Pressure changes in seawater affect the speed at which sound is transmitted, and the data set in DS 12.11.11 shows how the underwater speed of sound relates to the depth at which it is measured. Use a linear regression model to analyze the data with the depth as the input variable and with the speed of sound as the output variable.
(a) Show how to calculate the fitted regression line.
(b) Show how to calculate the estimate of the error variance.
(c) Perform a hypothesis test to assess whether it is a significant regression.
(d) Calculate a 95% confidence interval for the speed of sound at a depth of 4 meters.
(e) What is the value of the coefficient of determination R? '
The following data sets can be used to practice the regression techniques discussed in this chapter.