# The Wellntel Analytics Dashboard Compare Tool: Correlations and Linear Regression Analysis

The Wellntel Analytics Dashboard Compare tool allows you to compare two data sets using linear regression analysis. Linear regression analysis includes specifying one data set as the independent variable and another as the dependent variable. The resulting model relates the two variables with a linear relationship providing an analytical comparison of the variation and trend in the two data sets.

## What is your hypothesis?

Since the tool is designed to answer questions by showing the possibility of a relationship between these variables, it is best to begin your inquiry with a hypothesis, for example, you might ask:

“I believe that there is a relationship between Groundwater Levels at A and Surface Water Levels at B (or not) considering external feedback and influences, geographic or geologic proximity. Can I show that there is a statistical correlation?”

Then, start your analysis by assigning each data set as the independent (predictor or x-axis) variable or the dependent (response or y-axis) variable.

• To conduct the linear regression analysis and view the output linear model, select: Show Linear Regression.
• To view a summary of the linear regression applied to the selected data, select: Show Regression Stats.

## Understanding Results

Key metrics evaluated during a linear regression analysis – the “r-squared” value (R2) and the p-value – are available in the output summary and also shown at the top of the chart.

Correlation indicates that one data set, or variable, changes systematically as another variable changes. R2 is the ‘fraction of variance explained by the model’. In other words, R2 represents how well the linear regression model fits the data being compared and analyzed.

The “p-value” evaluates how well your data rejects the null hypothesis of the linear regression analysis. The null hypothesis is the opposite of your starting hypotheses and states that there is NO relationship between the two compared variables. A sufficiently small p-value, 0.05 or less for example, indicates that you can reject the null hypothesis. Successfully rejecting the null hypothesis tells you that the linear relationship and correlation are statistically significant.

## More Information:

By default, both the x-axis and y-axis data sets are aggregated by week (7 day) and presented as an average. Other aggregation statistics are available, such as maximum or minimum, and different periods of aggregation are available, such as daily, monthly, etc. If no aggregation is required for a comparison of individual measurements, “None” can be selected. If no aggregation is selected the dependent, or response, variable is linearly interpolated to match the timestamps of the independent, or predictor, variable to enable the regression analysis.

The feature set includes a linear regression analysis which utilizes the “Linear Model” or “lm” function within the base R statistical package. Details on the lm function are available here. “The lm function is used to fit linear models. It can be used to carry out regression, single stratum analysis of variance and analysis of covariance”. Details on the output summary are available here.

For more information about the Wellntel Analytics Dashboard see the Wellntel Operating Manual.

For technical support email techsupport@wellntel.com (include `Analytics Dashboard` in the subject line) or call 844-935-5426 between the hours of 8-5pm Central Time, Monday through Friday. If you reach us after hours, we will promptly respond the next weekday morning.