AP Statistics / Mr. Hansen 10/29/2004

Name: _________________________

Big Quiz on Chapter 4 (40 points)

1.	A linear least-squares model (LSRL) is appropriate when
	(A) r is close to 1
	(B) r^2 is close to 1
	(C) r^2 is close to 1, and the residual plot shows a clear pattern
	(D) r^2 is close to 1, and the residual plot shows a clear linear pattern
	(E) r^2 is close to 1, and the residual plot exhibits randomness
2.	Let x denote our explanatory variable, and let y denote our response variable. The hallmark of exponential growth is that ___________________ is well approximated by a linear function of ___________________ . Also, if the x values are equally spaced, the values will . . .
	(A) have a common difference (i.e., form an arithmetic sequence)
	(B) have a common ratio (i.e., form a geometric sequence)
	(C) follow a quadratic function
	(D) follow a cubic function
	(E) follow a power function (i.e., a polynomial function that has only one term)
3.	Let x denote our explanatory variable, and let y denote our response variable. The hallmark of power-function growth is that ___________________ is well approximated by a linear function of ___________________ .
4.	Let a, b, c, etc. denote the parameters of a model. A quadratic model has the general form = ________________________ . An exponential model has the general form = ________________________ . A power model has the general form = ________________________ .
5.	Here is a fake data set I made up for tree height and associated biomass:
	Height (m)	Biomass (kg)
	1.5	15.5
	2.2	27.1
	3	41.5
	3.7	54.4
	5	82.5
	6.2	106.8
	7.1	135
	9	186
	10.5	218.8
	12	266
	12.8	288
	13.75	319
	15	354
(a)	Compute a linear least-squares model (no work needed). Write your equation here: ________________________________________________________ Is your model appropriate for this situation? ____ In the space below, provide both graphical evidence and a brief explanation in words. Hint: Although a scatterplot of y versus x is certainly required, “graphical evidence” must consist of more than merely that one scatterplot.
(b)	Which x value has the largest positive residual? _______ Which x value has the largest negative residual (i.e., largest in absolute value)? _______ Circle these on your residual plot.
(c)	Compute an exponential model (no work needed). Write your equation here: ________________________________________________________
(d)	What biomass does your exponential model predict for a tree of height 9.8 m?
(e)	Explain briefly why no model based on this data set would be valid for predicting the mass of a tree 22 m tall. If possible, use the vocabulary word we learned.
(f)	Compute a power regression model (no work needed). Write your equation here: ________________________________________________________
(g)	What height does your power regression model predict for a tree of mass 120 kg?
(h)	Sketch the residual plot for your power regression model. Do you see any potential problems with the model?
6.	A citizens’ group has charged the tobacco industry with marketing a dangerous product. Alarmed by data showing that smoking rates have increased between 1990 and 2004 for all three age groups in the table below, the citizens’ group has concluded that smoking rates are on the rise and must be halted by political action. The tobacco industry has countered that the conclusion is not justified by the data. Curiously, the tobacco industry accepts the accuracy of the numbers in the table. Explain, using several complete, intelligible sentences. If there is a lurking variable, clearly identify what you think it is. You may assume that the population has increased between 1990 and 2004.
	Incidence of Smoking
			1990	2004
	Under-18 age group		4%	9%
	18-25 age group		11%	12%
	Adults over age 25		20%	28%