Consider The Following Multiple Regression Results Using A 0

Consider The Following Multiple Regression Results Usinga 05 As The

Consider the following multiple regression results. Using a = .05 as the significance level, identify all statistically significant predictors. In a relative sense, which variable has the strongest impact? What is the interpretation of the “constant” term? Independent variables, unstandardized coefficients, standard errors, standardized coefficients, t-values, and significance levels are provided.

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Consider The Following Multiple Regression Results Usinga 05 As The

Consider The Following Multiple Regression Results Usinga 05 As The

Multiple regression analysis is a powerful statistical tool used to examine the relationship between a dependent variable and multiple independent variables. It allows researchers to determine which predictors significantly influence the outcome and to assess the relative strength of each predictor. The interpretation of the regression coefficients, significance levels, and the constant term provides insights into the underlying data and helps in decision-making processes.

In the provided regression table, several independent variables are analyzed, with their corresponding unstandardized coefficients (B), standard errors (Std. Error), standardized coefficients (Beta), t-values, and significance levels (Sig.). The significance level used for hypothesis testing is α = 0.05, meaning any predictor with a p-value less than 0.05 is considered statistically significant.

Identification of Statistically Significant Predictors

Analyzing the significance levels, variables 3, 13, 14, and 16 exhibit p-values less than 0.05, indicating that they are statistically significant predictors of the dependent variable. Specifically:

  • Variable 3: p = 0.005
  • Variable 13: p = 0.021
  • Variable 14: p
  • Variable 16: p = 0.001

Other variables have p-values greater than 0.05, implying that their effects are not statistically significant at the 5% significance level. Therefore, the significant predictors influencing the dependent variable are Variables 3, 13, 14, and 16.

Relative Impact of Predictors

To determine the variable with the strongest impact, we examine the standardized coefficients (Beta), which provide a measure of the effect size of each predictor in standard deviation units. Among the significant variables:

  • Variable 14 has a Beta of 0.145
  • Variable 16 has a Beta of 0.075
  • Variable 3 has a Beta of 0.062
  • Variable 13 has a Beta of 0.050

Variable 14 has the highest absolute standardized coefficient (0.145), signifying that it has the strongest relative impact on the dependent variable among the significant predictors. A positive Beta implies that an increase in Variable 14 is associated with an increase in the dependent variable, holding other variables constant.

Interpretation of the Constant Term

The constant term (intercept) has a coefficient of 0.991 with a standard error unspecified but significantly different from zero (p = 0.000). This suggests that when all independent variables are held at zero, the expected value of the dependent variable is approximately 0.991. In real-world contexts, this could represent the baseline level of the outcome in the absence of the predictors’ effects, assuming zero is within the meaningful range of the predictors.

Implications and Conclusions

This analysis highlights that only certain variables significantly influence the dependent variable at the 0.05 significance level. Variable 14, with the highest standardized effect size, is the most influential predictor. The positive coefficient indicates a direct relationship, where increases in Variable 14 lead to increases in the outcome. Conversely, variables like 2, 4, 5, and others do not show statistically significant effects, implying their influence may be negligible or that the sample size might not be sufficient to detect smaller effects.

These findings assist in understanding which factors are most relevant and provide guidance for decision-makers or researchers interested in modeling the outcome variable. Future studies could explore possible interactions or nonlinear relationships, as well as increasing the sample size for more robust analysis.

References

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  • Osborne, J. W., & Waters, E. (2002). Four assumptions of multiple regression that researchers should always test. Practical Assessment, Research, and Evaluation, 8(2). https://doi.org/10.7275/r2278
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