## Solution for problem R12.5 Chapter 12

# Light intensity In physics class, the intensity of a

The Practice of Statistics | 4th Edition

Light intensity In physics class, the intensity of a 100-watt light bulb was measured by a sensor at various distances from the light source. A scatterplot of the data is shown below. Note that a candela (cd) is a unit of luminous intensity in the International System of Units. Physics textbooks suggest that the relationship between light intensity y and distance x should follow an inverse square law, that is, a power law model of the form y ? ax 2. We transformed the distance measurements by squaring them and then taking their reciprocals. Some computer output and a residual plot from a least-squares regression analysis on the transformed data are shown below. Note that the horizontal axis on the residual plot displays predicted light intensity. Predictor Coef SE Coef T P Constant 0.000595 0.001821 0.33 0.751 Distance^( 2) 0.299624 0.003237 92.56 0.000 S ? 0.00248369 R-Sq ? 99.9% R-Sq(adj) ? 99.9% (a) Did this transformation achieve linearity? Give appropriate evidence to justify your answer. (b) What would you predict for the intensity of a 100-watt bulb at a distance of 2.1 meters? Show your work. s Use transformations involving logarithms to achieve linearity for a relationship between two variables. s Determine which of several transformations does a better job of producing a linear relationship.

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The Flow of Energy Jean Baptista Van Helmont Flemish scientist in Belgium Used empirical formal/inductive reasoning to discover things Spontaneous Generation o Idea that living matter arises from inanimate matter o Experiment: Mice arise from wheat and fabric 1. Put bucket of wheat and fabric in corner for a month = MICE! o Incorrectly concluded spontaneous generation is real o Did NOT have a control o Incorrectly concluded that plants mass is from water/plants are made from water Plants are made from air Photosynthesis converts CO2 into sugar using energy of the sun Sugar is the building blocks of all other organic compounds

###### Chapter 12, Problem R12.5 is Solved

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Light intensity In physics class, the intensity of a