Video Transcript
Can we use the line of best fit to describe the trend in the data? Why?
Let’s begin by having a look at this graph. We can see that we have the 𝑥-variables plotted against the 𝑦-variables. We’re given lots of blue dots to represent some 𝑥- and 𝑦-values. And we’re also given this line and asked if we can use this line as a line of best fit to describe the trend in the data. Well, you might think, yes, as we can see that as our values of 𝑥 increase, so do our values of 𝑦. You might even think that we have some dots above the line and some dots below the line, so that’s okay too. But there’s actually a big problem with this line of best fit, and it’s actually that it doesn’t really show the trend in the data.
The trend in the data is not a linear trend. That is, as 𝑥 increases, 𝑦 does not increase by the same amount. What we have here is an exponential trend. And we can see the clue that it’s exponential, when we have very small values of 𝑥, our 𝑦-values are very close to zero. We can see more obviously at the right side of the graph that as the 𝑥-values increase, the 𝑦-values get exponentially larger. So to answer the question, can we use the line of best fit to describe the trends in the data, we’d have to say no. And as to why, it’s because the data shows an exponential trend, not a linear trend.
Lines of best fit can only be used when the data is linear. We’d have to do some curve fitting to find the curve or curved line of best fit for exponential data.
