Finding the regression equation and best predicted value for bear chest size

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to find the regression equation and best predicted value for bear chest size.  Here's our problem statement: The data show the chest size and weight of several bears.  Find the regression equation, letting chest size be the independent (or x) variable.  Then find the best predicted weight of a bear with a chest size of 48 inches.  Is the result close to the actual weight of 430 pounds?  Use a significance level of 5%.

Part 1

OK, the first part of the problem asks us for the regression equation.  To do this, I'm going to go ahead and take this data, and I'm going to dump it into StatCrunch.  StatCrunch!  Yes!  We love StatCrunch.  Yes.  Alright, here we go.  I'm going to resize this window so we can see everything's just a little bit better.  Actually, let's do it this way.  Right.  I'll get you first because I don't really see you as much as I need to see you.

Alright, here we go.  Regression equation --- so here's my data.  I'm going to click on Stat --> Regression --> Simple linear.  The x variable is usually the one that's mentioned first.  But just to make sure, let's check out the problem statement.  It says to make chest size the independent (or x) variable, and so that is the one that's mentioned first.  So we're going to select that the y variable or the dependent variable which is, of course, the other variable that we have to select from, and that's all I need to do.  Hit Compute!, and StatCrunch will do everything for me as far as the heavy lifting goes.

Here is my regression equation, right up here at the top.  It's kind of jumbled among tons lots of stuff, so it's a little harder for me to see the numbers.  So I go through and look at the parameter estimates table down here.  Notice these numbers here are the same numbers that you see up here, so I just go ahead and just use the numbers here from the parameters estimate table.  Don't forget your negative signs.  If you have a negative sign there, don't forget to put that in.  And we want round to one decimal place.

Oh, it did not like that!  What did I do wrong?  Oh, I typed in the wrong number.  Looking at the results, I'm looking at the wrong number.  It would help to look at the right number!  Waking up, making sure that you people out there in YouTube Land are awake!  Alright, that gives it to us.  Nice work!

Part 2

Alright, now the next part of this problem asks, "What is the best predicted weight of a bear with a chest size of 48 inches?"  Well, the first question we need to ask when looking for a prediction is "Can we use the regression equation?  Will the regression equation give us a reliable estimate or prediction?"  So to do that, we need to compare R squared values with the critical R squared value.

So if I click on this link right here, I have a table of critical R values.  Our sample size here is 6, so that's going to be looking at this column here.  And I believe --- yes, right here, a significance level of 5%.  So I want to look at the value in this first column for the row where we've got 6, and I get 0.811.  That's the bar that we have to clear in order to use the regression equation.

Over here, the regression equation, my R squared value is 0.995.  That's outstanding!  That's practically 1.  It's hard to get much better than that.  And yet look at when we compare with the critical R value, 0.811, we're actually greater than that.  So we're clearing the bar.  It's like a hurdle or a pole vault jump, and we're trying to clear the bar.  And we've cleared the bar because 0.99 is greater than 0.81.  So that means the regression equation is good to be using for predictions.

To use this for a prediction, I can either plug it in myself and do it old school style with my calculator, or I can come up here to Options, click on Edit, scroll down here to Prediction of y, put in my x value for the prediction (which here it says it wanted a chest size of 48), and a significance level of 5% so that matches here at the level of 95% confidence, hit Compute!, and I'm going to expand this out.  And if you scroll down to the bottom, look at this!  It actually calculated it out for me.  So there's my predicted value right there, which is a whopping 468 pounds.  Wow.  Round to one decimal place.  And that's a --- that's a big bear!  That's a big anybody!  Jeez.  Look at that!  Fantastic!

Part 3

Alright, is the result close to the actual weight of 438 pounds? Well, I don't know. Anything over 400 is pretty much all in the same category, I would think. But the difference is a good 30 pounds. 30 pounds! So they're probably not in the same neighborhood. So I would say the result is close --- no the result is not very close. I like that one; the result is very close. No, the result is exactly the same? Let's go with --- let's go with Answer option B. Excellent!

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