Some questions...

[horizon]

Just some questions I have so far.

1.
Fit a 3-median line to the following data.

Express the equation with exact values of m and c.

Ok, so with this question, once I've fit the 3 median line in on the sheet of paper, should I find the equation based on the line I've drawn on the paper? Or should I be putting in the individual data points in my calculator and working out the equation of the 3 median line that way?

If I am to do it based on the line I've drawn, won't that equation then be different for everyone? Is there any leeway given?

2. After you've transformed the data, is the r squared value interpreted in terms of the transformed variable?

For e.g. I have done a log_y transformation and I find the least squares regression line for that and get r squared= 0.89.
For the interpretation of r squared, would it be: 89% of the variation in the log (y variable) can be explained by the variation in the x variable.
OR, do you just ignore the transformation and just say, 89% of the variation in the y variable can be explained by the variation in the x variable?

Thanks in advance! 

[_avO]

1. You can do the equation manually (personally its faster for me)

Firstly split the data in 3 sections

Next find the median of the data in all 3 sections

Then find the gradient of the equation (use the median of the lower and upper sections)

Sub in all the information you found in the formula
c = 1/3[(yL + yM + yU) - m(xL + xM + xU)]; where c=y-int ,L=lower, M=middle, U=upper and m=gradient

Lastly substitute c and m in y=mx+c

[Shannon101]

1. Yeah to find the exact values, you'd either need to use your calculator or use the formula for finding the exact values of m and c.

You might find this video helpful. It explains how to find a three median line using both methods, the graphical way (where you slide the ruler a third of the way towards the middle point) and the arithmetic way (using the formula c=1/3[(yL + yM + yU) - m(xL + xM + xU)] which looks a bit scary written out that way, but it actually quite simple to apply).

2. That's a tough one - My guess is it depends what the question has asked you. You would definitely want to make it clear in your answer which r squared value you're stating, this is, for the linear regression applied to the original data, or to the transformed data. I would say something like "Once the data has been transformed using a log y transformation, the new linear regression model indicates that 89% of the variation in (y variable) can be explained by the variation in the (x variable)".

Hope that helps!

[horizon]

1. You can do the equation manually (personally its faster for me)

Firstly split the data in 3 sections

Next find the median of the data in all 3 sections

Then find the gradient of the equation (use the median of the lower and upper sections)

Sub in all the information you found in the formula
c = 1/3[(yL + yM + yU) - m(xL + xM + xU)]; where c=y-int ,L=lower, M=middle, U=upper and m=gradient

Lastly substitute c and m in y=mx+c

And

1. Yeah to find the exact values, you'd either need to use your calculator or use the formula for finding the exact values of m and c.

You might find this video helpful. It explains how to find a three median line using both methods, the graphical way (where you slide the ruler a third of the way towards the middle point) and the arithmetic way (using the formula c=1/3[(yL + yM + yU) - m(xL + xM + xU)] which looks a bit scary written out that way, but it actually quite simple to apply).

2. That's a tough one - My guess is it depends what the question has asked you. You would definitely want to make it clear in your answer which r squared value you're stating, this is, for the linear regression applied to the original data, or to the transformed data. I would say something like "Once the data has been transformed using a log y transformation, the new linear regression model indicates that 89% of the variation in (y variable) can be explained by the variation in the (x variable)".

Hope that helps!

Thanks, that clears this up!

Just another question:
I've learnt to recognize what transformations to apply (like y squared, log x, 1/x etc) on the data from the SCATTERPLOT, but is there a way to work this out from the RESIDUAL PLOT?

[Predator]

Just another question:
I've learnt to recognize what transformations to apply (like y squared, log x, 1/x etc) on the data from the SCATTERPLOT, but is there a way to work this out from the RESIDUAL PLOT?

Not particulary since the residual plot is going to either have a clear pattern or be completely random.
Whereas in the normal scatterplot you have it going in a direction and than go from there whereas with a residual plot you don't.

[horizon]

I'm so confused about the different trends in time series.
Whats the difference between secular, seasonal, cyclical and random trends? Is there a trick to differentiate between them?