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Psychology. The intelligence quotient (IQ) is defined to be the ratio of mental age (MA), as determined by certain tests, to chronological age (CA), multiplied by $100 .$ Stated as an equation, $$ Q(M, C)=\frac{M}{C} \cdot 100 $$ where $$ Q=\mathrm{IQ} \quad M=\mathrm{MA} \quad C=\mathrm{CA} $$ Find $Q(12,10)$ and $Q(10,12)$.

So this problem tells us that, um, it's the i Q. And how it differs with your age and all that kind of stuff. And so when it says that I Q is directly proportional, right, that's going to be in the form y equals X y equals K X, right? So it's gonna be I Q equals K. I am a sorry. It's having a hard time keeping up and then inversely right. That's Kate over eggs as the chronological age. So that's gonna be over the chronological age. So I set up my equation just like this. Um, just knowing that I've got 123 uh, quantities that I'm dealing list now. That being said, I'm gonna go ahead and take the information they gave us about, but boy, I'm gonna plug that in, but I can figure out Kate, which is the only thing that's really missing at this point. And so since the I Q. Is 120 I say that's equal to K times the mental age of 14 of four, divided by its chronological age of 12. And when I do that right, 14 point 4/12 gives me 1.2, right? And so I've got that Que There. Still So to get rid of the 1.2 I divided out by both sides, right, it gives me a one. We obviously concede there's relationship because we have one in twos more. If you move over two decimal places, that would become 1 20 Since that's two decimal places that would give us a 100. So I get that K is equal to 100 right there, right? And so now that I know that we're gonna go ahead and take it, take that along with all of this information and this formula are basically gonna put it all together, right? So I don't know this girl like, which is 11. And when I type that into my calculator, I got 140 100 40. However, they use whatever units used to measure like you

For this problem we are told about the stanford Binet test for I. Q. In which an individual's mental age M. Is divided by the individuals chronological age. See the question is multiplied by 100. The result being the individuals I. Q. So we have the equation I. Q. Equals M. Oversee times 100. We are asked to find the partial derivatives of I. Q. With respect to M. N. C. And then to evaluate the partial derivatives at the 0.12 10. So to begin we take D. I by D. M. It's just going to be 100 oversee than D. I by D. C. You need to apply the quotient rule that's going to be negative 100 M over C squared. Having that. We can then evaluate those at the request of point the .1210. And that gives us a value of 10 for D. I by D. M. And it gives us a value of negative 12 for D. I by D. C. Now the interpretation here is that increasing mental age means increasing IQ and vice versa. For chronological age I the older you are mentally specifically, the further beyond your chronological age you are mentally the higher the I. Q. And vice versa. If your chronological age exceeds your mental age, the goes down

But we're giving the regression lying reading score is equal to negative. 33.4 plus 0.882 times the I Q score. This is a regression line, so we know it's a y equals MX plus B, the way I figure out which one is, which is that The why is always by itself the m in the acts of the chew it or multiply together and the B is the one we're adding or subtracting. So what is the Slope M is always going to be slow. So that's 0.88 till now. Interpreted what the slope actually meet. Mint slope means that whenever X goes up by one, why goes up by slope? So in this problem, when I kill go So oh, wine reading score goes up 0.882 So what is the intercept now? Be is always going to be our intercept. So that's negative, Bertie. Free point or so why is this not mean? So our intercept is when X is equal to zero. So we haven't I two score of zero and we have a negative test score Lever of those things. Make any sense we can have a negative score. You could have also put the I Q score. Being zero is why it doesn't work. In general with these types of problems, negative numbers tend to be the problem. Not always, but you usually can't have negative amounts of objects Now fine reading score. If I Q is equal to 90 or charity or 100 parity, we're gonna take this number and plug it in or X So we have a reading score. Why is equal to negative? Very free point, or WAAS? 0.882 times 90 and the other one is Why equals negative? 33 point or plus point a chill Times 130. You can just use your calculator and you should get so 45 quite 98 and 80 wine 800.26 and we are done.

So we're giving the regression wine reading score is equal to negative. 33.4 was 0.882 times by Q score. Regression line means this is a y equals MX plus B, the way we tell which one is, which is that Why is always by itself the, um in the X are the two were multiplying together. It is the 20.82 on the I Q scores, but that I am being the constant and the X being the variable than the one we add is the B. So our first question is, what is the slope? Well, I am is always going to be the slow. So that's 0.82 Now we need to interpret what slope means slow. It means that when X goes up by wine, why goes up by the slope. So when our problem it's going to be when I Q scores go up by Wina, reading scores are then going to go up by 0.82 Okay, so what is the intercept? So be is always going to be our intercept, so that's negative, very free of point. For now, we're told, it's not really mean So what's wrong with having this? There's a few problems you could put here 1st 1 is that we can't have a negative reading score. That makes sense. We also can't have Ah I Q score of zero. See, the intercept means that X is equal to zero because when X is equal to zero is when this graph intercepts the access so we can't have an I Q score of zero. That's the one all put. But again, you could also play that the reading score cannot be a negative number if these types of problems negative numbers and zero zehr usually gonna be the problem. But not always so the last one is to find the reading score. If I key was equal to 90 or 130 so had take our equation and plug in 90 and 130 for access. So we have. Why is equal to negative 30 Free point or plus 0.882 times 90 and why is equal to negative? Very 3.4 was 0.8 a two times 130. You could use your calculator for this and you should get 45.98 and 81.26 and we are done


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