Bivariate Analysis: Linear Relationship Between X And Y

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IV. Analyses
A. Bivariate Analysis
Using Figure 1, 2, and Table 2, I discover that the correlation coefficients and linear relationship between the X and Y variables are not as strongly positive as I had thought. In fact, the correlation coefficient is negative with a very small absolute value. Both X_1 and X_2 have a slightly negative correlation coefficient of -0.05 with dependent variable Y. This indicates as the amount of acquirer initiations increase, sale premia will remain almost the same as it was before those initiations occurred. Similarly, as the target initiates contact with more potential acquirers, it will see hardly any change in sale premium. This evidence conflicts with my theory that more contacts lead to higher sale premia.
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Multivariate Analysis
The results from my multivariate analysis (See Table 3) are similar to the results of my bivariate analysis. Ultimately, my dependent variable has little relation to my independent
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The coefficient of determination moves from 0.01 to 0 (with rounding) for equations 2 and 3 and the Adjusted R2 is still negative at -0.02. This means that in these equations the linear relationship between my X and Y variables is even worse than the linear relationship for equation 1. In addition, there are no significant changes in the slope coefficients (β_1and γ_2) for X_1 and X_2. This indicates a consistency among my regressions that provides further evidence to accept my null hypothesis that the more contacts improve sale premia.
At all levels of alpha and with all equations, the F-test requires that I accept the null hypotheses that H_0: α_1=0 and H_0: α_2=0. The p-value for equation 2 is 0.7 and the p-value for equation 3 is 0.74. These p-values are much higher than all the applicable levels of alpha. Thus, I accept the null. In other words, the amount of acquirer initiations and the amount of potential acquirers that the target contacts has no effect on the sale premia.
Multicollinearity does not substantially affect my regression. In fact, the correlation coefficient between my two independent variables is -0.16. This is within the non-problem range of -0.7 and +0.7. Consequently, the results of this equation are applicable and my X_1 and X_2 have little

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