2.585 | 3.244 | 1.515 | 0.239890 |
| ti(age,sq_ft_total) | 2.618 | 3.366 | 0.960 | 0.597731 |
| ti(baths_total,sq_ft_total) | 2.741 | 3.349 | 3.677 | 0.009115 |
| ti(garage_spaces,sq_ft_total) | 5.769 | 6.894 | 2.253 | 0.035132 |
| ti(latitude,sq_ft_total) | 1.230 | 1.386 | 1.706 | 0.157135 |
| ti(age,baths_total) | 1.000 | 1.000 | 7.173 | 0.007567 |
| ti(age,garage_spaces) | 1.806 | 2.161 | 0.788 | 0.429055 |
| ti(baths_total,beds_total) | 3.659 | 4.355 | 7.283 | < 1e-04 |
| ti(baths_total,garage_spaces) | 2.810 | 3.537 | 1.079 | 0.371307 |
GAM Model Report
Dataset & Model
| Property | Value |
|---|---|
| Response | sale_price |
| Predictors | area, sq_ft_total, lot_size, age, baths_total, beds_total, garage_spaces, hoa_fee, latitude, view_hills, view_other, view_golf_course, view_water, view_panoramic, view_city_lights, view_valley, view_greenbelt, view_canyon |
| Observations | 781 |
| Family | gaussian |
| Smoothing method | REML |
| Smooth terms | 16 |
Results Summary
| Metric | Value |
|---|---|
| R-squared (adj) | 0.7349 |
| Deviance explained | 75.2% |
| CV R-squared | 0.5073 |
| AIC | 19178.1 |
| BIC | 19428.6 |
Model Equation
\begin{aligned} \widehat{\text{sale\_price}} ={}& 390261.6038 \\ & + f_{1}(\text{sq\_ft\_total}) \\ & + f_{2}(\text{lot\_size}) \\ & + f_{3}(\text{age}) \\ & + f_{4}(\text{baths\_total}) \\ & + f_{5}(\text{beds\_total}) \\ & + f_{6}(\text{garage\_spaces}) \\ & + f_{7}(\text{hoa\_fee}) \\ & + f_{8}(\text{latitude}) \\ & + f_{9}(\text{age, sq\_ft\_total}) \\ & + f_{10}(\text{baths\_total, sq\_ft\_total}) \\ & + f_{11}(\text{garage\_spaces, sq\_ft\_total}) \\ & + f_{12}(\text{latitude, sq\_ft\_total}) \\ & + f_{13}(\text{age, baths\_total}) \\ & + f_{14}(\text{age, garage\_spaces}) \\ & + f_{15}(\text{baths\_total, beds\_total}) \\ & + f_{16}(\text{baths\_total, garage\_spaces}) \\ & + \beta_{\text{area}} \text{ (2 levels)} \\ & + \beta_{\text{view\_hills}} \text{ (2 levels)} \\ & + \beta_{\text{view\_other}} \text{ (2 levels)} \\ & + \beta_{\text{view\_golf\_course}} \text{ (2 levels)} \\ & + \beta_{\text{view\_water}} \text{ (2 levels)} \\ & + \beta_{\text{view\_panoramic}} \text{ (2 levels)} \\ & + \beta_{\text{view\_city\_lights}} \text{ (2 levels)} \\ & + \beta_{\text{view\_valley}} \text{ (2 levels)} \\ & + \beta_{\text{view\_greenbelt}} \text{ (2 levels)} \\ & + \beta_{\text{view\_canyon}} \text{ (2 levels)} \end{aligned}
Smooth function definitions:
- f_1 →
s(sq_ft_total)— cubic regression spline, k = 3 - f_2 →
s(lot_size)— cubic regression spline, k = 10 - f_3 →
s(age)— cubic regression spline, k = 4 - f_4 →
s(baths_total)— thin plate regression spline, k = 5 - f_5 →
s(beds_total)— cubic regression spline, k = 5 - f_6 →
s(garage_spaces)— cubic regression spline, k = 3 - f_7 →
s(hoa_fee)— cubic regression spline, k = 10 - f_8 →
s(latitude)— thin plate regression spline, k = 10 - f_9 →
ti(age,sq_ft_total)— tensor product smooth, k = - f_10 →
ti(baths_total,sq_ft_total)— tensor product smooth, k = - f_11 →
ti(garage_spaces,sq_ft_total)— tensor product smooth, k = - f_12 →
ti(latitude,sq_ft_total)— tensor product smooth, k = - f_13 →
ti(age,baths_total)— tensor product smooth, k = - f_14 →
ti(age,garage_spaces)— tensor product smooth, k = - f_15 →
ti(baths_total,beds_total)— tensor product smooth, k = - f_16 →
ti(baths_total,garage_spaces)— tensor product smooth, k =
Smooth Terms
Parametric Terms
| Term | Estimate | Std_Error | t_value | p_value |
