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Linear transformation On this chapter, we will learn... Explain what is meant by transforming data Discuss the advantages of transforming linear data Tell where y=log (x) fits into the hierarchy of power transformation Explain the ladder of power transformation Explain how linear growth differs form exponential growth Activity 1 Number HOURS s 1.0 1.8 1.5 2.4 2.0 3.1 2.5 4.3 3.0 5.8 3.5 8.0 4.0 10.6 4.5 14.0 5.0 18.0 Graph and find the linear regression line for the number of bacteria present after 3.75 hours. Number HOURS s 1.0 1.8 1.5 regression 2.4 Linear 2.0 3.1 2.5 4.3 3.0 5.8 Scatter plots 3.5 8.0 4.0 10.6 4.5 14.0 Residual plots 5.0 18.0 Hours = -4.2744 + 3.9433 (bacteria) Predicted number of bacteria after 3.75 hours 2.024 bacteria IS THIS AN ACCURATE PREDICTION? Linear Transformation Applying a function such as the logarithm or square root to a quantitative variable is called transforming or reexpressing the data Properties of Logarithm First steps in transforming In unit of measurement: Celsius to Fahrenheit (in temperature) Miles to Kilometers (in distance) Pounds to Kilograms (in weight) Linear transformation However, our focus will be on: power and logarithmic transformation Punch these in... Average weight and length of harvested salmon A. Scatterplots B. Linear Model Weight = -299.0423 + 25.2024 (length) Correlation = .95 Now let’s transform the model by taking the cube of the lengths and then graph the weight versus length with this transformation Weight = a x 3 (length) A. Scatterplots B. Linear Model Weight = 4.0658 + .o1467 (length)3 Correlation = .99