Expand Your Knowledge: Logarithmic Transformations, Power Law Model Let x= boiler steam pressure in...

Expand Your Knowledge: Logarithmic Transformations, Power Law Model Let x= boiler steam pressure in 100 lb/in.2 and let y= 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’ = log xand y’ = log y. Thenmake a scatter plot of the (x’, y’)values. Does a linear equation seem to be a good fit to this plot?

(b) Use the (x’, y’) data points and a calculator with regression keys to find the least-squares equation y’ = a + bxoe. What is the sample correlation coefficient?

(c) Use the results of part (b) to find estimates for a and b in the power law y = ax^b. Write the power equation for the relationship between steam pressure and sheer strength of boiler plate steel.