Chapter 6. Analysis
6.4. Polynomial Regression Analysis
6.4.2. Using Edwards’ Framework
6.4.2.1. The detailed analysis of one exemplar
The detailed discussion is centred on the personality trait of Agreeableness as it relates to the outcome variables of trust, satisfaction, commitment, sales- outcome and word-of-mouth. To be clear, there is no specific reason for choosing agreeableness over the other personality traits or organisational
culture aspects. The respective graphs for Agreeableness are found in Figure 16, Figure 17, Figure 18, Figure 19 and Figure 20.
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Figure 17: Agreeableness against the outcome variable of trust
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Figure 19: Agreeableness against the outcome variable of sales
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Table 12: Stationary points and Principal axes for personality trait Agreeableness1
Personality Trait Outcome
Stationary Point First Principal Axis Second Principal Axis
X0 Y0 P10 P11 P20 P21 Agreeableness Sales 3.98 3.58 1.06 .63 9.87 -1.58 Agreeableness Word-of-mouth 3.32 3.75 3.35 .12 31.13 -8.25 Agreeableness Trust 3.93 3.79 3.04 .19 24.26 -5.22 Agreeableness Commitment 4.28 3.83 4.16 -.07 -8.74 13.35 Agreeableness Satisfaction 11.33 4.26 3.66 .05 216.87 -18.77
1 N =100. For the column labelled X0 and Y0 table entries are coordinates of the stationary point in the X, Y plane. For the columns labelled P10 and P11,
table entries are the intercept and slope of the first principal axis in the X, Y plane; and for the columns labelled P20 and P21, table entries are the intercept and
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Table 13: Slopes along lines of interest for personality trait agreeableness 2
Personality Trait Outcome
Y = X Y = -X First Principal Axis Second Principal Axis
Agreeableness Sales -2.70 .35 -1.34 -.52 -2.19 .28 7.83 -.98 Agreeableness Word-of-mouth 11.79 -1.45 -26.93 -3.22 -4.66 .70 1386.38 -207.84 Agreeableness Trust 19.87 -2.59 -5.80 -3.24 8.31 -1.06 419.10 -53.38 Agreeableness Commitment 20.04 -2.54 -8.74 -2.18 4.93 -.58 2734.03 -319.71 Agreeableness Satisfaction 11.51 -1.46 -12.05 -1.80 .35 -.02 12903.63 -569.68
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The first feature that should be discussed is the stationary points while the second is the principle axes as presented in Table 12. The last point of
discussion is the slopes along lines of interest, presented in Table 13. The salesperson’s agreeableness scores are presented along the Y-axis while along the X-axis are the customers’ agreeableness scores. The Z-axis represents the different outcome variables. The stationary point is represented by a small red dot (when applicable) while the first principal axis is represented by a dotted red line in the XY plane. The second principal axes are not represented in the graphs because it is not aesthetically elegant, and difficult to interpret. In the original work (Edwards, 2002), most second principal axes were omitted. Figure 16Error! Reference source not found. shows the polynomial regression and a surface response graph for the personality trait of agreeableness against commitment. The shape of the plot is concave and slightly elliptical with its stationary point at X = 4.28, Y = 3.83. This stationary point can be clearly seen towards the right side of the plot. The first principal axis crossed the intercept at Y = 4.16 and was within the bounds of the graph, but the slope was slightly negative (-.07).
When comparing behaviour along the first principal axis ( and , the linear and quadratic coefficients) to behaviour along the line of interest Y = X, there are differences in both coefficients. A similar thing is observed when comparing coefficients ( and ) along the second principal axis to the equation Y = -X. This confirms that the principle axes are not parallel to either the standard axes or the lines Y = X and Y = -X.
Taken together, the plot shows that when the salesperson or the customer exhibit extreme (either high or low) levels of agreeableness, the level of
commitment decreases. The stationary point seen on the graph is at the maximum level of commitment, suggesting that a moderate level of agreeableness by both the salesperson and the customer are required for
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maximum levels of commitment. Coefficients along lines of interest indicate that there is a non-linear relationship along these lines.
