Finding and using a specified multiple regression equation

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 and use a specified multiple regression equation.  Here's our problem statement: The accompanying table provides data for the sex, age, and weight of bears.  For sex, let 0 represent female and let 1 represent male.  Letting the response (y-variable) represent weight, use the dummy variable of sex and the variable of age to find the multiple regression equation.  Use the equation to find the predicted weight of a bear with the characteristics given below.  Does sex appear to have much of an effect on the weight of a bear?

Part 1

OK, the first thing we're asked to do is provide the multiple regression equation with these variables in the equation.  To do that, I'm going to take my data and dump it into StatCrunch.  So here's my data.  I click on this icon here so I can open it in StatCrunch.

Now that my data is in StatCrunch, I'm ready to make my model.  Since I know specifically what model I want to make, all I have to do now is go to Stat –> Regression –> Multiple Linear (because we're looking at multiple variables in a equation with the linear form).  The y-variable is the response, or what comes out of the model.  Here that's going to be the weight, which you can see listed here.  So for my y-variable, I'm going to select the column of the weight values.  The x-variables are these variables here.  This is what we input into the model, so I'm going to select each of those variables here.  Interactions we don't have, and we can tell we don't have any interactions because, if we did, we would see variables like sex and age being multiplied together.  But here we only see sex and age listed separately in separate terms and not multiplied together in the same term.  And so we don't have any interactions.

At this point we're ready to make our model, so I press Compute! and here in my results window I have the model that they're looking for.  To input those coefficients into my answer fields, I often find it easier to look here in the parameter estimates table.  Notice how these numbers here match the numbers than the listed model at the top.  So I'm just going to use the numbers here in my parameters estimate table to input the answers into my answer field.  I'm asked to round to one decimal place and so that is what I will do.  Nice work!

Part 2

The next part asks us to predict the weight of a female bear that is 22 months of age.  There is no prediction option when you're using multiple linear regression in StatCrunch.  If it were simple linear regression and we only had one x-variable, then, yes, you do have that option.  But whoever decided to code StatCrunch did not give that functionality to the multiple linear regression option.  So we're gonna have to go old school and actually calculate this out by hand.

Here we have a calculator.  I'm going to use this to calculate out the predicted weight for the female bear, which up here at the top we see is 22 months of age.  So first I put in my coefficient, which is the Intercept.  I’m going to add to that the variable for the sex.  Here this is a female bear.  And up at the top of the problem statement, we see it says for sex that zero represents female, so that's what I'll put in there.  And finally the age which is 22 months.  I'm asked to round to the nearest integer.

Part 3

Now the next part asks me to repeat the same calculation for the male bear.  That's easy enough to do.  Excellent!

Part 4

And how we see the last portion of our problem asks, “Does sex appear to have much of an effect on the weight of a bear?  Select the correct choice and fill in the answer box to complete your choice.”  If we look back here at the weights that we predicted with our model, notice how the weight of the male is more than twice the weight of the female.  So there's definitely a difference between them.

The temptation when they're asking here about which one is more than the other and how much more is to simply subtract these two values, the one from the other.  But what they're really looking for is the coefficient for the sex variable, because this is what determines the difference between the weight for the female and the weight for the male.  Remember that if the sex is female, then this 82.2 will not even enter into our calculation; it will be zeroed out.  But if the bear is male, then the 82.2 gets added in, and that's essentially the difference between the weight of the female on the male bear.

So I need the answer option that says yes, there is going to be an effect. and here it looks like that's answer options A and D.  And then the regression equation indicates the predicted weight of a male bear is more than the female, so I want this answer option.  And I'm going to put in here the coefficient for the sex variable because that is essentially the difference in the weight.  Excellent!

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