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4. The following table shows pressure, y, measured in pounds per square inch (psi), of air in a cans tire at different times, it, measured in seconds afterthe tire was punctured. a) Make a scatter plot of the data. b) Using exponential regression, find the equation of the form 9 = ab" that best ts the data. Write down the equation as well as the correlation coefficient and the coefficient of determination 5'; = r: r2: c) Complete the table on the next page by filling out the 3" column which is the common logarithm of the y-values. Recall from Algebra II, that the common logarithm is written log1 x. On your calculator this logarithm is found using the LOG key. Round your logarithm values to one decimal place. x (sec) y (psi) log(y) log y(psi) 5 27 2.0+ 10 21 1.8 4 15 16 1.6 - 20 13 25 9 1.4 - 30 7 1.2- 35 6 1.0+ 40 4 45 3 0.8- 50 3 0.6- 0.4- 0.2+ x(sec) 10 20 30 40 50 60 d) Graph x versus log(y) on the grid provided above. What does the shape of the graph look like? e) Run a linear regression on log y as a function of x. Write the equation, the correlation coefficient, ande) Run a linear regression on log y as a function of x. Write the equation, the correlation coefficient, and coefficient of determination. [Suggestion: Store your log(y) numbers in L3 and then build your linear function using L1 and L3.] D = r= 12 = f) How do the values of r and r2 compare to those in part (b) ? Your calculator computes the values of r and r2 by first linearizing the data (by taking the logarithm of y) and then computing the coefficient of correlation and coefficient of determination using the linear graph. Now you know