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Can someone explain why both answers A and B are not valid on the metacarpal problem? If the line indicates a linear relationship between these two values, and

Can someone explain why both answers A and B are not valid on the metacarpal problem? If the line indicates a linear relationship between these two values, and the choice of axis is arbitrary, it seems to me you could just as well predict one from the other as vice versa.

copascetic 12y ago
The line of best fit changes depending on the choice of independent variable, even for the same data. The quantity being minimized is different for the two cases. (sum of squares of vertical distances between the line and the data points vs. the same for the horizontal distance) The question is very specifically about the interpretation of the slope, and because the slope would be different for the other case, only one of the answers is correct.
Chinjut 12y ago
Sure, you could just as well predict one from the other. But the question asks "What is the following is the best interpretation of the _slope_ of the line of best fit in the context of this problem?", and you are expected to interpret "slope" in the usual jargon sense (as the the ratio of vertical change to horizontal change, rather than vice versa). (By "vertical" and "horizontal" here, I mean with respect to the graph, not the interpretation, although it happens to be the case that the vertical axis corresponds to height and the horizontal axis corresponds to length.)
- keypusher 12y ago
  This then seems like less of a test of math ability and more of a test of whether or not you have effectively absorbed the jargon and conventions around certain math concepts. Maybe that's what they want, but it doesn't really seem like problem solving at all.
  - copascetic 12y ago
    See my other response, but I don't think you're giving the question enough credit. The other responses don't mention the fact that the line would likely be different if we swapped the variables. The question tests both whether you know what a line of best fit represents, and also whether you know that the correlation in one direction is not necessarily equal to the correlation in the other direction. This is something that could be covered in an algebra class with a unit on linear regression. I remember seeing a demonstration and explanation of this in mine.
    - bsder 12y ago
      Except that there is no reason to choose the correlation in one direction versus the other in the given problem. It's a bad question.
  - nilkn 12y ago
    The definition of slope is an extremely basic fact from middle school math. This isn't exactly crazy trivia.
  - jlarocco 12y ago
    To be fair, knowing the jargon and conventions is almost just as important as knowing how to solve problems. If nothing else, in college, most of the problems will be posed in terms of standard jargon and conventions, so it helps to know it.
harryh 12y ago
You're right that the graph contains the data for both A and B (and for that matter C and D as well) but the question refers to what the slope means. Here we have a Y = MX + B graph. M indicates how much Y changes for every 1 unit change in X. So it's A.
bsder 12y ago
Both answers are valid. This question would not survive the statistical norming process that the SAT uses to make sure that questions are "well-behaved" with respect to their answers. By convention, X is supposed to be the independent variable and Y is supposed to be the dependent variable. Since it is not clear which variable really should be "dependent", the question would get thrown out.

copascetic 12y ago

The line of best fit changes depending on the choice of independent variable, even for the same data. The quantity being minimized is different for the two cases. (sum of squares of vertical distances between the line and the data points vs. the same for the horizontal distance) The question is very specifically about the interpretation of the slope, and because the slope would be different for the other case, only one of the answers is correct.

Chinjut 12y ago

Sure, you could just as well predict one from the other. But the question asks "What is the following is the best interpretation of the _slope_ of the line of best fit in the context of this problem?", and you are expected to interpret "slope" in the usual jargon sense (as the the ratio of vertical change to horizontal change, rather than vice versa). (By "vertical" and "horizontal" here, I mean with respect to the graph, not the interpretation, although it happens to be the case that the vertical axis corresponds to height and the horizontal axis corresponds to length.)

keypusher 12y ago
This then seems like less of a test of math ability and more of a test of whether or not you have effectively absorbed the jargon and conventions around certain math concepts. Maybe that's what they want, but it doesn't really seem like problem solving at all.
- copascetic 12y ago
  See my other response, but I don't think you're giving the question enough credit. The other responses don't mention the fact that the line would likely be different if we swapped the variables. The question tests both whether you know what a line of best fit represents, and also whether you know that the correlation in one direction is not necessarily equal to the correlation in the other direction. This is something that could be covered in an algebra class with a unit on linear regression. I remember seeing a demonstration and explanation of this in mine.
  - bsder 12y ago
    Except that there is no reason to choose the correlation in one direction versus the other in the given problem. It's a bad question.
- nilkn 12y ago
  The definition of slope is an extremely basic fact from middle school math. This isn't exactly crazy trivia.
- jlarocco 12y ago
  To be fair, knowing the jargon and conventions is almost just as important as knowing how to solve problems. If nothing else, in college, most of the problems will be posed in terms of standard jargon and conventions, so it helps to know it.

harryh 12y ago

You're right that the graph contains the data for both A and B (and for that matter C and D as well) but the question refers to what the slope means. Here we have a Y = MX + B graph. M indicates how much Y changes for every 1 unit change in X. So it's A.

bsder 12y ago

Both answers are valid. This question would not survive the statistical norming process that the SAT uses to make sure that questions are "well-behaved" with respect to their answers. By convention, X is supposed to be the independent variable and Y is supposed to be the dependent variable. Since it is not clear which variable really should be "dependent", the question would get thrown out.