# How to assess the fit of a horizontal trend line?

I have two trend-lines, both with a slight negative slope. The first has a greater slope, but significant scatter of the data points, while the second is nearly horizontal with an obvious better fit.

I would typically use an R^2 value to determine fit, but this does not work the closer a line comes to horizontal. Is there an alternate evaluation that assesses the scatter of data on a nearly horizontal line? The data is not meant to be horizontal, so standard deviation would not work either.

Actual Data

• Would help to know what procedures gave rise to such different regression lines. If line is 'nearly horizontal' in the sense that test (of slope) $H_0: \beta_1 = 0$ vs $H_a: \beta_2 \ne 0$ not rejected, that is a clue that regression of $Y$ on $x$ is not useful in predicting $Y$'s . In that case correlation not significantly different from $0,$ so $r^2 \approx 0$ is bad news, but not useless information. – BruceET May 26 '18 at 6:04
• The different plots are the result of data collected by two different pressure sensors. The trend lines are best fit linear lines from excel. The assessment of the data scatter will help determine which sensor outputs more reliable data. – greenhornet93 May 26 '18 at 16:47
• Plots of what against what? No time for this cat-and-mouse game. Voting to close pending a reasonable description of what you're doing. – BruceET May 26 '18 at 18:27
• The plot is pressure vs time. No games here, look at the posted graph. – greenhornet93 May 27 '18 at 22:48
• Thanks for the graph. A quick look suggests that the lines may be more alike than they seem in your plot. (Both seem to have slopes significantly different from 0.) Try plotting each line on its own vertical scale running in the interval from lowest pressure to highest. From what is available here (without digitizing the data and doing my own analysis, and without direct knowledge of the two types of evaluation) I'd use largest $R^2$ as the criterion. If you're trying to use time to predict pressure, see if the line with the largest $R^2$ doesn't give the tightest prediction intervals. – BruceET May 28 '18 at 1:59