hard math 1 question

Test Preparation SAT Subject Test Preparation
1

<p>In the SAT practice booklet for the subject tests, the level 5 question for the math test gave a table:</p>

<p>time t <strong><em>0</em></strong><strong>1</strong><strong><em>2</em></strong>__5
years</p>

<p>value v(t) 15,000 13,000 10,900 3,000
dollars</p>

<p>Question: When purchased, an automobile is valued at $15000. Its value deprecates at the rate shown in the table above. Based on a least- squares linear regression, what is the value, to the nearest hundred dollars, of the automobile when t=4?</p>

<p>Can someone explain to me this question? What's a least-squares linear regression? How do you solve this? </p>

<p>Thanks. :)</p>

2

<p>that’s math 1? I think we just covered that in my AP Stats course >.>
IIRC least squares regression is finding the best fit line that gives you the least total r^2 value, where r= the residual which is the distance from a point straight up/down to the line of best fit.</p>

3

<p>^ which means… ? Sorry. That explanation confuses me. I know what best fit is, i don’t get the whole residual/ straight up/down thing.</p>

<p>Yeah, when I searched least-squares linear regression, I got a bunch of AP Stats stuff so I thought it would be better if I just asked it here… ha</p>

4

<p>well, if you made a best fit line, in most cases, the line isn’t going to pass through all the points right? some will be above and some will be below the line. the residual (r) is the distance from the point to the line. by squaring r, we get a square that is r by r (which is where we get the square in the least-squares regression from). the goal of the best fit line is to have a line that has the least sum of r^2 values.</p>

<p>yeah I kinda suck at explaining things…</p>

5

<p>You’re right that the LSR line finds minimum r^2, but r is the correlation coefficient, not a direct measure of residuals.</p>

6

<p>I thought i got it… but then noname22 threw me off… lol. can someone explain how to do this problem?? Ill probably get the concept then… haha</p>

<p>and what do you mean by least sum?</p>

7

<p>How to do it on your handy TI-83/84</p>

<p>{0,1,2,5} STO —> L1 (2nd 1)
{15000, 13000, 10900, 3000} STO —> L2 (2nd 2)</p>

<p>STAT</p>

<p>CALC</p>

<p>4</p>

<p>LinReg (ax + b) should be on the screen. Type (L1, L2) and hit enter.</p>

<p>You now have a equation in the form of y = ax + b. Plug in whatever x value you want (i.e. time) to get the corresponding price.</p>

8

<p>I have a ti-89… lol. thanks though.</p>

9

<p>Sorry for throwing you off. I actually worded that wrong myself. The LSR is actually based on maximum r^2, because it is the line that best predicts the variance. It is consequentially the line with the minimum residuals squared.</p>

10

<p>lol ap stats</p>