ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE General & Further Mathematics => Topic started by: krzysiek on October 06, 2009, 08:26:43 pm

Title: Help with least squares regression line... very confused with how it works!
Post by: krzysiek on October 06, 2009, 08:26:43 pm

Hello,

So, on practise exams, the only part I struggle with it seems is the core section.

Especially when it comes to linear regression lines, I suck completely.

For example, it may give you a table where one column is "attempts and goal" and the other is "scored goals" and say make a linear regression line for goals scored = "_____" + "_____" x number of goal attempts.

When it comes to a question like this, I honestly can't say I know where to begin. I know that it must be in the form y = ax + b, and b = r x standard deviation y / standard deviation x and a = mean y - mean x times 'b'

but if someone could shed some more light onto how to approach these questions, I would greatly appreciate it.

Regards

Title: Re: Help with least squares regression line... very confused with how it works!
Post by: plato on October 06, 2009, 09:07:47 pm

Quote from: krzysiek on October 06, 2009, 08:26:43 pm

Hello,

So, on practise exams, the only part I struggle with it seems is the core section.

Especially when it comes to linear regression lines, I suck completely.

For example, it may give you a table where one column is "attempts and goal" and the other is "scored goals" and say make a linear regression line for goals scored = "_____" + "_____" x number of goal attempts.

When it comes to a question like this, I honestly can't say I know where to begin. I know that it must be in the form y = ax + b, and b = r x standard deviation y / standard deviation x and a = mean y - mean x times 'b'

but if someone could shed some more light onto how to approach these questions, I would greatly appreciate it.

Regards

Compare              goals scored = "_____" + "_____" x number of goal attempts
with                            y        =    b      +    a x
with                            y        =    c      +    m x

In the last two equations, you would put x values across the bottom of a graph (independent values) and the y values vertically (the dependent values)

Now, compare these two equations with the first equation and so the independent values will be the number of goal attempts. The dependent values will be goals scored.

Enter the table data into your calculator StatList page in two columns. Depending on your calculator, these may be labelled L1 and L2. Usually, you put the independent values in L1 and the dependent values into L2.

Then use the calculator LinReg (linear regression) function to produce the least squares equation. Effectively, you might enter LinReg by itself.  You could also achieve the same result by using  LinReg L1, L2.

If set up correctly, the same page that gives you the equation should also give the values of r and of r-squared.

There is no need to use  b = r x standard deviation y / standard deviation x and a = mean y - mean x times 'b'

If you accidently mix up L1 and L2 by putting the dependent values in L1 and the independent ones in L2, then you must give the instruction   LinReg L2, L1

Title: Re: Help with least squares regression line... very confused with how it works!
Post by: krzysiek on October 06, 2009, 09:23:34 pm

Thank you very much for that reply,

I will directly refer to this tomorrow or day after when doing more exams and when a question like this comes up - to see if this does indeed answer all the aspects needed - from what I can tell now, it will definitely help me in answering.

Much of the confusion was definitely wondering which column, L1 or L2 the dependant / independant gets plotted on, etc.