As part of the American Presidency Project, the annual State of the Union address has been analyzed going back to the first U.S. president. It turns out that the president's use of the word America has increased in relative frequency over the years. Here are the data for the number of the president and the percent of words that are America.

Here is a scatterplot of the data. There appears to be a strong curved relationship between the number of the president and the percent of words that are America.

The graphs below show the results of two different transformations of the data. The first graph plots the logarithm of percent America against the number of the president. The second graph plots the logarithm of percent America against the logarithm of number of the president.

(a) Based on the scatterplots, would an exponential model or a power model provide a better description of the relationship between percent America and number of president? Justify your answer.

(b) Here is computer output from a linear regression analysis on the transformed data in the first graph. Give the equation of the least-squares regression line. Be sure to define any variables you use.

(c) Use your model from part (b) to predict the percent America for the 46th president.

(d) Here is a residual plot for the linear regression in part (b). Do you expect your prediction in part (c) to be too large, too small, or about right? Justify your answer.