H2 Maths Regression Question

Snoopyies SG

Question

An instrument used to measure the level of glucose in a person's blood is monitored on a random sample of 10 people. The levels are also measured using a very accurate laboratory procedure. The following table gives the instrument mesure, x, and the laboratory measure y.

x 4.6 5.0 6.6 6.5 7.5 7.8 8.1 9.0 9.2 12.0

y 4.1 5.3 6.3 6.8 7.1 7.5 8.4 8.6 9.5 12.5

Calculate the equation of a suitable least squares regression line, giving a reason for your choice of the line.

Calculate an estimate for the error in an instrument reading of 5.5.

Need help on the identification of the independent variable (cause) and dependent variable (effect) for this question as there seems to be no cause and effect relationship between the instrument measure and the laboratory measure.

Thanks.

eagle SG

I saw this in my student's H1 Paper.

If I'm not wrong, in the question itself, the word "accurate" is bolded to ensure you see it.

By accurate, it means that it is the independent variable. All other instruments that are not as "accurate" will be dependent on this accurate value

Snoopyies SG

I saw this in my student's H1 Paper.

If I'm not wrong, in the question itself, the word "accurate" is bolded to ensure you see it.

By accurate, it means that it is the independent variable. All other instruments that are not as "accurate" will be dependent on this accurate value

But the laboratory measure value will not cause the changes in the instrument measure value ie there is not a cause and effect relationship between the instrument measure value and laboratory measure value as required by the least square regression line eg the change in the floor space will cause the change in sales revenue ie there is a cause and effect relationship between floor space and sales revenue.

Mad Hat SG

Snoopyies, you can think this way. The instrument measure is causally influenced by the actual amount of glucose in the blood. But since this actual amount is reflected by the lab measure, the lab measure is essentially identical to it.

The actual amount of glucose in the blood is (strictly speaking) the independent variable. But the lab measure (being accurate) is essentially the same thing.

So I agree with eagle – treat the lab measure as the independent variable.

Snoopyies SG

The actual amount of glucose in the blood is (strictly speaking) the independent variable. But the lab measure (being accurate) is essentially the same thing.

So I agree with eagle – treat the lab measure as the independent variable.

The actual amount of glucose in the blood will cause the change in the laboratory reading ie there is a cause and effect relationship and indeed it is being accurate there will be a strong and positive linear relationship ie the product moment of correlation coefficient, r will be close to 1. Indeed, actual amount of glucose in the blood will be the independent variable (cause) and the laboratory reading will be the dependent variable (effect).

The actual amount of glucose in the blood will cause the change in the instrument reading ie there is a cause and effect relationship and it is being INACCURATE there will be not be a strong but still positive linear relationship ie the product moment of correlation coefficient, r will be less closer to 1. Also, actual amount of glucose in the blood will be the independent variable (cause) and the instrument reading will be the dependent variable (effect).

However, the laboratory reading will not cause the changes in the instrument reading ie there is not a cause and effect relationship between the laboratory reading and the instrument reading.

Since the question has asked to calculate an estimate for the error in an instrument reading of 5.5, can we use the instrument reading as the independent variable (cause) and error in reading (the difference between the instrument reading and laboratory reading) as the dependent variable (effect) ie there will be a cause and effect relationship between instrument reading (independent variable ie cause) and error in reading (dependent variable ie effect). So, when this regression line is found, we can substitute the instrument reading of 5.5 as the independent variable to find an estimate error in reading for the dependent variable.

Mad Hat SG

Original by Snoopyies:
Since the question has asked to calculate an estimate for the error in an instrument reading of 5.5, can we use the instrument reading as the independent variable (cause) and error in reading (the difference between the instrument reading and laboratory reading) as the dependent variable (effect) ie there will be a cause and effect relationship between instrument reading (independent variable ie cause) and error in reading (dependent variable ie effect). So, when this regression line is found, we can substitute the instrument reading of 5.5 as the independent variable to find an estimate error in reading for the dependent variable.

Not sure if you can do it this way. The reasoning is not straightforward. Why should the error in the reading depend on the instrument reading? Wouldn't the error in the reading depend on the blood glucose level instead? (E.g. the more glucose in the blood, the more likely the instrument will malfunction.)

More straightforward is to use the line of x on y. Although y is the lab reading, this is the same as the blood glucose level. (Because the lab reading is accurate.) So you can safely treat y as the blood glucose level. It is as though you measured the blood glucose directly! So it is safe to assume that x depends on y.

Why don't you do it both ways, see if you get the same answer, then let us know the result?