Tableau, Scatterplot with Trendlines to show confidence levels

Question

I have scatterplot in Tableau, and I displayed trendlines. However, I cannot understand why there are three of them.

When I research this on Tableau, they say upper line is upper 95% confidence, and lower line is lower 95% confidence.

When I think of confidence levels, I think if there are 100 black and white marbles and I take a sample, and see the ratio, I can say 95% of the time, white marbles will be 40% to 60%

And to create confidence bounds, 92% to 98% of the time, white marbles will be 40% to 60%

But I'm having difficulty translating this to tableau trendlines. Please advise.

Answer 1

Think of your data set as just one random sample drawn from a larger population of possible data sets. You could have sampled another time or place or in a parallel universe.

If you could build a scatter plot for the entire population, it would have a best fit trend line also. You can think of your trend line as a sample trend line attempting to estimate this true population trend line.

Now imagine you actually did collect many different sample data sets from that same population. Also imagine you used identical procedures to create scatter plots and trend lines for hundreds or thousands of these data sets (samples). Different samples would lead to (slightly?) different trend lines in each plot.

The confidence bands are constructed in such a way that you can expect them to enclose the true population trend line in 95% of your samples.

You are using statistical inference to estimate the confidence in the population trend model parameters. All based on the Central Limit Theorem.