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AP Statistics 2016-2017
Chapter 3: Examining Relationships
3.1: Scatterplots
3.2: Correlation
3.3: Least-Squares Regression
"As the sun eclipses the stars by its brilliancy, so the man of knowledge will eclipse the fame of others in assemblies of the people if he proposes algebraic problems, and still more if he solves them." -- (Brahmagupta)
Brahmagupta (c. 598 A.D.): One of the greatest of Indian mathematicians, Brahmagupta was instrumental in the development of algebra for problem solving. Among other things, he wrote an amazing mathematical treatise in which he covered subjects such as square and cube roots, and fractions. He also enjoyed working with irrational numbers, such as the square root of 2, and calculated values of irrational numbers accurate to many decimal places.
Assignment # 1 (Introduction & § 3.1) Th:[09-22-16]
Read pp. 121 – 122; pp. 123 – 124. Take notes on all terminology.
pp. 122 – 123 # 3.1 – 3.5; pp. 125 – 126 # 3.6 – 3.7
Assignment # 2 (§ 3.1) F:[09-23-16]
Read pp. 126 – 128; pp. 130 – 131. Take notes on all terminology.
pp. 129 – 130 # 3.9 – 3.11; pp. 132 # 3.12; pp. 135 – 136 # 3.15 – 3.18
Assignment # 3 (§ 3.2) M:[09-26-16]
Read pp. 140 - 142; pp. 143 - 145. Take notes on all terminology.
p. 142 # 3.24; p. 146 # 3.25 – 3.28; p.147 # 3.29 – 3.31
Assignment # 4 (§ 3.3) T:[09-27-16]
Read pp. 149 - 156; pp. 157 - 165. Take notes on all terminology.
pp. 156-157 # 3.38 – 3.41; pp. 165-167 # 3.42 – 3.45
Assignment # 5 (§ 3.3) W:[09-28-16]
Read pp. 167 – 172. Take notes on all terminology.
pp. 173 – 176 # 3.46 – 3.49; Do Technology Toolbox
Assignment # 6 (§ 3.1 Review) Th:[09-29-16]
Read pp. 134 – 135.
pp. 135 – 140 # 3.19 – 3.23
Assignment # 7 (§ 3.2 Review) F:[09-30-16]
Read pp. 146 – 147.
pp. 147 – 149 # 3.32 – 3.37
Assignment # 8 (§ 3.3 Review) W:[10-05-16]
Read p. 176.
pp. 176 – 181 # 3.50 – 3.61; p. 189 #3.76
Assignment # 9 (§ 3.3) Th:[10-06-16]
Read pp. 181 – 183
Take-home Study Quiz
Assignment # 10 (§ 3.1-3.3 Test) F:[10-07-16]
Key Words, Skills, Terminology and Concepts
Response Variable
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Explanatory Variable
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Dependent Variable
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Independent Variable
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Scatterplot
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Overall Pattern
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Deviations
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Form
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Direction
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Strength
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Linear Relationship
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Outlier
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Positive Association
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Negative Association
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Adding Categorical Variables
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Correlation
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R
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Least-Squares Regression
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Model
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Regression Line
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LSRL
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Prediction
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Interpolation
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Extrapolation
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Slope (b)
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Intercept (a)
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Plotting the Line
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r2
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Coefficient of Determination
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Residual
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Roundoff Error
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Residual Plot
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Curved Residual Pattern
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Influential Observation
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ŷ
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Usage of the TI-83 – Naming Lists (ex; DEGDA, GAS); Transferring Data Between Lists: (ex: LDEGDA L1); Defining a Scatterplot: 2nd Y= , Highlight Plot 1 On, Make sure the Scatterplot Icon is Selected, Check to see the Xlist and Ylist are what you want, Use ZOOM 9:Stat to automatically set up the window to fit the data;
2nd LIST OPS 5:seq(formula, X, begin input integer, end input integer); STAT CALC 2:2-Var Stats; VARS 5:Statistics 2: , 3:Sx, 5: , 66:Sy; 2nd LIST MATH 5: sum(List); STAT CALC 8:LinReg(a + bx) L1, L2, Y1 (where Y1 is found under VARS Y-VARS 1:Function: Y1; 2nd 0 D Page Down 9 times; to DiagnosticOn, ENTER ENTER; L3 = L2 – Y1(L1); Plotting the residuals; 2nd LIST NAMES #:RESID.
"Nothing has afforded me so convincing a proof of the unity of the Deity as these purely mental conceptions of numerical and mathematical science which have been by slow degrees vouchsafed to man, are are still granted in these latter times by the Differential Calculus, now superseded by the Higher Algebra, all of which must have existed in that sublimely omniscient Mind from eternity." -- (Mary Somerville, 1780-1972)
David Hume (Scotland, 1711-1776): One of a number of eighteenth-century philosophers who did not believe in the doctrine of an external world following fixed mathematical laws. As did Immanuel Kant (1724-1804), Hume claimed that mathematics is not inherent in the physical world but comes from the human mind. The intuitionist school of mathematical thought that was founded by Dutch mathematician Luitzen Brouwer (1881-1966) built their beliefs around the philosophies of Hume and Kant.
"To us probability is the very guide of life." -- (Bishop Butler, Preface to Analogy)
Emilie du Chatelet (France, 1706-1749). Her major work, Mathematical Principles of Natural Philosophy, was a French translation on Newton's Principia. She also produced a scholarly manuscript entitled Dissertation on the Nature and Propagation of Fire. du Chatelet was brilliant with numbers. The French philosopher Voltaire claimed he witnessed her find the product of two nine-digit numbers using only mental calculation.
"Angling may be said to be so like mathematics that it cannot fully be learned." -- (The Complete Angler, 1653)
Trigonometry: An amazing number of useful relationships come from the three simple definitions for sine, cosine, and tangent. The Muslims introduced these ratios and established many of the extremely important trigonometric relationships that we use today. Muslim developers of trigonometry include
Al-Battani (ca. 920) Abu Wafa (ca. 980) Ibn Yunus (ca. 1000)
Thabit ibn Qurra (ca. 900) Nasir al-Din al-Tusi (ca. 1260)
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