In a regression, our null hypothesis is that the slope of the best fit line is zero. We can frame this situation using the same language of Section 5.2. Because there were only five data points, this would be a fairly likely outcome. However, one could make the case that tail-waging rate is unrelated to treat size and that it was simply a coincidence that the points on the right side of the graph were higher than those on the left side. In the example to demonstrate how to create a scatter plot in Excel, we saw that the best-fit line through the treat size/tail-wagging rate data had a positive slope. A linear regression can facilitate both of these uses. If the tail wagging rate were completely random and not affected by the size of the treat, the best-fit line would be horizontal, showing that the average wag rate was the same regardless of the treat size. In that case, what we want to know is whether the slope of the best fit line is different from zero or not. We may not actually care about describing the way that the factors vary (the equation) we may just want to know if they vary significantly or not. In that case, we simply want to know if changing the size of the treat has a significant effect on the rate of tail wagging. The other important use of linear regression is as a statistical test of significance. If we know the equation of the best-fit line we can plug numbers into it to calculate the predicted value. In the example, we might like to predict how fast the tail will be wagged given a treat which is a size that we didn't specifically measure. One important use of linear regression is predictive. When we fit the best line through the points of a scatter plot, we usually have one of two goals in mind. (There is another chart type that Excel makes which does that - don't use it!) The name of the process used to create the best-fit line is called linear regression. In scientific graphs, one almost never 'connects the dots'. That's why another name for trendline is best-fit line. It may or may not actually pass through any particular points. You should notice that the trendline is the best line that fits through the points. In the example above, we had Excel calculate and plot a linear trendline through the points.

Experimental Design Project Toggle Dropdown.11 Reporting the Results of a Statistical Test.6 Scatter plot, trendline, and linear regression.5.6 Discussing statistics in your scientific writing.5.4 A test for differences of sample means: 95% Confidence Intervals.5.2 P and Detecting Differences in Variable Quantities.3.3 Calculating Descriptive Statistics using Excel.3.1 Describing Quantities and Their Variation.Excel Reference and Statistics Manual Toggle Dropdown.Appendix A: Calculation Final Concentrations.3.1 Specific details regarding scientific writing.Scientific Literature Guide Toggle Dropdown.

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