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A least squares regression line was calculated to relate the length (cm) of newborn girls to their weight in kilograms. The line is weight = -6.23 + 0.1234 length. Explain in words what this model means. Should new parents (who tend to worry) be concerned if their newborn's length and weight don't fit this equation?

User Winfried
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Explanation:

the least squares regression line is a kind of visualization of the standard deviation of a set of data points from the mean it expected value.

it tries to minimize the sum of the distances of all the data points from the line that represents the expected value for the x coordinate of every data point.

in our case, the x coordinate of a data point is the length of a baby girl, the y coordinate is the weight of the baby.

the line is typically going in between the data points and will never (or only rarely) contain data points and represents the expected weight of a baby girl when knowing her length.

given the equation we can say that a newborn baby girl must be more than

6.23/0.1234 = 50.48622366... cm (for weight 0)

long to have a positive weight and therefore for the equation to make any sense. in fact, to bring at least 2.5 kg on the table, she should be more than 70 cm long.

-6.23 + 0.1234×70 = 2.408 kg

the data points can be close to the line or jump wildly above and below the line. it is still the same line, as it correlates with the mean value.

therefore, it would be highly unusual if a newborn baby girl fits the equation. it is normal to NOT fit the equation.

so, no need to worry in such a case.

but what makes sense is to see and compare how wildly the data points of the other baby girls deviate from the line and if the own baby girl is fitting into that "cloud", or if she represents an extreme case.

User Jethro Hazelhurst
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