Figure 17 shows the polynomial regression and a surface response graph for the personality trait of agreeableness against trust. The shape of the plot is concave and largely elliptical with its stationary point at X = 3.93, Y = 3.79. This stationary point can be clearly seen towards the right side of the graph. The first principal axis crossed the intercept within the bounds of the graph though the slope was slightly positive (.19). The second principal axis has a strongly negative slope (-5.22), indicating these axes are almost parallel to the X- and Y- axes.
When comparing coefficients ( and ) along the first principal axis to the line Y = X, there appear to be substantial differences in both coefficients. This may suggest a large clockwise rotation can be seen along the Y = X plane. Similarly, when comparing coefficients ( and ) along the second principal axis to the line Y = -X, there appear to be significant differences which confirms the clockwise rotation. In other words, the principal axes do not coincide with the lines of interest, nor are they expected to, given their slopes and intercepts.
Taken together, the plot shows that when the salesperson and the customer exhibit extreme levels of agreeableness, the level of commitment decreases. The stationary point can be seen on the graph; the maximum level of trust can be found at here, signifying that a moderate level of agreeableness by both the salesperson and the customer are required for maximum level of trust.
Figure 18Error! Reference source not found. shows the polynomial regression and surface response a graph for the personality trait of
agreeableness against satisfaction. The shape of the plot is concave and almost cylindrical along the X-axis. The graph has its stationary point at X = 11.33, Y = 4.26, but it cannot be seen on the graph. The first principal axis has intercept within the bounds of the graph (3.66) and the slope is slightly positive (.05). The second principal axis does not lie within the space of the graph and has a
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severely negative slope (-18.77), indicating that the principal axes are slightly rotated compared to the X- and Y-axes.
Taken together, the plot shows that when the salesperson exhibits extreme levels of agreeableness, the level of satisfaction decreases. It is different for the customer because when the customer exhibits high levels of agreeableness the satisfaction is highest. There is a nonlinear relationship along the various lines of interest for the personality trait of agreeableness on satisfaction. It is
interesting to note an extreme negative curvilinear relationship for agreeableness on commitment from the salesperson and a more “linear” relationship (the coefficient of X2 is close to zero) when viewing the same
relationship from a customer perspective.
Figure 19 shows the polynomial regression and a surface response graph for the personality trait of agreeableness against sales. This plot has a saddle shape with its stationary point at X = 3.98, Y = 3.58. This stationary point can be seen towards the right side of the graph. The first principal axis has a slope of .63, and the second principal axis again did not cross within the space of the graph (its intercept is 9.87) and has a slope of -1.58.
When comparing coefficients along the first principal axis to coefficients along the line Y = X, there appears to be a large similarity between the two. This suggests that the first principal axis runs near to (but not exactly on) the Y = X line maintaining little deviation. In contrast, when comparing the second
principal axis to the line Y = -X, there are some noticeable differences, explained mostly by the fact that that the second principal axis is off-set from the line Y = - X.
Taken together, the plot shows that when there is incongruence between the customer’s and salesperson’s agreeableness (X and Y values are different), there is a negative curvilinear relationship, though when there is congruence between the customer and salesperson there is a positive curvilinear
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Y = X and Y = -X reinforce the suggestion that congruence (at extreme ands of the scale) improves sales while incongruence decreases sales.
Figure 20 shows the polynomial regression and a surface response graph for the personality trait of agreeableness against word-of-mouth. This plot has a saddle shape, with its stationary point at X = 3.32, Y = 3.75. This stationary point can be seen towards the near side of the graph. The first principal axis can be seen in the graph, with an intercept of 3.35 and has a slope of .12. The second principal axis has an intercept of 31.13 and a slope of -8.25.
Taken together, the plot shows that the salesperson’s level of agreeableness has a negative curvilinear relationship with word-of-mouth. In contrast, the customer’s agreeableness has a subtle positive curvilinear relationship with word-of-mouth.