interpreting simple linear regression equation

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If the scatterplot just looks like one big blob, and you can’t really see any relationship in the data, then we would say there’s no relationship or correlation at all. If the data more closely follows a parabolic curve, we would say the relationship in parabolic. If the data roughly follows a linear trend line, we can say the relationship is linear.

The form (linear, parabolic, sinusoidal, etc.), Whenever you describe a relationship in the data, you should describe

So the next question we need to answer starts to become obvious, and that is “Is the regression line even a good estimate of the data?” Luckily, there are ways to measure how good of a fit this line is to the data points, and we’ll look at those techniques a little bit later on. If you look at the scatterplot we made, you might even say it has more of a sinusoidal shape, and we can see that the point around ?x=8? looks like an outlier. With this last example, you might notice that the data actually wasn’t super linear.

So the equation of the regression line is ?m=rac?, (pronounced “y-hat”), to indicate that it’s a regression line, and remind us that it’s an approximation for the data set. The regression line formula then calculates the slope ?m? and the ?y?-intercept ?b? using The equation for a regression line is most often given in slope-intercept form, ?y=mx+b?. There are a few ways to calculate the equation of the regression line. For the rest of this lesson we’ll focus mostly on linear regression. For example, the relationship might follow the curve of a parabola, in which case the regression curve would be parabolic in nature. The regression line is a trend line we use to model a linear trend that we see in a scatterplot, but realize that some data will show a relationship that isn’t necessarily linear. A regression line is also called the best-fit line, line of best fit, or least-squares line. It’s the line that best shows the trend in the data given in a scatterplot. The most common way that we’ll do this is with a regression line. The plot alone isn’t super helpful, but if we can use the plot to observe some kind of a trend in the data, then we might be able to use that trend to draw conclusions or make predictions about the data. And, in fact, spotting trends is probably what we spend most of our time doing when we work with scatterplots. It was intuitive for us to start looking for trends in the scatterplots as soon as we saw the plotted points. The regression line is one of the most important approximating curves we’ll talk about, so let’s take a look at that now. No matter the shape of the curve that the data follows, we call it the approximating curve, and the process of finding the equation of the approximating curve is called curve fitting. When we say that the data in a scatterplot appears to follow a trend, what we’re really saying is that it appears to follow some line, or maybe some other kind of curve, like for example an exponential curve or sinusoidal curve. The graph in the upper right looks like it might be following a positively-sloped line, but if it is, the trend is not as clear as either of the graphs on the left.Īnd the graph in the lower right doesn’t look like it’s following any trend at all. For example, the two graphs on the left definitely seem to be roughly following a line: the one on top looks like it follows a line with a positive slope the bottom one looks like it follows a line with a negative slope. Even though scatterplots can look like a mess, sometimes we’re able to see trends in the data.

Interpreting simple linear regression equation