GLM 2

Loading Data

airbnb <- read_delim("./airbnb_austin.csv", delim = ",")

## Rows: 15244 Columns: 18
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr   (3): name, host_name, room_type
## dbl  (12): id, host_id, neighbourhood, latitude, longitude, price, minimum_n...
## lgl   (2): neighbourhood_group, license
## date  (1): last_review
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

Model 1

Response Variable: `price` (continuous) Predictors:

room_type (categorical)
minimum_nights (continuous)
availability_365 (continuous)
neighbourhood (categorical, top 5 neighbourhoods by frequency)

airbnb_model <- airbnb |>
  filter(!is.na(price)) |>
  mutate(
    neighbourhood = fct_lump(as.factor(neighbourhood), n = 5)

  )

model_lm <- glm(price ~ room_type + minimum_nights + availability_365 + neighbourhood,
                data = airbnb_model, 
                family = gaussian(link = "identity"))

summary(model_lm)

## 
## Call:
## glm(formula = price ~ room_type + minimum_nights + availability_365 + 
##     neighbourhood, family = gaussian(link = "identity"), data = airbnb_model)
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            288.18811   31.88156   9.039  < 2e-16 ***
## room_typeHotel room     62.46749   86.24670   0.724 0.468904    
## room_typePrivate room -112.19368   23.63949  -4.746 2.10e-06 ***
## room_typeShared room  -280.87334  108.65357  -2.585 0.009749 ** 
## minimum_nights          -2.05384    0.44808  -4.584 4.62e-06 ***
## availability_365         0.62833    0.06751   9.307  < 2e-16 ***
## neighbourhood78702    -124.62240   36.68021  -3.398 0.000682 ***
## neighbourhood78704    -122.79667   35.27290  -3.481 0.000501 ***
## neighbourhood78741    -130.64521   43.60979  -2.996 0.002743 ** 
## neighbourhood78745    -191.71629   44.00071  -4.357 1.33e-05 ***
## neighbourhoodOther    -102.12786   30.35368  -3.365 0.000769 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for gaussian family taken to be 697860.3)
## 
##     Null deviance: 7911282172  on 11182  degrees of freedom
## Residual deviance: 7796495326  on 11172  degrees of freedom
## AIC: 182225
## 
## Number of Fisher Scoring iterations: 2

Summary

Room Type Effects (reference: Entire home/apt)

Private rooms: $112 cheaper than entire homes
Shared rooms: $281 cheaper
Hotel rooms: Not significantly different

Minimum Nights

Each additional required night is associated with a $2.05 price decrease
Contrary to expectations that longer stays might command premiums

Availability

Each additional available day is linked to a $0.63 price increase
Suggests more desirable listings stay available longer

Neighborhood Effects (reference: likely downtown)

All listed neighbourhoods are significantly cheaper than the reference
78745 shows the largest discount ($192 less than the reference)
Neighbourhood differences range from 102 to 192

Model Diagnostics & Issues

vif(model_lm)

##                      GVIF Df GVIF^(1/(2*Df))
## room_type        1.042339  3        1.006935
## minimum_nights   1.017435  1        1.008680
## availability_365 1.019470  1        1.009688
## neighbourhood    1.039429  5        1.003875

The model has very low multicollinearity i.e All the predictors are statistically independent enough to be in the model together
The model explains some variation in price (Residual deviance < Null deviance) but has limited predictive power (Large residual deviance suggests room for improvement)
The high residual variance is likely due to extreme outliers or untransformed, skewed prices.
AIC of 182,225 is very high, indicating this may not be the best model specification
Large gap between min/max residuals (-398 to 37,766) suggests unequal variance
Extreme maximum residual indicates some very overpriced listings
The availability effect contradicts typical market behaviour (higher availability usually indicates lower demand)
Minimum nights showing negative relationship need investigation

Model 2

model_log <- glm(log(price) ~ room_type + minimum_nights + availability_365 + neighbourhood, 
                data = airbnb_model)

summary(model_log)

## 
## Call:
## glm(formula = log(price) ~ room_type + minimum_nights + availability_365 + 
##     neighbourhood, data = airbnb_model)
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            5.468e+00  2.974e-02 183.873  < 2e-16 ***
## room_typeHotel room    5.387e-01  8.045e-02   6.696 2.24e-11 ***
## room_typePrivate room -7.608e-01  2.205e-02 -34.502  < 2e-16 ***
## room_typeShared room  -1.901e+00  1.014e-01 -18.754  < 2e-16 ***
## minimum_nights        -5.262e-03  4.180e-04 -12.590  < 2e-16 ***
## availability_365       8.159e-04  6.297e-05  12.957  < 2e-16 ***
## neighbourhood78702    -3.103e-01  3.422e-02  -9.070  < 2e-16 ***
## neighbourhood78704    -3.490e-01  3.290e-02 -10.608  < 2e-16 ***
## neighbourhood78741    -6.827e-01  4.068e-02 -16.783  < 2e-16 ***
## neighbourhood78745    -5.373e-01  4.104e-02 -13.092  < 2e-16 ***
## neighbourhoodOther    -4.837e-01  2.831e-02 -17.084  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for gaussian family taken to be 0.6072235)
## 
##     Null deviance: 8341.2  on 11182  degrees of freedom
## Residual deviance: 6783.9  on 11172  degrees of freedom
## AIC: 26170
## 
## Number of Fisher Scoring iterations: 2

Key Improvements Over Previous Model

Median residual near zero (-0.143) and smaller range (-2.9 to 5.3 vs. -398 to 37,766)
Suggests the log transform addressed severe skewness in price data
Standard errors are now tiny fractions (e.g., 0.02974 for intercept vs. 31.88 previously)
All neighbourhood effects became highly significant

Interpreting Key Coefficients

Room Type Effects (reference: Entire home/apt)

Room Type	Coefficient	Interpretation (Multiplicative Effect)
Hotel	+0.5387	Costs 71% more (e^0.5387 ≈ 1.71)
Private	-0.7608	Costs 53% less (e^-0.7608 ≈ 0.47)
Shared	-1.901	Costs 85% less (e^-1.901 ≈ 0.15)

Example: An entire home at $200 would compare to:

Hotel roomn 200×1.71= **342**:
Private room: 200×0.47= **94**
Shared room: 200×0.15= **30**

Minimum Nights (-0.00526)

Each additional required night reduces price by 0.525%
For a 30-night minimum: 30 × -0.525% ≈ 15.7% discount

Availability (+0.000816)

Each available day increases price by 0.0816%
365-day availability → 365 × 0.0816% ≈ 30% higher price

Neighborhood Effects

Zip Code	Coefficient	Price Multiplier	Equivalent Discount
78741	-0.6827	0.51×	49%
Other	-0.4837	0.62×	38%
78704	-0.3490	0.71×	29%

Model Diagnostics

Maximum residual (5.32) still suggests some overpriced outliers
Consider winsorizing extreme log(price) values
Dispersion Parameter (0.607), close to 1, suggesting reasonable variance structure
AIC (26,170) is a vast improvement over the first model’s AIC (182,225)

GLM 2

P.Aina

Loading Data

Model 1

Response Variable: price (continuous) Predictors:

Summary

Model Diagnostics & Issues

Model 2

Key Improvements Over Previous Model

Interpreting Key Coefficients

Room Type Effects (reference: Entire home/apt)

Minimum Nights (-0.00526)

Availability (+0.000816)

Neighborhood Effects

Model Diagnostics

Response Variable: `price` (continuous) Predictors: