Regression Analysis
This report contains the results of multiple linear regression analyses that were conducted for the three brands of flavored water (Dasani, Tropicana and Kellogg's) in order to determine the relationship between each brand's change score, which describes the change in the respondents' perception of the brand after seeing the three advertisements on a constant-sum scale, and the ten Likert questions about attributes of each brand. The brand attributes served as independent variables and the change score of each brand as the dependent variable. The data for this analysis was obtained from an online questionnaire, which collected 82 usable responses.
Table 1: Multiple linear regression analysis of Dasani, Tropicana, and Kellogg's
Brand |
Multiple correlation coefficient (R) |
Coefficient of multiple determination (R²) |
Standard error of the estimate (Se) |
F-ratio |
Dasani |
0.2 |
3.7% |
3.0 |
0.27 |
Tropicana |
0.4 |
19.5% |
2.6 |
1.72* |
Kellogg's |
0.4 |
16.1% |
1.7 |
1.36 |
* p ≤ 0.15 |
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The Multiple Correlation Coefficient (R) measures the relationship between respondents' perception of the brand and their impressions of the advertisement of the brand as tested through the ten Likert items. A strong, positive relationship is indicated by an R of 1.0. All three brands show rather weak correlations, and the correlation for the Dasani brand in particular is extremely weak (0.2).
The Coefficient of Multiple Determination (R²) refers to the amount of variance in respondents' impressions of the ads as explained by their feelings about the brands. R² values are reported in percent; low R² values represent a weak correlation and high R² values represent a strong correlation. As table 1 shows, there are only weak, and in the Dasani case (3.7%) even extremely weak correlations between how respondents feel about a brand and their impressions of the brands' ads.
Table 2: Dasani, Tropicana and Kellogg's brand attributes
Likert Item |
Dasani |
Tropicana |
Kellogg's |
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Constant |
1.0 / t-ratio: 0.27 |
-0.5 / t-ratio: -0.13 |
0.2 / t-ratio: 0.06 |
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|
b |
Beta |
t-ratio |
b |
Beta |
t-ratio |
b |
Beta |
t-ratio |
…good brand |
-0.4 |
-0.1 |
-0.56 |
0.4 |
0.1 |
0.52 |
1.3 |
0.5 |
3.08* |
…makes me feel healthy. |
-0.1 |
0.0 |
-0.16 |
-0.5 |
-0.1 |
-0.69 |
-0.1 |
0.0 |
-0.28 |
...tastes great. |
-0.2 |
-0.1 |
-0.37 |
1.8 |
0.3 |
2.35* |
-0.4 |
-0.1 |
-0.88 |
…brand I trust. |
0.0 |
0.0 |
0.08 |
0.2 |
0.0 |
0.31 |
-0.1 |
0.0 |
-0.28 |
…fits my lifestyle. |
0.6 |
0.2 |
0.92 |
-0.6 |
-0.1 |
-0.89 |
-0.1 |
0.0 |
-0.29 |
…is too expensive. |
0.0 |
0.0 |
0.06 |
-0.3 |
-0.1 |
-0.56 |
0.5 |
0.2 |
1.17 |
…just like any other… |
-0.2 |
- 0.1 |
-0.42 |
-0.7 |
-0.2 |
-1.43 |
0.2 |
0.1 |
0.66 |
…would recommend… |
-0.4 |
- 0.1 |
-0.61 |
0.3 |
0.1 |
0.59 |
-0.7 |
- 0.3 |
-1.61* |
…prefer over regular water. |
0.3 |
0.1 |
0.57 |
0.0 |
0.0 |
0.04 |
-0.1 |
-0.1 |
-0.40 |
…doesn't taste artificial |
-0.2 |
- 0.1 |
-0.40 |
-0.4 |
-0.1 |
-0.71 |
-0.3 |
-0.1 |
-0.79 |
* p ≤ 0.15 |
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b=unstandardized coefficient; Beta=standardized coefficient
The brand attributes for Dasani accounted for an extremely small portion (3.7%) of the variance in pre/post change scores. However, the results of this analysis are not statistically relevant and cannot be projected to the population. Moreover, 7 of the 10 Likert items (bold numbers in table) are important in this analysis as they influence the change score most. However, neither of the Dasani brand attributes had a statistically significant impact and thus cannot be projected to the population.
The brand attributes for Tropicana accounted for a larger yet still rather small portion (19.5%) of the variance in pre/post scores. The results of this sample are statistically significant and can be projected to the population. In 85 samples out of 100 samples drawn from the same population as this sample, it would be expected that the ten Tropicana brand attitude items would account for a small portion (19.5%) of the variance in the pre/post change scores for Tropicana. 2 Likert items (“Tropicana flavored water tastes great” and “Tropicana flavored water is just like any other brand of flavored water”) are important in this analysis. However, only one of these two attributes – Tropicana flavored water tastes great – is statistically significant; in 85 samples out of 100 samples drawn from the same population as this sample, it would be expected that the results would be about what they are here.
The brand attributes for Kellogg's accounted for about 16.1% of the variance in pre/post scores. This result also indicates a rather weak correlation. However, the results of this analysis as indicated by the t-ratio are not statistically relevant and cannot be projected to the population. Again, only a very small number of attributes, two in this case – “Kellogg's is a good brand of flavored water” and “I would recommend Kellog's flavored water to my friends” – are important in this analysis and also had a statistically significant impact; in 85 samples out of 100 samples drawn from the same population as this sample, it would be expected that these two coefficients would be about what they are here.
Multiple Regression equation for Dasani:
Change score Dasani = 1.0 + (-0.4) + (-0.1) + (-0.2) + 0.0 + 0.6 + 0.0 + (-0.2) + (-0.4) + 0.3 + (-0.2)