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I am currently undertaking a project where I aim to explore the relationship between a single independent variable and a dependent variable. I have five questions that are answered on a 5-Point Likert scale by each respondent, representing a specific concept, i.e. $X$. I also have a corresponding metric for each respondent, which serves as my dependent variable, hypothetically representing an outcome, i.e. $Y$.

Here's what I plan to do with the data:

  • Calculate the average of the four Likert scale responses to create a single composite score for each participant's score for concept $X$.

  • Perform a simple OLS regression analysis to determine if there is a significant linear relationship between the composite score of $X$ (independent variable) and the outcome $Y$ (dependent variable).

  • Examine the $R^2$ value to assess how much variance in $Y$ is explained by $X$.

  • Look at the $F$-statistic and its associated $p$-value to determine the overall model fit.

Does that sound reasonable or is there anything further that I could do?

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  • $\begingroup$ How is Y measured? If Y can be seen as a continuous variable, then yes your plan is very reasonable. It's common to focus on the regression coefficient of X and its magnitude along with R-squared and F. $\endgroup$
    – Sointu
    Commented Mar 18 at 11:36
  • $\begingroup$ My outcome is a categorical variable, with low, medium and high $\endgroup$ Commented Mar 30 at 17:18
  • $\begingroup$ In that case ordinal logistic regression seems like a good choice. $\endgroup$
    – Sointu
    Commented Mar 30 at 18:17
  • $\begingroup$ Thanks, do I still apply the same assumptions like linearity, and qq plots etc. $\endgroup$ Commented Mar 30 at 18:59
  • $\begingroup$ Not exactly. I'm afraid using ordinal logistic makes things a bit more complex (than with OLS) with regards to regression diagnostics and also interpreting coefficients. It might be best if you read some tutorials of both ordinal logistic regression in general and of its diagnostics. There are quite many good tutorials online. Search for one using the same software you use. $\endgroup$
    – Sointu
    Commented Mar 30 at 19:14

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Your plan sounds appropriate if your outcome is measured as continuous. I would also suggest assessing your model assumptions, e.g. linearity, independence of errors, normality of residuals, and homoscedasticity. This can mostly be done using qqplots and residual vs. fitted plots.

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