NS FL 9 P/S Q48
NS FL 9 P/S Q48
Since there is no clear plot or data given that can relate employment to children born then I would make assumptions based on two different plots. I see that with time unemployment decrease more or less linearly in both north and south. Now looking at 1B  Namely the only source of information regarding number of children born I see that there is in every age cohort a decrease of more or less 50%60% consistent all throughout. so if employment increased linearly and children born by cohort also decrease steadily how would I arrive to the conclusion that the data is non linear. an increased in children born in one of the age groups or even a deep in the employment rate will hint data that is not correlated linearly but that is not the case.

 Posts: 282
 Joined: Sat Mar 30, 2019 8:39 pm
Re: NS FL 9 P/S Q48
Most importantly:
This question wants you to use the data provided in the text, and only the first of the 4 graphs in figure 1. The other graphs are not at all useful in answering this question.
The explanation given in the material has a small mathematical flaw: Disproportionate increases over the base quantity are perfectly possible in a linear relationship. If each time one of us works an hour, we get paid 10 dollars, but I started with 10 dollars and you started with 100, then the relationship between hours worked and dollars earned is clearly the same, even though I doubled my cash on hand and you only increased yours by 10%.
To convincingly prove or disprove linearity would mean to attempt to fit it into a linear regression model. But all we need to know about that is that on the fitted linear regression model will pop out a line, and lines are described by good ol' y = mx + b. And that if both datasets (north and south) had the same correlation between female employment and births per woman, then our slope, m, would be the exact same.
I've attached an image here, to show this worked out really quickly:
As you can see, we get a much stronger correlation in the north than in the south. So we couldn't say that they are both inverse and linear, at least not the same linear correlations. For the MCAT, I would recommend consistently testing linearity as deltaY/deltaX in many contexts (including C/P, reaction order testing).
A few notes:
Since we lack intermediate datapoints, we cannot really infer the shape of the fitted regression curve or line between these two variables with any certainty, and the question should probably specify that it is only asking for the MOST LIKELY type of correlation as well as as an average between both regions. The stem should also be asking about a correlation between female employment and births per woman, not birth rate  which is a populationwide measure.
This question wants you to use the data provided in the text, and only the first of the 4 graphs in figure 1. The other graphs are not at all useful in answering this question.
The explanation given in the material has a small mathematical flaw: Disproportionate increases over the base quantity are perfectly possible in a linear relationship. If each time one of us works an hour, we get paid 10 dollars, but I started with 10 dollars and you started with 100, then the relationship between hours worked and dollars earned is clearly the same, even though I doubled my cash on hand and you only increased yours by 10%.
To convincingly prove or disprove linearity would mean to attempt to fit it into a linear regression model. But all we need to know about that is that on the fitted linear regression model will pop out a line, and lines are described by good ol' y = mx + b. And that if both datasets (north and south) had the same correlation between female employment and births per woman, then our slope, m, would be the exact same.
I've attached an image here, to show this worked out really quickly:
As you can see, we get a much stronger correlation in the north than in the south. So we couldn't say that they are both inverse and linear, at least not the same linear correlations. For the MCAT, I would recommend consistently testing linearity as deltaY/deltaX in many contexts (including C/P, reaction order testing).
A few notes:
Since we lack intermediate datapoints, we cannot really infer the shape of the fitted regression curve or line between these two variables with any certainty, and the question should probably specify that it is only asking for the MOST LIKELY type of correlation as well as as an average between both regions. The stem should also be asking about a correlation between female employment and births per woman, not birth rate  which is a populationwide measure.