Advanced Functions

Nadia collected the data in the table on the left using a CBR after a ball was
dropped.
(a) Enter the data into L1 and L2 using a TI-83 Plus. Graph the relation.
(b) Without looking at the graph, how do you know that the relation is not
linear?
(c) Use regression to find the equation of the quadratic of best fit.
(d) Is this equation a good model? Justify your answer.
You can use the TI-83 Plus to estimate different regression models, but
often the model does not perfectly fit the data. A common method in data
analysis is to transform one variable until the graph becomes linear. In this
case, observe that time increases by a constant, but height decreases by a
larger amount in each successive observation. This suggests a
transformation that compresses height or expands time.
(e) Calculate the square root of each entry in L2 (height) and store the
values in L3.
(f) Graph the square root of height versus time. Does this relation appear
to be linear? Calculate the correlation coefficient for the relation.
What can you conclude?
(g) Calculate the square of each time-value in L1 and store the results in
L3.
(h) Graph height versus time2. Does this relation appear to be linear?
Calculate the correlation coefficient. What can you conclude?
(i) Let h represent height and t represents

TIME(S) HEIGHT(M)
0.0 3.0
0.2 2.8
0.4 2.2
0.6 1.2
0.8 0.0

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  1. look at the differences.
    1st: -0.2, -0.6, -1.0, -1.2, ...
    2nd: -0.4, -0.4, -0.4, ...

    so, look for a linear relationship between y and x^2:

    y = 3-5x^2

    fits pretty well, at least at first

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