4.1 Transformations.

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Presentation transcript:

4.1 Transformations

Why do we transform? Purpose of transforming is to achieve linearity Once linear, can use LSRL to make predictions transforming/re-expressing—when applying a function such as logarithm or square root to a quantitative variable

Rockfish Tournament Organizing a fish tournament where prizes are rewarded to the heaviest fish caught Know fish will be measured and released Know using delicate scale while fish is floppy around is not accurate Easier to measure length—need a way to convert length to weight

Rockfish Tournament Length (L1) Weight (L2) 5.2 2 28.2 318 8.5 8 29.6 371 11.5 21 30.8 455 14.3 38 32.0 504 16.8 69 33.0 518 19.2 117 34.0 537 21.3 148 34.9 651 23.3 190 36.4 719 25.0 264 37.1 726 26.7 293 37.7 810

Rockfish Tournament Make a scatterplot—what is the pattern? R= Make residual plot  What do you see?

Rockfish Tournament Use the model and cube all the length measurements in table and recreate scatterplot (L3, L2) L3 = (L1)^3

Rockfish Tournament What is LSRL on transformed points? What is r? r2? So _______of the variation in the weight of Atlantic Ocean rockfish is predicted by the LSRL given length3.

Rockfish Tournament Now make original scatterplot (L1, L2) with new LSRL equation (make x^3) Now what would be the weight of a fish 36 centimeters?

Pg 265 #2 a) Make a scatterplot of data. Describe what you see Length (cm) Period (s) 16.5 0.777 17.5 0.839 19.5 0.912 22.5 0.878 28.5 1.004 31.5 1.087 34.5 1.129 37.5 1.111 43.5 1.290 46.5 1.371 106.5 2.115 b) Find LSRL. Is it a good model for the data? c) Pendulum should be proportional to the square root of the length d) What is the equation of LSRL? How well does it fit transformed data? Justify using residual plot and r2. e) Predict the period of an 80 cm pendulum

HW: pg 266 #3