Expand Your Knowledge: Logarithmic Transformations, Power Law Model Let x 5 boiler steam pressure in 100 lb/in.2 and let y 5 critical sheer strength of boiler plate steel joints in tons/in.2. We have the following data for a series of factory boilers.

x 4 5 6 8 10 y 3.4 4.2 6.3 10.9 13.3

(a) Make the logarithmic transformations x 5 log x and y 5 log y. Then make a scatter plot of the x , y values. Does a linear equation seem to be a good fi t to this plot?

(b) Use the x , y data points and a calculator with regression keys to fi nd the least-squares equation y 5 a 1 bx . What is the sample correlation coeffi cient?

(c) Use the results of part

(b) to fi nd estimates for a and b in the power law y 5 axb. Write the power equation for the relationship between steam pressure and sheer strength of boiler plate steel. Hint: See Problem 24.