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Friends,

I have a dataset of 7446 with one dependent variable which is " service time" and 8 independent variables. the dependent variable and one of the independent variables are numeric variables and rest of the independents are all binary variables. as the attached picture shows, the Pearson correlation between the dependent variable ( "service time") and all the independents is very low. also, the linear regression has an R-squared of 0.047.
correlations matrix from SPSS

how can I fix the problem with these data? is this because I have a lot of binary variables (6 binary variables out of my 8 variable)?

I appreciate your comments.

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  • $\begingroup$ There is no problem with the data. Service time is weakly-correlated with your predictors. $\endgroup$
    – Mark White
    Commented Feb 23, 2018 at 3:16
  • $\begingroup$ thanks Mark, I was wondering if I need to do any transformation, or try nonlinear regression or any other thing that can reveal the relationship between the service time and other variables. because I believe there is a relationship between them. $\endgroup$
    – Maryam
    Commented Feb 23, 2018 at 3:32
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    $\begingroup$ Try plotting the dependent variable against each of the independent variables. This isn't conclusive, but if there is a nonlinear relationship between one or more of the independent variables and the dependent variable, the plot should help identify it. $\endgroup$
    – jbowman
    Commented Feb 23, 2018 at 4:13
  • $\begingroup$ Just try a regression model and see! Even if individual correlations are low, collectively they might be quite informative. And please, show us some plots, or even a link to download the data. And tell us the context, that is, what does your variables measure? $\endgroup$
    – kjetil b halvorsen ♦
    Commented Feb 23, 2018 at 9:45

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If you are reasonably sure that there ought to be relationships between each of the IVs and the DV then you should plot the DV against each of the IVs. For the continuous IV you can try a scatterplot and add a loess line. For the dichotomous IVs, one fairly simple option is to jitter the IV and then do a parallel boxplot with the DV. With so much data, you will probably need quite a bit of jitter and you might also try making the points open circles.

See what that reveals.

For the full regression model, one possible option with a lot of IVs is a regression tree - this may reveal interesting interactions. If it looks promising, then you might investigate things like random forests.

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    $\begingroup$ The low correlations already tell us what the boxplots will show about the means: they will scarcely differ. At best this will reveal skewed and heteroscedastic relationships, thereby possibly suggesting a transformation of the dependent variable. After that, the way to explore these data further is to begin considering interactions. $\endgroup$
    – whuber ♦
    Commented Feb 23, 2018 at 15:33

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