|---|---|---|---|---|
| (Intercept) | 390300 | 8202 | 47.584 | < 1e-04 |
| area30925 | -15630 | 6931 | -2.255 | 0.024423 |
| view_hillsTRUE | 1509 | 4111 | 0.367 | 0.713595 |
| view_otherTRUE | -16900 | 4476 | -3.776 | 0.000173 |
| view_golf_courseTRUE | -5442 | 6211 | -0.876 | 0.381200 |
| view_waterTRUE | 42680 | 4843 | 8.811 | < 1e-04 |
| view_panoramicTRUE | 39470 | 12700 | 3.107 | 0.001962 |
| view_city_lightsTRUE | 9981 | 14560 | 0.685 | 0.493360 |
| view_valleyTRUE | 805 | 17490 | 0.046 | 0.963309 |
| view_greenbeltTRUE | -7670 | 14300 | -0.536 | 0.591873 |
| view_canyonTRUE | -11890 | 24980 | -0.476 | 0.634142 |
Variable Importance
Smooth Effects
sq_ft_total
lot_size
age
baths_total
beds_total
garage_spaces
hoa_fee
latitude
age × sq_ft_total
baths_total × sq_ft_total
garage_spaces × sq_ft_total
latitude × sq_ft_total
age × baths_total
age × garage_spaces
baths_total × beds_total
baths_total × garage_spaces
Predictor Correlations
Diagnostics
Actual vs Predicted
mgcv Summary
Family: gaussian
Link function: identity
Formula:
sale_price ~ area + s(sq_ft_total, bs = "cr", k = 3) + s(lot_size,
bs = "cr") + s(age, bs = "cr", k = 4) + s(baths_total, bs = "tp",
k = 5) + s(beds_total, bs = "cr", k = 5) + s(garage_spaces,
bs = "cr", k = 3) + s(hoa_fee, bs = "cr") + s(latitude, bs = "tp") +
view_hills + view_other + view_golf_course + view_water +
view_panoramic + view_city_lights + view_valley + view_greenbelt +
view_canyon + ti(age, sq_ft_total, bs = c("tp", "tp")) +
ti(baths_total, sq_ft_total, bs = c("tp", "tp")) + ti(garage_spaces,
sq_ft_total, bs = c("tp", "tp")) + ti(latitude, sq_ft_total,
bs = c("tp", "tp")) + ti(age, baths_total, bs = c("tp", "tp")) +
ti(age, garage_spaces, bs = c("tp", "tp")) + ti(baths_total,
beds_total, bs = c("tp", "tp")) + ti(baths_total, garage_spaces,
bs = c("tp", "tp"))
Parametric coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 390262 8202 47.584 < 2e-16 ***
area30925 -15629 6930 -2.255 0.024423 *
view_hillsTRUE 1509 4111 0.367 0.713595
view_otherTRUE -16898 4476 -3.776 0.000173 ***
view_golf_courseTRUE -5442 6211 -0.876 0.381200
view_waterTRUE 42676 4843 8.811 < 2e-16 ***
view_panoramicTRUE 39466 12701 3.107 0.001962 **
view_city_lightsTRUE 9981 14564 0.685 0.493360
view_valleyTRUE 805 17493 0.046 0.963309
view_greenbeltTRUE -7670 14300 -0.536 0.591873
view_canyonTRUE -11892 24978 -0.476 0.634142
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Approximate significance of smooth terms:
edf Ref.df F p-value
s(sq_ft_total) 1.000 1.000 174.230 < 2e-16 ***
s(lot_size) 1.912 1.985 7.380 0.000885 ***
s(age) 2.599 2.859 9.568 6.67e-06 ***
s(baths_total) 3.705 3.848 10.433 < 2e-16 ***
s(beds_total) 1.000 1.000 0.691 0.406118
s(garage_spaces) 1.831 1.952 3.862 0.024498 *
s(hoa_fee) 5.492 6.042 15.491 < 2e-16 ***
s(latitude) 2.585 3.244 1.515 0.239890
ti(age,sq_ft_total) 2.618 3.366 0.960 0.597731
ti(baths_total,sq_ft_total) 2.741 3.349 3.677 0.009115 **
ti(garage_spaces,sq_ft_total) 5.769 6.894 2.253 0.035132 *
ti(latitude,sq_ft_total) 1.230 1.386 1.706 0.157135
ti(age,baths_total) 1.000 1.000 7.173 0.007567 **
ti(age,garage_spaces) 1.806 2.161 0.788 0.429055
ti(baths_total,beds_total) 3.659 4.355 7.283 4.52e-06 ***
ti(baths_total,garage_spaces) 2.810 3.537 1.079 0.371307
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
R-sq.(adj) = 0.735 Deviance explained = 75.2%
-REML = 9292.9 Scale est. = 2.5267e+09 n = 781Report generated by mgcvUI on 2026-06-21 00:23:20.