Video: Using Straight Lines to Model Relationships between Two Quantitative Variables

How useful would a line of best fit be for the scatter plot? [A] not useful at all since the data is not linearly correlated enough to apply to a line of best fit. [B] just as useful as the data since the line goes through every point anyway. [C] possibly useful, as there is a pattern but the data points do not match up that well. [D] very useful, since it will be close enough to the data points to give reasonable approximation.

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Video Transcript

How useful would a line of best fit be for the scatter plot? a) Not useful at all since the data is not linearly correlated enough to apply to a line of best fit. b) just as useful as the data since the line goes through every point anyway. c) possibly useful as there is a pattern but the data points do not match up that well. d) very useful since it will be close enough to the data points to give reasonable approximation.

A line of best fit is a straight line that best represents the data on the scatter plot. This line may pass through some of the points, none of the points, or all of the points. Looking at this data should show us that there is no way to draw a straight line that will include every point on the scatter plot. One of our answer choices, answer choice b, claims that the line of best fit would go through every data point. And that can’t possibly be true. But looking at the data, we can see that it is generally trending upward. So it’s not true that we couldn’t apply a line of best fit. Option a won’t work.

Now we have to decide between this graph being possibly useful or very useful. If we do our best to sketch a line of best fit, we realize that many of the points are far from that line. And we have a lot of outline data. Because of that, it’s better for us to say that this is possibly useful. There is a pattern, but the data points do not match up that well. It wouldn’t be very useful since the line of best fit would not give reasonable approximation at all points. So we just stick with c: this line of best fit is possibly useful.

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