Data Description

Please download the data from Canvas before you run the codes.

# get a sneak peak of the data 
load("super_bock.RData")
head(super_bock)
##   obs_id ratings respondent_id prfile_id price      brand capacity   shape
## 1      1      57             1         1  70ct     Sagres    200ml Spanish
## 2      2      55             1         2  30ct    Cristal    200ml Spanish
## 3      3      55             1         3  60ct Super Bock    250ml Spanish
## 4      4      37             1         4  70ct Super Bock    250ml Spanish
## 5      5      44             1         5  30ct     Sagres    330ml Spanish
## 6      6      15             1         6  50ct    Cristal    330ml Spanish

The data has 4 product attributes for beers and 3 or 4 levels for each attribute. The levels of these attributes are as below:

## $price
## [1] "30ct" "50ct" "60ct" "70ct"
## 
## $brand
## [1] "Cristal"    "Sagres"     "Super Bock"
## 
## $capacity
## [1] "200ml" "250ml" "330ml"
## 
## $shape
## [1] "Long Neck" "Rocket"    "Spanish"

Estimating the Coefficients

We first estimate a linear regression with ratings as DV and the 4 attributes as IV’s: \[Ratings = \alpha + \beta_1*Brand + \beta_2*Capacity + \beta_3*Shape + \beta_4*Price + e\] The baseline levels are already set for you. The baseline levels are as below:

## $price
## [1] "30ct"
## 
## $brand
## [1] "Cristal"
## 
## $capacity
## [1] "200ml"
## 
## $shape
## [1] "Long Neck"

With the data, we run a linear regression as below:

# running the logistic regression 
mdl <- lm(ratings ~ brand + capacity + shape + price, super_bock)

# get a summary of the model results
results <- summary(mdl)
results
## 
## Call:
## lm(formula = ratings ~ brand + capacity + shape + price, data = super_bock)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -42.196  -7.506   0.619   7.612  35.474 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      76.4519     1.1401  67.055  < 2e-16 ***
## brandSagres      16.7147     0.9309  17.955  < 2e-16 ***
## brandSuper Bock  18.6763     0.9309  20.062  < 2e-16 ***
## capacity250ml   -18.7788     0.9309 -20.172  < 2e-16 ***
## capacity330ml   -22.2917     0.9309 -23.946  < 2e-16 ***
## shapeRocket     -12.9071     0.9309 -13.865  < 2e-16 ***
## shapeSpanish    -22.5000     0.9309 -24.170  < 2e-16 ***
## price50ct        -5.0769     1.1401  -4.453 9.51e-06 ***
## price60ct        -1.7115     1.1401  -1.501    0.134    
## price70ct        -8.3494     0.9309  -8.969  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 11.63 on 926 degrees of freedom
## Multiple R-squared:  0.6635, Adjusted R-squared:  0.6602 
## F-statistic: 202.8 on 9 and 926 DF,  p-value: < 2.2e-16

Obtaining the Partworths

Three rules to transform the coefficients to partworths:

  1. Baseline levels partworths = 0
  2. Insignificant levels partworths = 0
  3. Significant levels partworths = coefficients

We first create a table to record coefficients and partworths.

Attributes Levels Coefficients P-value Partworths
Brand Cristal 0.000 0.000
Sagres 16.715 0.000 16.715
Super Bock 18.676 0.000 18.676
Capacity 200ml 0.000 0.000
250ml -18.779 0.000 -18.779
330ml -22.292 0.000 -22.292
Shape Long Neck 0.000 0.000
Rocket -12.907 0.000 -12.907
Spanish -22.500 0.000 -22.500
Price 30ct 0.000 0.000
50ct -5.077 0.000 -5.077
60ct -1.712 0.134 0.000
70ct -8.349 0.000 -8.349


To Evaluate the 4 Strategies

Given the partworths, we can now evaluate and compare the 4 strategies. The 4 strategies are:

  1. To attack with Cristal long-neck shape 200ml priced at 50 cents
  2. To attack with Super Bock rocket shape 330ml priced at 60 cents
  3. To launch a Super Bock long-neck shape 200ml priced at 50 cents
  4. To re-launch a Super Bock long-neck shape 250ml priced at 50 cents

Here, I will use the 1st strategy as an example. You can follow the same procedure to calculate other strategies.

Strategy_1 <- 0.000 + # Cristal 
  0.000 + # 200 ml 
  0.000 + # long neck
  -5.077 # 50 cents
Strategy_1
## [1] -5.077

The results are as follows:

Strategy Brand Capacity Shape Price Utilities
Competitor Sagres 200ml Long Neck 50ct 11.638
1 Cristal 200ml Long Neck 50ct -5.077
2 Super Bock 330ml Rocket 60ct -16.523
3 Super Bock 200ml Long Neck 50ct 13.599
4 Super Bock 250ml Long Neck 50ct -5.18