AP Statistics / Mr. Hansen
10/25/2000

Name: ________________________

1.

Choose explanatory & response vbls. Choice usu. clear, but if not, then __________________________ .

2.

Follow Admonition #0: __________________________ . In other words, make a __________________________ .

3.

If pattern looks linear, then punch __________________________ to fit a line. Be sure to check the __________________________ plot.

4.

If __________________________ shows a __________________________ , then you need something other than a linear fit. Check to see if X and __________________________ have a good linear fit; if so, ExpReg is a good choice, especially if the problem has to do with __________________________ , where the rate of change is __________________________ . You can check this last fact by doing a __________________________ analysis (constant ratio between Y values when X is equally spaced suggests __________________________ model).

Nuts and Bolts for #4

For a mult. choice problem, don’t mess around! Use __________________________ . But for free-response, you must show work. Compute a 3rd col., namely __________________________ . Punch __________________________ to linearly fit 1st and 3rd cols. Since we now have __________________________ = a + bx, we can "__________________________" both sides of this eqn. to get __________________________ = __________________________ , or letting A = 10^a, B = 10^b, we can simply write ___ = __________________________ .

Of course, these A and B correspond to the a and b you would have gotten by simply using __________________________ . At least you have a quick and easy check on your work. Don’t forget to check the __________ plot!

5.

If ExpReg is no good (esp. if data appear to pass through the __________________________ ), try a __________________________ . This is appropriate for many real-world problems such as wind resistance, turbulence, volume (or weight) vs. height, or anything where Y seems to be __________________________ to some unknown power of X. The key indicator is that __________________________ will be linearly related to __________________________ . You can easily check this by computing 3rd and 4th cols. for log X and log Y, then punching __________________________ and checking the _____ value and __________________________ .

Nuts and Bolts for #5

For a mult. choice problem, don’t mess around! Use __________________________ . But for free-response, you must show work. Compute a 3rd and 4th col., namely _________________ and _________________ . Punch __________________________ to linearly fit 3rd and 4th cols. Since we now have __________________________ = a + b log x, we can "__________________________" both sides of this eqn. to get __________________________ = __________________________ , or letting A = 10^a, B = b, we can simply write ___ = __________________________ .

Of course, these A and B correspond to the a and b you would have gotten by simply using __________________________ . At least you have a quick and easy check on your work. Don’t forget to check the __________ plot!

6.

If none of these work, try other sensible regressions: _________________ , _________________ , _________________ , _________________ , etc. It is not enough to check the _____ value; you must also check the __________ plot! Your ideal resid. plot would show ________________________ .

7.

If everything fails, but you are told that function f is a good candidate for fitting Y to X, then you can always use the __________ method, affectionately known amongst us (though never on a test or exam) as the __________ method. We suspect that col. 1 (X) can be __________ to give col. 2 (Y), so we compute a 3rd col., namely __________ (or, if you prefer, ___________________ ), and see whether there is a good __________ fit between cols. 1 and 3. We do this by punching ________________ and checking the ____ value and ____________ plot.

If the linear fit between cols. 1 and 3 looks good, then we write the eqn. __________ = ____________________ to summarize the association between cols. 1 and 3. Then, we "____________________" both sides to get ___________ = ____________________ , which is a decent model.

Nuts and Bolts for #7

X data: 18, 35, 94, 115, 132, 196, 217, 238, 294
Y data: 6, 6.5, 7, 7, 7.1, 7.3, 7.3, 7.4, 7.5

Suppose we are told that in our data, y » f (x) = log (x – 7) + 5. Then, using techniques of precalculus, we can compute f ^–1 (x) = __________________ . So, punch in X as col. 1, Y as col. 2, and ______________________ as col. 3. Then punch _______________________ to do a linear fit between cols. 1 and 3. Write the eqn. _______ = _________________________ to summarize the relationship between cols. 1 and 3. Finally, apply ______ to both sides to get the answer: _________ = __________________________ .

You will want to store this eqn. into _________________ so that it can be overlaid on the XY scatterplot like this:







Are we finished? ___________ , since ___________________________ . Unfortunately, since we didn’t use a "built-in" _______________ , we must compute the _________________ manually. Recalling that residuals are defined to be _______________ , we punch in a 4th col. defined as ____________________ and build a ______________ involving ____ and ____ , i.e., a ________ . Because this _____________________ , we say that the model _____= ______________________________ is an acceptable fit to the data. The model predicts y = _______ when x = 150 (show your work).