Question

[Naive Bayes] Prove the following formula (show step-by-step)

for each of possible outcomes or classes $C_{i}$ and $f_{j}$ representing a feature of vector

arg max(Plc,) . Π PI; C)) = arg max(log(P(C))+y log(Plf1C))) feF Ci ,EF th

Answer 1

The regression model for brand contains 20 variables that together account for 57 percent (adjusted R²) of the variance in brand recognition (see Table 2).

As with product recognition, in the explanatory model for brand recognition, the strongest effect is found in the content characteristics — specifically, the negative influence of the number of information cues (β = -0.45). Information cues slow down the brand recognition, especially information about product ingredients or technical specifications. Brand recognition is further slowed by information on ingredients or product components, long headlines, the use of humor, and images of women. On the other hand, the display of new-product information and one information cue (but not more) was found to speed up the brand recognition.

It was not surprising to find that brand identification had an effect on brand recognition. Logos enhance the speed of recognition, unless they are placed in the bottom right corner of the poster. Including the brand name in the copy text and especially in the headline (preferably in a large font) also has a positive influence on brand recognition.

Regarding layout, photographs were found to be more favorable than drawings for quick brand recognition. Large headlines were found to slow down brand recognition, possibly because of their distraction from the brand. The use of a black font proved to enhance brand recognition.

As for characteristics that cannot be manipulated, we can see that well-known brand names and fashion labels are recognized quickly. Since 1992, the average time it takes to recognize brands on outdoor posters has been decreasing. This may be the result of better creative execution of outdoor posters (controlling for all effects in the model), but it may also indicate an increasing capacity among consumers to recognize visuals in a split second, as the numbers of frames per second in television drama, music video clips, and television commercials have increased as well in the last decade.