AP Statistics / Mr. Hansen
Big Quiz #1 (10/12/2000)

Honor Signature: ____________________
(By your signature, you agree not to discuss this quiz with anyone other than Mr. Hansen until Oct. 19, 2000. You further agree not to use other people, textbooks, the Web, or notes (other than the official formula sheet).

1.

In a linear regression having an r value of –0.318, we would say that there is a _________ _________ _________ association between the _________ (x) variable and the _________ (y) variable. With this LSRL, we can conclude that _________ % of the variation in y is explained by the variation in x.

2.

What name is given to r? __________________ to r²? __________________

3.

We say that an observed difference between two samples is statistically significant if _______________________________________________________________ .

4.

We learned a number of interesting facts about the LSRL. The LSRL, represented by the equation ______________ , is used as a linear fit (i.e., straight-line estimator) to a cloud of data points that have a generally linear trend. In this equation, the letter ______ denotes slope, and the letter ______ denotes the y-intercept. The slope can be found by calculator or also by the formula __________________ . The intercept, which is (fill in "always," "sometimes," or "never") _________ meaningful in its own right, can be found by the formula __________________ .

5.

One fact about the LSRL that we never discussed in class, although it was covered in the textbook, is that the sum of the residuals for a LSRL always equals ________ .

6.

The LSRL is the unique line that minimizes _______________________________ .

7.

A residual is defined to be _________________________________ (use either words or symbols, your choice).

8.

Joe’s position y (measured in miles northeast of the Cathedral) is an approximately linear function of his time t (measured in hours) since he left STA in his car, bound for New York City. If we measure time every half hour, starting at time 0, and note Joe’s position for each of these times during a 5-hour trip, we will have __________ (how many?) y values altogether. Suppose that the mean of all these y values is 131.6. When we make a LSRL to show the association between time and distance, what one point must be on the LSRL? Answer: ( ___ , ___ ). What one point must be in the scatterplot (though not necessarily on the LSRL)? Answer: ( ___ , ___ ). Is there any guarantee that Joe is exactly 131.6 miles from the Cathedral at time t = 2.5 hours? ______ Why or why not? Explain. _________________________________________________________
_________________________________________________________

9.

Which, if any, of the following are resistant to outliers? LSRL, r, r²

10.

A regression outlier is defined to be ___________________________________ . An influential observation is defined to be ___________________________________ .

11.

X
44
48
52
56
60
64
68
72
76
80

(a)

Consider the following data set:

Y
11.451
12.906
12.496
13.769
16.302
18.061
21.074
23.439
26.713
30.552

Comment on the strength, direction, and suitability of a linear fit to the data. You will almost certainly want to show a ______________________ plot as part of this problem!

(b)

What value for y does the linear model predict when x = 56.5? Show your work.

(c)

Compute log y as a list. Raise your hand and show this to me. Then perform a linear fit between x and log y. Use algebra (show your work) to find a new yhat function that is exponential in form. In other words, your final answer should be of the form yhat = ab^x.

(d)

What does your calculator’s ExpReg command give you as an exponential fit? Compare your answer with part (c) and comment on the difference, if any.

(e)

What does the exponential model (indicate whether you are using (c) or (d)) predict for y when x = 56.5? Show your work; don’t just give an answer.

(f)

Comment on the suitability of the exponential model. (Use a ratio analysis, showing your results, and a residual plot.)