So, I've obtained a graph of lab data an it's a plot of thermal resistance versus pressure. Pressure on the x and thermal resistance on the y. If I plot all the points, there doesn't seem to be any trend. The y values are just as likely to decrease as they are to increase with increasing x values. So, even though the y values do change with increasing x, you couldn't say that there's a trend. So, for analysing this, would I say that the y values are independent of x or would I just say that the y values are dependent on x, just with no discernible trend? I've attached the excel sheet, see graph 1. Not sure if that more suited to the homework section or here because it's not so much a homework question, as a general mathematics one to do with interpreting graphs.
I would suggest that you repost that chart as a PDF or at least as an Excel 97-03 format. More people will be able to see it. Also there are many who are, rightfully, reluctant to open and unknown Office files, such as yours.
Since the graph has a ".xlsx" extension rather than a ".xlsm" extension, it should not have any macros, so I am reasonably confident the file is safe and I have gone ahead and opened the file. The OP is asking about the Graph 1 tab. If you're asking about wording, I would say there is "no statistically significant dependence (or trend)" in contact resistance vs. pressure. If you want to go into more detail, you could say that for the blue curve only 0.1% of the variance in the values of contact resistance can be attributed to the pressure, while 99.9% of the variance is due to random error or other causes. Recall that variance is the square of the standard deviation in a set of values. The 0.1% figure comes from the r^{2} value (0.001) given in the data fit. By the way, it looks like you have ignored the red data points around 99 kPa, 0.6 ohms, causing the r^{2} value to be an artificially high 0.23. If you include those data points, you should get an even lower value for r^{2} for the red data set.
is there a specific question you need to answer in respect of this data, or is it just a commentary you're after? Questions I'd be asking / thinking about would include the following; 1. Are you actively controlling the pressure variable during data gathering, or are these just measurements of opportunity? 2. If they are measurements of opportunity, maybe there is some other variable that is changing during your data gathering, and that this other variable is actually more important than pressure? 3. Why is the 'red' data much noisier than the 'blue' data? 4. Have you attempted to quantify your measurement noise -by controlling/fixing the pressure variable and making repeated resistance measurements for example? Maybe this isn't possible? As the previous poster suggests, I suspect your data is completely dominated by measurement noise to the extent that drawing any conclusions about trends is pretty much impossible