VCE General & Further Maths Question Thread!

[Lear]

Its not really about definition, its about understanding. We should all know by now that adding all residual equals to 0 and that residual is vertical distance between the line and the actual dot, so by using the previous example. Its pretty obvious...

I think it’s reasonable for a person to not make the connection between ‘least squares’ and residual values. Often even the term 'least squares' is not taught and rather students are simply told to press certain buttons on their calculator to get ‘the line’ of the graph.
What may be obvious to you is not obvious to all students

[galaxy21]

I think it’s reasonable for a person to not make the connection between ‘least squares’ and residual values. Often even the term 'least squares' is not taught and rather students are simply told to press certain buttons on their calculator to get ‘the line’ of the graph.
What may be obvious to you is not obvious to all students

Completely true. I made the exact same mistake, and a few other people I know (including one student who is probably rank 1 in our cohort) made the exact same mistake. It's a very easy thing to not connect these two ideas.

[userrrname]

Its not really about definition, its about understanding. We should all know by now that adding all residual equals to 0 and that residual is vertical distance between the line and the actual dot, so by using the previous example. Its pretty obvious...

Well I honestly didn’t know that... but thanks for the enlightenment lol

[userrrname]

I think it’s reasonable for a person to not make the connection between ‘least squares’ and residual values. Often even the term 'least squares' is not taught and rather students are simply told to press certain buttons on their calculator to get ‘the line’ of the graph.
What may be obvious to you is not obvious to all students

This is spot on. I didn’t even know what the least square line did until I literally just google searched “least squares meaning”, which pretty much gives the answer to question 7. We weren’t really taught what it is or what it does, just how to find it and use it. (Gotta love atarnotes tho, thanks guys!)

[theomccoy]

Have never had a great understanding of inverses so can't wrap my head around this question...

Anyone able to explain why the answer is A?

[S_R_K]

Have never had a great understanding of inverses so can't wrap my head around this question...

Anyone able to explain why the answer is A?

By definition of inverses, Q^–1 * Q gives the identity matrix.

Since Q = wP, we require that Q^–1 * wP is the identity matrix. Hence Q^–1 = (1/w) * P^–1, since P * P^–1 is the identity matrix, and w * (1/w) = 1.

[Lear]

Have never had a great understanding of inverses so can't wrap my head around this question...

Anyone able to explain why the answer is A?

For questions like these I just like to define each term/variable and do the process. Following this I equate it with each answer to check which one is correct.

[theomccoy]

By definition of inverses, Q^–1 * Q gives the identity matrix.

Since Q = wP, we require that Q^–1 * wP is the identity matrix. Hence Q^–1 = (1/w) * P^–1, since P * P^–1 is the identity matrix, and w * (1/w) = 1.

Ahhh very helpful! Thank you!

[anne198]

Hey Guys,

When drawing a least square regression line in exam 2 are you supposed to extend the line past the max and min x values of the data points given? I was thinking you don't extend the line because that would show extrapolation but the 2017 answers had a question that extended the line to reach the y axis etc.

[galaxy21]

Hey Guys,

When drawing a least square regression line in exam 2 are you supposed to extend the line past the max and min x values of the data points given? I was thinking you don't extend the line because that would show extrapolation but the 2017 answers had a question that extended the line to reach the y axis etc.

I would always just do it to the ends of the graph that it gives you. That way you can show the x intercept. Also, generally the line wont have a boundary or anything, so just go to the edges, even if it is extrapolation.

[Lear]

Hey Guys,

When drawing a least square regression line in exam 2 are you supposed to extend the line past the max and min x values of the data points given? I was thinking you don't extend the line because that would show extrapolation but the 2017 answers had a question that extended the line to reach the y axis etc.

Related to this, are we supposed to label the end points? I don’t recall any of the normal VCAA exams requiring labelling for the least square regression line but did 2018 NHT EXAM 2 last night and they had the end points labelled?

[galaxy21]

Related to this, are we supposed to label the end points? I don’t recall any of the normal VCAA exams requiring labelling for the least square regression line but did 2018 NHT EXAM 2 last night and they had the end points labelled?

Not sure whether it is required, but I always label a couple of points just in case my line is slightly off. Definitely label the y intercept, because this is generally easy enough to find from the line, and may be something in the middle and at the end.
If you are rushed for time, I would just leave it and come back and do it at the end.

[Lear]

The issue is if we haven’t been given an instruction to label we don’t know exactly how many decimal places we should label to. And VCAA often mentions how kids lose marks for putting extra yet incorrect information (haven’t said anything specifically on lines though)

[VeryJuicyLemon]

The issue is if we haven’t been given an instruction to label we don’t know exactly how many decimal places we should label to. And VCAA often mentions how kids lose marks for putting extra yet incorrect information (haven’t said anything specifically on lines though)

That's overkill, there is no need to label, just make sure your end points are accurate. Label or not, Vcaa still needs to check whether the line is correct.

[Lear]

That's overkill, there is no need to label, just make sure your end points are accurate. Label or not, Vcaa still needs to check whether the line is correct.

That's what I thought too until I saw the VCAA 2018 NHT Exam 2 report having them labelled. Now I am not too sure.
Interesting...