I believe that, for anyone to provide any guidance on your question, the dataset in which the problem occurred should be shared (or at least some way to replicate it). I'm really curious about this issue.

Sorry that I cannot share the original data file. It is my file but I used it for my textbook. So, my publisher might have the copyright for the data.

Instead, I created a simulation file based on my data. I ran the same analyses and replicated the same issue.

Please do the following. Choose two variables that are negatively correlated (PA&BDI). Run a simple regression while saving the predicted value (either unstandardized or standardized). Then calculate the correlation between the predicted value and the original predictor. It came out as -1. Do the same with two variables (NA&BDI) with a positive correlation. It will come out as 1. The output file shows only the first example.

I sent a ticket to SPSS. FYI, the version I am using is ver.28.0.0. Jamovi version is 2.3.16.

I see. I may be missing something but... aren't the predicted values (y_hat) a simple linear transformation of the predictor (x)? That is, y_hat = intercept (ie. a constant) + beta(another constant)*x. Isn't it just logical that there's a perfect correlation between x and y_hat? I'll be happy to receive feedback in case I'm missing something.

Yes, I agree. But, it should be a positive perfect correlation to my understanding. In a simple regression, the predicted value is the original predictor. Or I miss something here.

If the "form" of the association modeled is negative, then the correlation between x and y_hat will be perfect and negative (ie. -1). Let's say, for instance, that the model obtained is 46.34 - 1.04*x.

With x = 1, y_hat would be 45.30

With x = 2, y_hat would be 44.26

With x = 3, y_hat would be 43.22

You can see that, with every unit-increase in x, there is a 1.04 decrease in y_hat. A different pattern would be observed when beta is positive.

As a sidenote, we would expect a positive correlation between y and y_hat (this would be sign of a good predictive model).

Wow.... that makes perfect sense! I indeed miss something big. This should be obvious but I never thought about this in the right way. Have assumed that this would be the same as a positive relationship.

Thank you very much!

No worries. Happy to help :-)

The issue you described regarding the calculated predicted values showing a negative perfect correlation with the predictor variable in SPSS and jamovi is indeed odd and seems contradictory. It's important to note that the interpretation of the results should be based on the scatterplot and the direction of the relationship rather than the correlation coefficient itself.

There could be several reasons why this issue occurred in both SPSS and jamovi. Here are a few possibilities to consider:

1. Data or input error: Double-check your data to ensure that there are no errors or inconsistencies. Verify that the variables are correctly defined and coded, and that the data points are accurately entered.

2. Software settings: Check if there are any specific settings or options within SPSS and jamovi that could affect the calculation or presentation of results. It's possible that default settings or options were selected that could cause this unexpected behavior.

3. Regression assumptions: Ensure that the assumptions of linear regression are met. Violation of assumptions, such as nonlinearity, outliers, or heteroscedasticity, can sometimes lead to unexpected results. Consider examining residual plots to assess the assumptions.

4. Sample size: The issue could potentially be influenced by the size of your sample. If the sample size is relatively small, it can sometimes lead to unreliable or unstable estimates.

5. Software bug: Although less likely, it's possible that there could be a bug or an issue specific to the version of the software you are using. You can check for any updates or consult the software documentation or user forums to see if others have encountered similar problems.

To further investigate this issue, you may want to consult with experts in statistical analysis or reach out to the support teams for SPSS and jamovi. They may be able to provide more specific guidance or insights into the problem you encountered.

FAKE ANSWER WARNING

The answer by Samira Akter Tumpa was analysed by https://gptzero.me, and the result was

Your text is likely to be written entirely by AI

This person uses ChatGPT to answer questions without apparently knowing or caring whether they are right or wrong. Reported to RG.

Pablo D Valencia has already given you an excellent explanation. Here's another way to understand (or perhaps even grok) it. Look at the attached scatter-plot, and consider that the fitted values (i.e., the Y-hat values) all fall on the regression line (which has a negative slope). ;-)

https://www.merriam-webster.com/dictionary/grok

Ronan,

Thanks for the information. In fact, ChatGPT could not generate correct answers to my questions related to this (and other questions before). It kept producing inaccurate answers. So, I had to correct the errors but couldn't do it without going through multiple steps. As soon as I saw Samira's answer, I knew it was ChatGPT's answer. In fact, I have seen many errors in ChatGPT's answers to various stat-related questions.

The issue you encountered with the calculated predicted value showing a negative perfect correlation with the predictor in both SPSS and jamovi is indeed puzzling. It seems contradictory to have a negative relationship between the predictor (Extraversion) and the dependent variable (Depression), yet observe a positive trend when plotting the predicted values against the DV in the regression menu of SPSS. It's difficult to pinpoint the exact cause of this issue without more information, but it could potentially be attributed to a software bug or a misinterpretation of the data. It would be advisable to double-check your data and analysis procedures to ensure accuracy and consider consulting with experts or the support teams of SPSS and jamovi to address this discrepancy.

The situation you described seems puzzling indeed. It is highly unlikely for a negative relationship between the predictor variable (Extraversion) and the dependent variable (Depression) to yield a calculated predicted value that exhibits a perfect negative correlation (-1) with the predictor. Such a result contradicts the expected behavior and raises concerns about the accuracy of the analysis. The fact that this issue was replicated in both SPSS and jamovi suggests that it may be related to a common underlying factor or an inherent limitation in the algorithms employed by these software programs. While it is difficult to pinpoint the exact cause without further investigation, it is essential to critically evaluate the data, variables, and analysis procedures to ensure their validity and to consider seeking assistance from experts in statistical analysis or the support forums of these software tools to address this peculiar issue.