VCE General & Further Maths Question Thread!

[spursy]

what would you do for this

[xdmemeguy]

what would you do for this

Look at the residual plot and if points are not randomly scattered above and below the x-axis the association is not linear, that association does not look linear as it tends to dip under the x-axis a lot towards the middle. To find the transformation compare the plot to the transformation circle. Maybe because a residual plot is given, draw a diagonal line accross all quadrants in the middle of the data. Then kind of pretend that line is the x-axis for your residual plot and compare the "make-do residual plot" with the actual one and chose the transformation depending on the one that is the most similar.

[galaxy21]

Hey guys I need help with this VCAA question form 2015 exam 2.
The answer says the modal inerval is 70-75, but shouldnt it be 70-74 becaues its a histogram, and like 75+ are part of the following intervals?
Thanks

You would say 70-75, because if this interval was 70-74 and the next was 75-80, then all of the values between 74 and 75 (e.g. 74.5) would be excluded. It would really be 74.9999999999999999999 going on forever but you would just say 75.

what would you do for this

If a question asks for whether a residual plot is linear or non-linear, you have to look at whether the data is randomly skattered or not.

(Images are from here)
I would say that this plot would say that the residuals would be non-linear, as it doesn't appear to be randomly scattered, and there is a patch around the centre that has no data (or little) above the x axis, but a lot below the axis.
To linearise this, you need to apply a transformation to the data. To do this, you need to go back to the original graph and look at the shape of the data. Your teacher might have given you a diagram about what transformation to use when the graph looks a certain way. If not, you could try looking it up.
This question is 2 marks, so I would say that it would be non-linear, and therefore requiring a transformation as the question asks.

[PopcornTime]

what would you do for this

Search up "circle of transformations" online and include in your bound reference.

[PopcornTime]

Why is the mean affected by outliers and skewness?

[AngelWings]

Why is the mean affected by outliers and skewness?

The mean takes into account all data points, including outliers and ones that would influence the skew of the data. Think back to how you calculate the mean and you'll notice that outliers will pull them in the direction they're in e.g. an outlier higher than the rest of the data will make the mean much higher than if the outlier's data was excluded.

Hope that makes sense.

Side note: Please modify posts instead of double posting unnecessarily. You can do so via the "modify" button on the top right of your posts.

[finnystew]

Question 4 from VCAA sample exam attached
Requires you to create an equation for some log(x) transformed data. However the y is population (000's)
Looked at itute solutions and they come up with the equations population=7700+7700(log area)       ...2sf.
This is done if you x1000 the population data before graphing.

However if you don't do this you get the equation population=7.7+7.7(log area). Which also works but in the following question you just have to multiply your prediction by 1000 to get the answer.

Thoughts? Do you think they'd give marks for either equation?

[PopcornTime]

Hi,
I was confused with one of the questions on NHT 2018  exam 2 (probably something simple that I am overseeing).
With Q7d) - how did they get an annual interest rate of 9.5%?
With the starting amount being ($5000) compounding monthly (assuming), how is the annual interest rate 9.5%?
I keep on getting 9.2% using both the eqn – (6000=(1+x/12/100)^24x5000) and finance solver (N=24, PV = -5000, PMT = 0, FV = 6000, CYPY = 12, giving I% as 9.2).
Thank you!

Its not compounding monthly though. Your thinking is correct, but get rid of the 12 (cause not compounding monthly and change 24 months to 2 years).

So it should be:

(1+x/100)^2 x 5000 = 6000, x

Hope that helps and good luck tomorrow!

[VeryJuicyLemon]

Question 4 from VCAA sample exam attached
Requires you to create an equation for some log(x) transformed data. However the y is population (000's)
Looked at itute solutions and they come up with the equations population=7700+7700(log area)       ...2sf.
This is done if you x1000 the population data before graphing.

However if you don't do this you get the equation population=7.7+7.7(log area). Which also works but in the following question you just have to multiply your prediction by 1000 to get the answer.

Thoughts? Do you think they'd give marks for either equation?

considering the response variable isn't listed as population (in thousands) but rather population, then 7700 should be the correct answer

[pm123]

Its not compounding monthly though. Your thinking is correct, but get rid of the 12 (cause not compounding monthly and change 24 months to 2 years).

So it should be:

(1+x/100)^2 x 5000 = 6000, x

Hope that helps and good luck tomorrow!

Ok... that explains a lot.

Thank you!

[spicyunicorn]

Can someone please help me with Question 7 of the Graphs from the MC exam? I'm shocking at objective functions 

[galaxy21]

I don't know if anybody has noticed this yet, but the VCAA sample exam is basically just questions from a couple of past exams mixed together.
Most of the Data section is from the 2014 VCAA exam 2, the finance and matrices sections makes reference to a question that came up in the 2013 exam 2, and I am not sure about the others. Just thought I'd mention it as some of the questions overlap and if there aren't answers for the sample exam questions (there might be - I have no clue), you could probably use these for some answers.

Question 4 from VCAA sample exam attached
Requires you to create an equation for some log(x) transformed data. However the y is population (000's)
Looked at itute solutions and they come up with the equations population=7700+7700(log area)       ...2sf.
This is done if you x1000 the population data before graphing.

However if you don't do this you get the equation population=7.7+7.7(log area). Which also works but in the following question you just have to multiply your prediction by 1000 to get the answer.

Thoughts? Do you think they'd give marks for either equation?

I highly doubt that they would accept both answers. Even if something is written like population (thousands) you need to leave the data in it's original form to find the linear regression line, otherwise inputing data into the line would result in extremely incorrect results.

Edit: According to the 2014 examiners report (this exam has the same question in it), your answer would be required as 7.7, rather than 7700.

[VeryJuicyLemon]

I don't know if anybody has noticed this yet, but the VCAA sample exam is basically just questions from a couple of past exams mixed together.
Most of the Data section is from the 2014 VCAA exam 2, the finance and matrices sections makes reference to a question that came up in the 2013 exam 2, and I am not sure about the others. Just thought I'd mention it as some of the questions overlap and if there aren't answers for the sample exam questions (there might be - I have no clue), you could probably use these for some answers.
I highly doubt that they would accept both answers. Even if something is written like population (thousands) you need to leave the data in it's original form to find the linear regression line, otherwise inputing data into the line would result in extremely incorrect results.

So which one do you mean original? 7700 or 7.7?

[galaxy21]

So which one do you mean original? 7700 or 7.7?

oh sorry the 2014 examiners report has 7.7 so this would be what they would accept. I'll edit to make clearer.

considering the response variable isn't listed as population (in thousands) but rather population, then 7700 should be the correct answer

The original data in the table along the side has it listed as population (thousands), so the thousands is the unit. If it were to say length (mm), the equation generally would not use the variable as length (mm), but just state length. It is the same for this, as thousands is simply the unit.

[VeryJuicyLemon]

oh sorry the 2014 examiners report has 7.7 so this would be what they would accept. I'll edit to make clearer.
The original data in the table along the side has it listed as population (thousands), so the thousands is the unit. If it were to say length (mm), the equation generally would not use the variable as length (mm), but just state length. It is the same for this, as thousands is simply the unit.

that cleared some misunderstandings, neap (or some other companies, can't remember) did the full "7700" for regression, got me confused

always listen to vcaa