VCE General & Further Maths Question Thread!

[Dr. Nick]

Hi, thank you so much for the response! This question was from the online work sheets that comes with the textbook, and it's not an actual textbook question which is why it's probably inaccurate but I'll make sure to double check with my teacher once school starts, thanks again for the help 

[Dr. Nick]

What's the best way to determine the type of association depicted in a scatter plot through inspection/without calculating the correlation coefficient? These questions are usually multiple choice, and I always get them wrong because I keep overthinking it... is there any mathematical method or do you have to just know on your own?

[Aaron]

I have merged your threads with our stickied VCE Further Maths Question thread @Dr. Nick. Please post content-related queries here instead rather than creating a separate thread for each question. Thanks

[MissSmiley]

What's the best way to determine the type of association depicted in a scatter plot through inspection/without calculating the correlation coefficient? These questions are usually multiple choice, and I always get them wrong because I keep overthinking it... is there any mathematical method or do you have to just know on your own?

Here's a diagram for all the scatterplot associations (linear), strong, moderate, weak and positive and negative. And obviously non-linear would be curved somewhere in the scatterplot.
Whilst this is a useful visual aid, please don't fall into VCAA's trap of merely looking at any scatterplot without calculating the 'r' value and jumping to conclusions about its associations. Because you never know, for e.g. 'strong' and 'moderate' relationships can look very very similar!
Instead, judge by the correlation coefficient value! (And it's really easily found on the CAS, so no need to stress about that, if you've got all your x and y values sorted out!)
To judge from the 'r' value, I'm sure you have some sort of table or diagram that has the range of values of 'r' and then what relationship that would mean (e.g. strong positive relationship, weak negative relationship)
Hope this helps!

[snowisawesome]

Here's a diagram for all the scatterplot associations (linear), strong, moderate, weak and positive and negative. And obviously non-linear would be curved somewhere in the scatterplot.
Whilst this is a useful visual aid, please don't fall into VCAA's trap of merely looking at any scatterplot without calculating the 'r' value and jumping to conclusions about its associations. Because you never know, for e.g. 'strong' and 'moderate' relationships can look very very similar!
Instead, judge by the correlation coefficient value! (And it's really easily found on the CAS, so no need to stress about that, if you've got all your x and y values sorted out!)
To judge from the 'r' value, I'm sure you have some sort of table or diagram that has the range of values of 'r' and then what relationship that would mean (e.g. strong positive relationship, weak negative relationship)
Hope this helps!

If r is a positive association, then would r^2 also be a positive association?

[jazzycab]

If r is a positive association, then would r^2 also be a positive association?

This tells us the proportion of variability in the response variable that can be explained by the variability in the explanatory variable (other variability can be attributed to other factors).
Although values closer to 1 would indicate stronger associations, the coefficient of determination on its own doesn't tell us anything about the direction. This is a property that can only be attributed to the r value

[Dr. Nick]

Here's a diagram for all the scatterplot associations (linear), strong, moderate, weak and positive and negative. And obviously non-linear would be curved somewhere in the scatterplot.
Whilst this is a useful visual aid, please don't fall into VCAA's trap of merely looking at any scatterplot without calculating the 'r' value and jumping to conclusions about its associations. Because you never know, for e.g. 'strong' and 'moderate' relationships can look very very similar!
Instead, judge by the correlation coefficient value! (And it's really easily found on the CAS, so no need to stress about that, if you've got all your x and y values sorted out!)
To judge from the 'r' value, I'm sure you have some sort of table or diagram that has the range of values of 'r' and then what relationship that would mean (e.g. strong positive relationship, weak negative relationship)
Hope this helps!

Thanks! I prefer the method of calculating r, but some questions say to do it through inspection but from now on i'll just calculate r just to be sure.

[Dr. Nick]

Hi again
why does 12.47 round to 13 (if you want it to be to two significant figures?)

wouldn't you just look at the next number after 2 which in the case of this example is 4 and according to the rule numbers 0-4 you dont round up? My answer was 12 but my textbook says its 13.

I understand why 12.57 would round to 13 (for two sig fig) but why would 12.47?

[Vaike]

My answer was 12 but my textbook says its 13.

Hiya. I'd be inclined to assume it's an error in the textbook's answers;  there a often small mistakes like this in the answer section and from what I can I tell your answer of 12 should indeed be correct.

[Dr. Nick]

Hiya. I'd be inclined to assume it's an error in the textbook's answers;  there a often small mistakes like this in the answer section and from what I can I tell your answer of 12 should indeed be correct.

Thanks for the help!! ill double check with my teacher once school starts.

[AngelWings]

Hi again
why does 12.47 round to 13 (if you want it to be to two significant figures?)

wouldn't you just look at the next number after 2 which in the case of this example is 4 and according to the rule numbers 0-4 you dont round up? My answer was 12 but my textbook says its 13.

I understand why 12.57 would round to 13 (for two sig fig) but why would 12.47?

Aside from the small leeway given to some questions (e.g. to compensate for preemptive rounding), it could also be the scenario it is in. If the question is a worded question about the minimum number of trees that will line the side of a freeway (just a random example) and the answer becomes 12.47, then it'll have to be rounded up to 13, not 12. This is due to the feasibility of the scenario, as 12 wouldn't quite reach the minimum. (If that makes sense. If it doesn't, I'll find an example to explain what I mean.)

As you stated, normal rules state that to round to 2 sig. fig.s, you'd round 12.47 to 12. Depending on the nature of the question, however, it might be one of these exceptions.

[ellimurphy]

Can someone please explain correcting for seasonality to me?
I've been trying to work it out for a solid hour!

[AngelWings]

Can someone please explain correcting for seasonality to me?
I've been trying to work it out for a solid hour!

Correcting for seasonality is a bit of a long one to explain. In the shortest explanation of this, the main equation you'll need is: actual value = deseasonalised value x seasonal index. Basically what you want to do is to correct it to 1 or 100 (whatever the case may be) to get it back to 'normal', so that 1 or 100 is the actual value and apply the above equation. 
Some classic questions regarding correcting for seasonality are found: here, here, How to calculate seasonal indices, VCAA Exam 1 2014 Core Q12 and VCAA Exam 1 2011 Core Q12*.

* I explained this question on this thread ages back, so I don't remember where it's gone, but here's a quick explanation.

VCAA E1 2011 Core Q12

The 'actual value' you want is 1. The seasonal index you have been given is 0.80.
Apply to formula: actual value = deseasonalised value x seasonal index
1 = deseasonalised value x 0.80
deseasonalised value = 1 / 0.80 = 1.25   <--- I switched the subject around
1.25 - 1.00 = 0.25                                     <--- I took away 1 to see its relative position against the actual value. Multiply by 100 to get percentage.
This provides a 25% increase. (Note: It was + 0.25.)

Yeah, sorry that doesn't quite explain correcting for seasonality, but I've run out of time to throw up a document. I'm sure someone will give a much better explanation than my two minute one above.

[Lear]

Does anyone have a cas guide on doing seasonal adjustments quickly on the spreadsheet?

[AngelWings]

Does anyone have a cas guide on doing seasonal adjustments quickly on the spreadsheet?

See “how to calculate seasonal indices” link in previous post.