The article by Jason W. Osborne and Elaine Waters discusses four key assumptions of multiple regression that researchers should test to ensure the validity and reliability of their statistical analyses. These assumptions are: 1. **Normal Distribution of Variables**: Variables should be normally distributed. Non-normally distributed variables can distort relationships and significance tests. Researchers can test this assumption using visual inspections, skew, kurtosis, P-P plots, and Kolmogorov-Smirnov tests. Data cleaning, including the removal of outliers, can improve the accuracy of estimates. 2. **Linear Relationship Between Independent and Dependent Variables**: The relationship between variables should be linear. Non-linear relationships can lead to underestimating the true relationship, increasing the risk of Type II errors. Detection methods include theoretical considerations, residual plots, and incorporating curvilinear components in regression analyses. 3. **Reliability of Measurement**: Variables should be measured reliably. Measurement errors can under-estimate relationships and over-estimate effect sizes. Correction for low reliability is essential to obtain more accurate results. Simple regression and multiple regression equations are provided to illustrate the impact of reliability on effect sizes. 4. **Homoscedasticity**: The variance of errors should be constant across all levels of the independent variable. Heteroscedasticity can lead to serious distortions and increase the risk of Type I errors. Visual examination of standardized residuals and formal tests like the Goldfeld-Quandt test or Glejser test can help identify heteroscedasticity. The authors emphasize the importance of checking these assumptions to avoid Type I and Type II errors and to boost effect sizes. They also suggest that researchers should be familiar with non-parametric statistical techniques as alternatives when parametric assumptions are not met.The article by Jason W. Osborne and Elaine Waters discusses four key assumptions of multiple regression that researchers should test to ensure the validity and reliability of their statistical analyses. These assumptions are: 1. **Normal Distribution of Variables**: Variables should be normally distributed. Non-normally distributed variables can distort relationships and significance tests. Researchers can test this assumption using visual inspections, skew, kurtosis, P-P plots, and Kolmogorov-Smirnov tests. Data cleaning, including the removal of outliers, can improve the accuracy of estimates. 2. **Linear Relationship Between Independent and Dependent Variables**: The relationship between variables should be linear. Non-linear relationships can lead to underestimating the true relationship, increasing the risk of Type II errors. Detection methods include theoretical considerations, residual plots, and incorporating curvilinear components in regression analyses. 3. **Reliability of Measurement**: Variables should be measured reliably. Measurement errors can under-estimate relationships and over-estimate effect sizes. Correction for low reliability is essential to obtain more accurate results. Simple regression and multiple regression equations are provided to illustrate the impact of reliability on effect sizes. 4. **Homoscedasticity**: The variance of errors should be constant across all levels of the independent variable. Heteroscedasticity can lead to serious distortions and increase the risk of Type I errors. Visual examination of standardized residuals and formal tests like the Goldfeld-Quandt test or Glejser test can help identify heteroscedasticity. The authors emphasize the importance of checking these assumptions to avoid Type I and Type II errors and to boost effect sizes. They also suggest that researchers should be familiar with non-parametric statistical techniques as alternatives when parametric assumptions are not met.