Correlation

By Nathan B. Smith

Correlation is a method for determining how two variables are related in a dataset. Regression is the study of how one variable influences another. In correlation analysis, the two variables are symmetrically considered, whereas, in regression analysis, one is assumed to be unsymmetrically dependent on the other (Lindley, 1990).

Discussion

Part 1

Leadership at a large corporation states that they want to identify the influence of years of service on workers' productivity levels and anticipate future productivity based on the length of experience in years. The corporation has statistics on all its personnel and assesses each associate's productivity using a reasonable measure. This type of inquiry and analysis is common in business administration; various ways address these questions.

To determine if a variable (X) (in this case, years of experience) is beneficial in forecasting another variable (Y) (level of productivity), a significance test can be used. This test can be considered a test of one of the following null hypotheses: The population correlation coefficient and the population slope weight equal zero (Green & Salkind, 2017).

The significance test can be calculated using two key assumptions: fixed-effects model assumptions and random-effects model assumptions. The fixed-effects model appears to be more suited to experimental investigations, whereas the random-effects model appears to be better suited to non-experimental studies. The predictor and criterion can have linear or nonlinear connections if the fixed-effects assumptions are valid. If the random-effects assumptions are accurate, the only direct correlation between different variables is a linear one (Green & Salkind, 2017).

Irrespective of the conditions used, a bivariate scatterplot of the predictor (years of experience) and criterion (productivity level) variables should be examined before running a regression analysis to see a nonlinear relationship between X and Y for outliers. Suppose the link appears to be nonlinearly relying on the scatterplot. In that case, one might consider including higher-order terms (variables that are squared, cubed, and so on) in the regression equation rather than standard bivariate regression analysis (Green & Salkind, 2017).

Part 2

The company discovered that years of experience are significantly related to performance levels after analyzing the results of the Part 1 investigation. However, after reviewing the data, a statistician concluded that the findings do not account for much of what is going on in the overall association.

Irrespective of the conditions used, a bivariate scatterplot of the predictor (years of experience) and criterion (productivity level) variables should be examined before running a regression analysis to see a nonlinear relationship between X and Y for outliers. Suppose the link appears to be nonlinearly relying on the scatterplot. In that case, one might consider including higher-order terms (variables that are squared, cubed, and so on) in the regression equation rather than standard bivariate regression analysis (Green & Salkind, 2017).

The slope and intercept and the confidence interval are two essential findings of a bivariate linear regression study, as they demonstrate a part of the relationship that can be used to make predictions. The R square value is another crucial metric representing the association's strength. These two pieces of data are crucial in determining the overall relationship between variables. However, if the statistician does not have information about the variables and only evaluates the findings, the results may not fully explain the relationship.

Conclusion

Bivariate regression analysis entails examining two factors to determine the strength of their association. The two variables are commonly referred to as X and Y, with one as an independent (or explanatory) variable and the other as a dependent variable (or outcome variable). Bivariate Regression Analysis employs a linear regression line (since the relationship between the variables is linear) to help measure how the two variables change simultaneously to establish the link. This will be represented on a scatter chart by a line of best fit drawn through the plotted values of the independent variable (X-axis) and the dependent variable (Y-axis) (Y-axis) (DJS Research, 2022).

References

DJS Research. (2022). Bivariate Regression Analysis. Retrieved from DJS Research: https://www.djsresearch.co.uk/glossary/item/Bivariate-Regression-Analysis

Green, S. B., & Salkind, N. J. (2017). Using SPSS for Windows and Macintosh: Analyzing and understanding the data. New York, NY: Pearson.

Lindley, D. V. (1990). Regression and correlation analysis. In J. Eatwell, M. Milgate, & P. Newman, Time series and statistics (pp. 237-243). London, UK: Palgrave Macmillan.






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