AP Statistics / Mr. Hansen 11/19/2002

Name: _________________________ Honor signature (read carefully below): ________________________ Test #3

Take-Home Portion of Test on §§4.1 through 5.2
Due at Start of Class Wed., 11/20/2002

Instructions for this portion:

• Open book permitted, but closed book is strongly recommended. (Open book will probably not help and will definitely slow you down.) Check to indicate whether you __ used or __ did not use the textbook as a resource. Your score will not be affected either way.
• Closed notes, closed friends, closed Internet. No tutors, parents, or other assistance. Honor system applies. Please sign below your name to indicate that you are complying with these requirements.
• No time limit. However, please indicate the total elapsed time that you spent on this problem: ____________
• Justify all steps in the manner described by the questions.
• Work top to bottom, left to right, and write legibly.
• Mark with a single neat “X” any portion you wish to be ignored during grading. (Do not waste time with large erasures.)

7.	A researcher notes the following relationship between annual income and happiness, where happiness is measured on a scientifically developed scale that takes a variety of factors into account.
	Income ($thousands)	Happiness index
	10	0.91
	20	0.94
	30	0.96
	40	0.99
	50	1.01
	60	1.04
	70	1.06
	80	1.08
	90	1.09
	100	1.11
(a)	Is a linear regression model, treating income as explanatory and happiness as response, appropriate for these data? Plot the data, and assess the r value and any other relevant indicators.
(b)	Another researcher proposes a shifted logarithmic model (i.e., response variable as a logarithm of a linear function of the explanatory variable). Explain why this conclusion is more intuitively appealing than a linear model.
(c)	Provide graphical and/or quantitative evidence to support a decision to consider a shifted logarithmic model. Do not actually compute the shifted logarithmic model just yet.
(d)	Now use an inverse transformation to find the appropriate shifted logarithmic model.
(e)	Show quantitative evidence to decide which model is superior, the linear regression model or the shifted logarithmic model. What do you conclude?
(f, g)	Estimate the happiness index value that is predicted for an annual income of $18,500, using both the linear model and the shifted logarithmic model. Show your work.
(h)	What income (approximately) is needed for a happiness index of 1.02? Describe briefly how you obtained this value, or if you could not, state why not. Full work is not required.
(i)	What income (approximately) is needed for a happiness index of 1.45? Describe briefly how you obtained this value, or if you could not, state why not. Full work is not required.