Tag: Generalised linear model

# Generate mock coffee shop dataset (15 days)

## Set seed for reproducibility
set.seed(123)

## Generate
coffee_shop <- data.frame(
  
  ## Generate 15 days
  day = 1:15,
  
  ## Generate daily temperature
  temp = round(rnorm(15,
                     mean = 25,
                     sd = 5),
               1),
  
  ## Generate promotion day
  promo = sample(c(0, 1),
                 15,
                 replace = TRUE),
  
  ## Generate weekend
  weekend = c(0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1),
  
  ## Generate the number of sales
  sales = round(rnorm(15,
                      mean = 300,
                      sd = 50)),
  
  ## Generate the number of daily customers
  customers = rpois(15,
                    lambda = 80),
  
  ## Generate sold-out
  sold_out = sample(c(0, 1),
                    15,
                    replace = TRUE)
)

## Convert binary variables to factors
coffee_shop$promo <- factor(coffee_shop$promo,
                            levels = c(0, 1),
                            labels = c("NoPromo", "Promo"))

coffee_shop$weekend <- factor(coffee_shop$weekend,
                              levels = c(0, 1),
                              labels = c("Weekday", "Weekend"))

coffee_shop$sold_out <- factor(coffee_shop$sold_out,
                               levels = c(0, 1),
                               labels = c("No", "Yes"))

## View the dataset
print(coffee_shop)

   day temp   promo weekend sales customers sold_out
1    1 22.2 NoPromo Weekday   246        73      Yes
2    2 23.8   Promo Weekday   296        76      Yes
3    3 32.8 NoPromo Weekday   354        83       No
4    4 25.4   Promo Weekday   293        87       No
5    5 25.6   Promo Weekend   242        78      Yes
6    6 33.6 NoPromo Weekend   259        91      Yes
7    7 27.3 NoPromo Weekday   334        71      Yes
8    8 18.7 NoPromo Weekday   284        76       No
9    9 21.6 NoPromo Weekday   234        72      Yes
10  10 22.8   Promo Weekend   270        79       No
11  11 31.1 NoPromo Weekend   294        82      Yes
12  12 26.8   Promo Weekday   344        79       No
13  13 27.0   Promo Weekday   292        79       No
14  14 25.6 NoPromo Weekday   316        92       No
15  15 22.2 NoPromo Weekend   139        77      Yes

# Create a regression model with glm()
linear_reg <- glm(sales ~ temp + promo + weekend,
                  data = coffee_shop,
                  family = gaussian)

# Get model summary
summary(linear_reg)

Call:
glm(formula = sales ~ temp + promo + weekend, family = gaussian, 
    data = coffee_shop)

Coefficients:
               Estimate Std. Error t value Pr(>|t|)   
(Intercept)      96.599     59.669   1.619  0.13375   
temp              7.703      2.283   3.373  0.00621 **
promoPromo       23.014     18.537   1.241  0.24025   
weekendWeekend  -73.444     19.654  -3.737  0.00328 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 1222.243)

    Null deviance: 39702  on 14  degrees of freedom
Residual deviance: 13445  on 11  degrees of freedom
AIC: 154.54

Number of Fisher Scoring iterations: 2

# Create a logistic regression model
log_reg <- glm(sold_out ~ temp + promo + weekend,
               data = coffee_shop,
               family = binomial)

# Get model summary
summary(log_reg)

Call:
glm(formula = sold_out ~ temp + promo + weekend, family = binomial, 
    data = coffee_shop)

Coefficients:
               Estimate Std. Error z value Pr(>|z|)
(Intercept)     1.30934    3.92442   0.334    0.739
temp           -0.04448    0.15189  -0.293    0.770
promoPromo     -1.73681    1.31881  -1.317    0.188
weekendWeekend  2.15038    1.45643   1.476    0.140

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 20.728  on 14  degrees of freedom
Residual deviance: 16.426  on 11  degrees of freedom
AIC: 24.426

Number of Fisher Scoring iterations: 4

# Transform coefficient
exp(coef(log_reg))

   (Intercept)           temp     promoPromo weekendWeekend 
     3.7037124      0.9564938      0.1760812      8.5881237

# Create a poisson regression model
poisson_reg <- glm(customers ~ temp + promo + weekend,
                   data = coffee_shop,
                   family = poisson)

# Get model summary
summary(poisson_reg)

Call:
glm(formula = customers ~ temp + promo + weekend, family = poisson, 
    data = coffee_shop)

Coefficients:
               Estimate Std. Error z value Pr(>|z|)    
(Intercept)    4.108939   0.192499  21.345   <2e-16 ***
temp           0.010077   0.007299   1.381    0.167    
promoPromo     0.010327   0.059616   0.173    0.862    
weekendWeekend 0.012692   0.062739   0.202    0.840    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 7.0199  on 14  degrees of freedom
Residual deviance: 4.8335  on 11  degrees of freedom
AIC: 106.06

Number of Fisher Scoring iterations: 3

# Transform the coefficients
exp(coef(poisson_reg))

   (Intercept)           temp     promoPromo weekendWeekend 
     60.882073       1.010127       1.010381       1.012773