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Does bivariate data suggest a linear relationship?
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(A) Yes.
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Otherwise, drawing a scatter plot would not be possible.
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(B) No, because some variables are not correlated linearly or at all.
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(C) No, because lines of best fit work for nonlinear relationships as well.
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And (D) yes, that is what bivariate means.
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To answer this question, we’re going to recall the definition of two of our key terms.
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Our first is the term bivariate or bivariate data.
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We know the prefix bi- means two.
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For instance, if we’re riding a bicycle, we know that that has two wheels.
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Bivariate data then means data for two variables.
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For example, we might look to compare the amount of ice cream sold on a given day and the maximum temperature for that day.
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So, what does the second term mean?
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That’s linear relationship.
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Well, if two things are correlated, they might have a linear relationship.
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This is a relationship of direct proportionality.
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And when we plot it on a graph, we trace a straight line.
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Consider the ice cream sales and temperature example.
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It might follow that the higher the temperature on a given day, the more ice creams are sold.
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And so, a scatter graph or a scatter plot might look like this.
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We can draw a line of best fit on this scatter graph.
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This is a straight line.
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And so, ice cream sales and temperature might have a linear relationship.
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So, this is an example of bivariate data that might suggest the linear relationship.
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But does all bivariate data suggest this kind of relationship?
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Well, let’s take another set of bivariate data.
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For instance, let’s look at cloud cover on a given day, measured in oktas, and the maximum wind speed in that day, measured in kilometers per hour.
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We cannot be convinced that there is any strong correlation between the amount of cloud cover and wind speed on a given day.
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And so, a scatter plot might look a little something like this.
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There appears to be no correlation at all, no relationship.
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And so, we wouldn’t be able to draw a line of best fit.
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And so, we see that this is an example of bivariate data which doesn’t have a linear relationship at all.
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So, we compare these to our answers.
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Answer (A) says, “yes, it must be true.
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Otherwise, drawing a scatter plots would not be possible.”
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We’ve just shown that it is possible, and so it cannot be answer (A).
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(B) says, “no, because some variables are not correlated linearly or at all.”
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Now, we’ve shown that this is true.
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And so, the answer could be (B).
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But then, we have option (C) and this says no again.
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But this time, the reason is because lines of best fit work for nonlinear relationships as well.
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Well, yes, that is true.
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We can have nonlinear correlation, but this doesn’t take into account the fact that some bivariate data will not have a relationship at all.
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And so, it cannot be (C).
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Option (D) says, “yes, that’s what bivariate means.”
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And we have actually shown that bivariate data simply means data for two variables.
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So, it’s not option (D).
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And so, our answer must be (B) no, because some variables are not correlated linearly or at all.