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I know that these laboratory analysis reports each have a linear regression relationship and two have a positive slope and one has a negative slope. I am taking my first statistics class and want to be able to explain these very well in a research poster I am doing for work. Am I missing any important information? The negative slope indicates that the values are decreasing together negatively. The positive means they are increasing together. The ADL concentration chart does not have a very good relation but there is still a relation. ADL linear regression

ADF linear regression r^2, p-value

NDF linear regression

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    $\begingroup$ I would add the regression line to them. $\endgroup$ Oct 17, 2013 at 15:36
  • $\begingroup$ "The negative slope indicates that the values are decreasing together negatively". If they 'decrease together' (i.e. one decreases when the other one decreases) they'd have a positive slope. You mean that one decreases as the other increases, which is the opposite of any sense of 'together'. Adding 'negatively' to the end of that doesn't serve to make it less confusing. $\endgroup$
    – Glen_b
    Oct 17, 2013 at 22:27

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In addition to the regression line that Jeremy suggested, it would be helpful to your audience to have the p-value of the slope and the R-squared. I'm not sure how new you are to this, but you can the p-value of the slope is really part of a test of whether or not the slope = 0. If the p-value is statistically significant (p < 0.05 usually) then you can be pretty confident that the slope is not zero and that there is likely to be a "real" relationship between the independent and dependent variables. The R-squared shows how much of the variation in y is explained by variation in x. For instance, I would suspect that the ADL relationship is probably real (significant p-value) but that the R-squared will be low-ish. This isn't bad, but simply means that there are probably other things affecting ADL sorghum silage aside from ADL fresh sorghum.

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    $\begingroup$ When working w/ novices, it's helpful to keep explanations simpler even if you sacrifice a little nuance & accuracy; however, describing what p-values are as telling "you if there is actually a relationship between the independent and dependent variables" may be a bit too far in that direction for comfort. $\endgroup$ Oct 17, 2013 at 16:43
  • $\begingroup$ I appreciate the comment gung. I haven't ever answered a question before on here before. I only ventured to help on this one as I have taught simple linear regression to about 150 biology students in the last year but perhaps I've gotten too used to toning it down. I'll see if there's a way to delete answers. $\endgroup$
    – HFBrowning
    Oct 17, 2013 at 16:48
  • $\begingroup$ What is the difference between the r^2 value and the adjusted r^2 value? Also if you look at the blue chart on the bottom this includes a p-value and adjusted r^2 $\endgroup$ Oct 17, 2013 at 17:40

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