Using StatCrunch to find a regression line equation from a given scatterplot

Intro

Howdy!  I’m Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we’re going to learn how to use StatCrunch to find a regression line equation from a given scatterplot.  Here’s our problem statement: Using the pairs of values for all 10 points, find the equation of the regression line.  After removing the point with coordinates (2,9), use the pairs of values for the remaining 9 points and find the equation of the regression line.  Compare the results from Parts A and B.

Part A

OK, Part A asks us for the regression line for all 10 points that are shown on the scatterplot.  Let’s blow this scatterplot up a little bit so we can see a little bit better what we’re dealing with here.  Notice there’s no icon here to actually dump the data into StatCrunch.  So I’m going to call up StatCrunch, and we’re going to have to put the ordered pairs for each of these data points in manually.

To start off with, I’m actually going to label my columns X and Y.  It makes a later portion of solving this particular problem a little more easy.  And now I’m going to go and get the ordered pairs for each of my data points.  So starting here with this point all by itself, the X value for that is 2, and the Y value is 9, so that’s (2,9).  Then for the points here that are in a square formation, we’ve got three points that have an X coordinate of 4, three points that have an X coordinate of 5, and three that have an X coordinate of 6.  And then we’ve got three points — these three points have Y values of 2, 3, and 4, as do the next three and the last three.  So there’s the ordered pairs for all 10 data points here in my scatterplot.

Now I’m ready to make my regression line.  To do that, I go to Stat –> Regression –> Simple Linear.  Here’s where labeling those columns becomes very useful.  The X variable is the X.  The Y variable is the Y.  And that’s all I really need to get the actual regression equation, so I go ahead and hit Compute!  And let’s expand this window so we can see better what’s going on.

So we see the actual regression equation here.  But notice how the answer fields are just asking for the coefficients of the regression equation.  I can take them from here, but there’s a lot of business going on here.  And it’s actually easier for me to see those values if I go down here to my parameter estimates table.  So see the 9 that is here originally?  That same 9 is here.  And then that’s your y-intercept.  And then the slope — the slope value here is the same as the slope value down here.  So I actually prefer to get my values for my regression line down here in the parameter estimates table.

So the first value here is my intercept.  And the next value — notice I’m carrying the negative sign with me.  Good job!

Part B

Now, Part B asks for the regression line equation for the set of nine points.  So in the problem statement, it asks us to remove this one point that is an outlier and get the regression equation for just these nine.  To do that, first I’m going to clear out this results window.  And then I’m going to come up to this row and select it.  And then his little arrow next to it gives me a drop down menu, and I’m going to select Delete row.

Now I’m going to bring back my results window.  Select Options –> Edit, and then I don’t need to change any of the settings, so I hit Compute! And it recalculates everything with the new columns that I have after I deleted that data point.  So now we can see we’ve got the values here.  So now my regression equation is y-hat equals 3.  Of course, zero slope means there is no X variable for my equation.  Well done!

Part C

And now Part C is the last part of the problem, and it asks us to “choose the correct description of the results below.”  We’ve got four options here, so let’s look at them one at a time.

Option A says, “The regression line is very similar in both cases.”  Ah, well, that’s not true.  I mean, just look at the regression line equations here.  This is a line with a negative slope to it.  This is a line with — well, there’s no slope to it because it’s just a straight, horizontal line.  So answer option A isn’t going to work for us.

Answer option B says, “The regression line changes, but the change is small.”  Hello?  You go from having a negative slope to having no slope at all.  And, you know, your y-intercept changes quite a bit, so I wouldn’t call that change small. So answer option B isn’t going to work for us.

Answer option C says, “The removal of the point has a significant effect on the regression line.”  Well, that’s true.  But let’s check out answer option D before we select this answer.

Answer option D says, “There is no regression line for the second case because the data are in a pattern.”  Well, there actually is a regression line; we’ve got the equation right here.  So answer option D isn’t going to work for us.  Answer option C is the one we want.  Good job!

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