Hugo - looking at your output it seems as though only one predictor is associated uniquely with the outcome in the final model. The other predictors have t values

Hello Hugo. Even if each variable has a positive coefficient when it is the only variable in the model, there is no requirement that all coefficients have positive signs when all variables are in the model. If your library has the 1977 book by Mosteller & Tukey (link below), I urge you to take a look at chapter 13, Woes of Regression Coefficients. HTH.

https://www.pearson.com/us/higher-education/program/Mosteller-Data-Analysis-and-Regression-A-Second-Course-in-Statistics/PGM154255.html

Thank you for your answer. I asked this mostly because all values with no exception shouldn't have a decreasing effect when trying to predict the "Evaluation" variable. Although the model, when comparing the model's predictions with the results I had beforehand, mostly showcases values with a small difference, the logic of the problem doesn't make much sense if those coefficients possess a negative value. About that book, I'll check if it is possible to read it and understand better these things.

Are the negative effects 'significant' (relatively large in comparison to their standard error) and substantial ( a small change in X producing a relatively large change in Y) - if so , congratulations - you have found something interesting and new that counters current expectations and theory.

Kelvyn Jones, one of the negative effects isn't significant but possesses the highest std error, the other has above average significancy when compared to the others and 2nd highest standard error (not as big as the previous one, just slightly above average. I'll annex the output in case you want to see. The output has 2 regressions, one with an outlier and the second without that one.

Hi Hugo. Readers who do not have SPSS will not be able to view your output. You could make it accessible to more readers by exporting it to Excel, for example. When exporting, export All Visible Output so that the Notes fields and other non-essential parts of the output are omitted. HTH.

Bruce Weaver thank you for the suggestion, I will soon update the post with an Excel file.

In regression analysis, the beta coefficient represents the change in the outcome variable for a unit change in the independent or predictor variable. A negative beta coefficient indicates the decrease in the dependent variable for a unit change in the independent variable.

Taiwo Sogunle, thank you for your answer. The effects you referred are valid but it isn't something expected from the data I have. Using an example from my results, it isn't expected that heterogeneity of boxes (one of the negative values) decreases the complexity of a box arrangement on a pallet.

Also here are the Excel files of the database and the outputs. In the output file, there's a regression with an outlier and below the same regression but without the outlier.

Hugo - looking at your output it seems as though only one predictor is associated uniquely with the outcome in the final model. The other predictors have t values

Thom thank you for your answer. So, considering those issues, what can be done to overcome this issue, besides I presume, getting more data. I have only a few days to finish this report so getting more data would be a deadline killer.

About the t values I wasn't aware that t>1 would explain that those are the variables that add the most significancy to the prediction. The ones with t>1 are the number of boxes and number of column piles, so I'd say the model is accurate when it comes to what impacts the model the most.

About the df value, what can be considered as an acceptable value for that?

There aren't any simple cut-offs for df. However, with error df of 9 this means that some predictors are adding noise and reducing the accuracy of your estimate of error variance. It is likely running a model with 10 or so data points rather than 40.

You can simplify the model by taking out conceptually redundant predictors. You could also combine predictors that are highly correlated / collinear with other predictors. One would normally use tolerance or other collinearity stats for this. I don't know enough about the topic to suggests principled ways to reduce the model beyond those general points.

A t value of 1 is the expected value of adding random noise to a model (expected in the long run - not necessary for any given set of noise).

Thom thanks for the answer. In case i finish the leftovers of my report in time, I will follow your suggestion and try to combine possible highly correlated variables and see if the model improves.

Hi Hugo,

in case you still got some time:

There is a special thing standing out in what you say, namely, that every of the independent variables should be positively related to the dependent variable. Let's take this as a 'given'. Further, given you have 10 IV's, you should assume, that there will be correlations among these IV's, since they all share information with the DV (which not necessarily has to be the same, but the information might overlap).

Now: Given this, think over a multiple regression (MR). For a rough illustration, the MR works like this: Assume you have 2 IV''s, now when you predict a DV, the IV1 explains some variance of the DV, but before IV2 is considered, the explained variance by IV1 is partialed out from the DV (very similar to partial correlation). The remaining variance of the DV is then explained by IV2. (Details in the standard text books :)).

Now coming back to your statement, and the first thing I noticed above: If the 10 IV's correlate, they explain the same/similar variance in the DV, however, if there is one (strongest) predictor which does the job, this variance is partialed out, which leaves nothing for the remaining 9 IV's to predict, despite some 'other' influence. And the remaining variance of the DV could, indeed, also be negatively regress to some of those 9 remaining IV's, but this has nothing to do with the 'major part' of variance which you wanted to explain, and might be due to experimental design or participant characteristics (which should not be reliable).

Sidenote: If the remaining 9IV's, in fact, would be assumed to have a -different- influence on the IV than the strongest IV1, then, in fact, taking out this variance from the DV, increases the statistical power in detecting relations between the left over variance in the DV to some of the other predictors. This is just because the overall variance was reduced, which was not related to the other 9 DV's (and therefore could not be explained by them).

So in sum... if all your 10 variables measure the same thing... (which is not the same as increasing the DV in some way), the result you got can, and should, be anticipated, and therefore is a 'somehow' good result :)) . However, if the 10 IV's do not measure the same thing, e.g. you could predict the growth of a plants by the amount of supplied sunlight and water..., and it turns out that only sunlight predicts the growth (sorry this is a moderation actually :), but the logic is hopefully clear)... but not the amount of supplied water, then, the only thing left to conclude is, that your result is inconclusive, regarding the predictor of water supply, unless you have made an a priori power analysis for how much observations you need to detect (a significant) effect of water supply, independent from sunlight.

Hope this helps,

Best René

René thanks for answering and sorry for being late. I got no extra time to change things so I had to submit with what I had. So basically, I guess some of the variables have inconclusive effects, since they don't measure the same things directly, although indirectly they may be affected by the same parameters, like measuring heavy boxes (considered as having more than 8 kg) and the average weight of the boxes, which measure respectively the immediate effort on the picker and a progressive effort.

Is there any possibility to convert negative values of beta into positive values?