Regression

The purpose of performing a regression analysis on this data set is to observe any notable relationships between a respondent’s opinion of a certain brand and how they viewed the brand’s print advertisement. The dependent variable in the equations will be the pre to post ad exposure change score, while the independent variables will be the ten descriptive brand characteristics (or Likert items).

Multiple Regression Analysis
Brand Name	Multiple Regression (R)	Coefficient of Multiple Determinative (R²)	Standard Error of the Estimate (s e)	F-Ratio
Winterfresh	.2	5.5%	2.8	.42
Big Red	.4	13.7%	2.2	1.14
Orbit	.3	10.7%	2.5	.86

* indicates p ≤ 0.15 

Brand Characteristic Coefficients
Brand Characteristic	Winterfresh			Big Red			Orbit
	b	Beta ( b )	t-ratio	b	Beta ( b )	t-ratio	b	Beta ( b )	t-ratio
Constant (a)	-3.1		1.28	3.5*		1.80	1.4		.68
1. Is a flavorful gum.	-.3	-.1	.63	.04	.02	.11	-1.1*	-.3	1.82
2. Is an excellent brand of gum.	.5	.2	.94	.2	.09	.55	.3	.1	.78
3. Has a long lasting flavor.	.1	.03	.21	.07	.03	.25	.5	.2	.83
4. Is too overwhelming.	.09	.03	.18	-.3	-.2	1.10	.6	.2	1.41
5. Keeps your breath fresh.	.004	.001	.01	-.3	-.1	1.16	-.4	-.1	.81
6. Has an odd texture.	.03	.01	.06	-.2	-.06	.44	-.2	-.1	.51
7. Packaging is appealing.	.4	.1	.93	.1	.03	.26	.4	.1	.99
8. Is too sugary.	.1	.01	.1	-.3	-.1	.94	-.3	-.1	.61
9. Gets hard after chewing.	.3	.1	.76	-.4	-.2	1.29	-.02	-.02	.14
10. Prefer over other gums.	-.02	-.01	.05	-.2	-.1	.69	-.1	-.1	.33

* indicates p ≤ 0.15

Multiple Regression Analysis: Winterfresh

The Multiple Regression analysis performed above confirms that the Multiple Regression value (R) is a very small number which represents a very low positive correlation between the ad exposure change score and the ten brand attributes assessed. Because the Coefficient of Multiple Determinatives is especially minute (5.5%), this percentage purports that there is a large amount of unexplained variance (around 94.5%). This proportion, 5.5%, says that only 5.5% of the variance in how well these respondents liked the ad, is explained by the pre to post ad exposure change score. 94.5% of the variance is not accounted for or explained by the pre to post advertisement exposure change score. Because the Coefficient of Multiple Determinatives value is small, than the Standard Error of the Estimate ( s e ) amount has to be large, due to the two descriptive statistics inverse relationship. The Standard Error of the Estimate represents the unexplained variance in a multiple regression analysis and signifies that the average distance the survey respondents were from the regression line was 2.8 units. The F-ratio (F=.42) in this data output was not statistically significant, meaning that in 85 or more samples, drawn from the same population as this sample, we could not project any of the tabulated results onto the population. Meaning, we would not be able to project R = .2, R² = 5.5%, and s e = 2.8 to the population as a whole.

The Regression Linear Equation for the Winterfresh brand can be written as:

y = -3.1 - .3(flavor) + .5(excellent) + .1(long) + .1(overwhelming) + .004(fresh) + .03 (texture) + .4(packaging) + .1(sugary) + .3(hard) - .02(prefer)

The Regression Linear Equation for the Winterfresh brand can be interpreted as:

1. The more respondents thought that Winterfresh was a flavorful chewing gum, the less they liked the ad.
2. The more individuals thought that Winterfresh was an excellent brand of chewing gum, the more they liked the ad.
3. The more individuals thought that Winterfresh had a long lasting flavor, the more they liked the advertisement.
4. The more people thought that Winterfresh was overwhelming, the more they liked the print ad.
5. The more respondents thought that Winterfresh kept their breath fresh, the more they liked the ad.
6. The more people thought that Winterfresh had an odd texture, the more they liked the ad.
7. The more individuals thought that Winterfresh had an appealing packaging, the more they liked the ad.
8. The more individuals thought that Winterfresh was too sugary, the more they liked the advertisement.
9. The more respondents thought that Winterfresh became hard after extensive chewing, the more they liked the print ad.
10. The more respondents believed that they preferred Winterfresh over other brands, the less they liked the ad.

Four of the ten brand characteristics could be considered important when explaining the variance of the dependent variable, which is the pre to post ad exposure change score. Those attributes being that: Winterfresh is flavorful (#1), Winterfresh is an excellent brand of gum (#2 and the most significant in explaining the variance of the four), Winterfresh has appealing packaging (#7), and that Winterfresh becomes hard after extensive chewing (#9).

Multiple Regression Analysis: Big Red

The Multiple Regression analysis performed for Big Red reveals that the Multiple Regression value equaled .4, which represents a moderate positive correlation between the ten Likert items and the pre to post ad exposure change score. The Coefficient of Multiple Determinatives (R²= 13.7%) is rather low, and indicates that the Likert items account for only 13.7% of the variance in the pre to post ad exposure change score. The Standard Error of the Estimate is high at 2.2, signifying that respondents were an average of 2.2 units away from the regression line. At 1.14, the F-ratio was not significant, so we can not project our findings onto the population.

Six of the ten brand characteristics could be considered important when explaining the variance of the pre to post ad exposure change score. The most important attribute asked if Big Red became hard after extensive chewing (#9), and the other five brand characteristics are as follows: Big Red is an excellent brand of gum (#2), Big Red is overwhelming (#4), Big Red keeps ones breath fresh (#5), Big Red is too sugary (#8), and preferring Big Red over other gums (#10). Although none of the brand attributes where found to be significant, the Constant (a) was with a t-ratio equaling 1.80. It can be said that in a sample of 85 or more of 100 samples, drawn from the same population as this sample of 83, we would expect the dependent variable (b) to be similar to the y-intercept found in this equation.

Multiple Regression Analysis: Orbit

The regression analysis for Orbit does not differ a great deal from the other two chewing gum brands. The Multiple Regression value equaled .3, which shows a low positive correlation between the ten descriptive items and the dependent variable (pre to post ad change score). The Coefficient of Multiple Determinatives, R² = 10.7%, claims that only 10.7% of the variance in the pre – post ad exposure change score, can be explained by the ten Likert items. The Standard Error of the Estimate is large at 2.5, suggesting that individuals were an average of 2.5 units from the regression line. At .86, the F-ratio was again, not statistically significant, so we can not project the samples Multiple Regression value or the Coefficient of Multiple Determinatives onto the population.

Three of the ten brand characteristics could be considered important when explaining the variance of the pre to post ad exposure change score. The most important of the characteristics asked respondents if they thought Orbit was a flavorful gum (#1). The other two important characteristics are: Orbit has a long lasting flavor (#3), and if Orbit was an overwhelming gum (#4). It is interesting to note that all the important attributes identified above deal with flavor.

It can be concluded, from these results, that there is not much of a connection between how respondents liked the chewing gum brand, and how they viewed the ad. One issue to address is the fact that the brand characteristics questioned were not very significant and telling attributes of the brand, and that others could have been asked in order to obtain data that was more significant and conclusive of the relationship between each gum’s brand characteristic and how respondents favored each brand’s advertisement.