Question

the daily print publication of newspapers has declined in many large cities over the past 25 years. the philadelphia inquirer weekday print circulation was at its highest in 2001, with an average daily circulation of 220,000 copies, and has decreased every year since then. to develop a linear model for estimating yearly circulation, the log of the daily circulation in thousands was taken. based on the scatterplot of the transformed data and the residual plot, which type of model is appropriate for estimating print publication each year? a linear model is appropriate because the residual plot does not show a clear pattern. a power model is appropriate because the scatterplot of years and the log of circulation is roughly linear. an exponential model is appropriate because the scatterplot of years and the log of circulation is roughly linear and the residual plot shows no distinct pattern. both an exponential and a power model would be appropriate because the log of circulation was used to develop the model.

Explanation:

• For an exponential model \( y = ab^{x}\), taking the logarithm gives \( \log(y)=\log(a)+x\log(b)\). If the scatter - plot of \( x\) (years since 2000) and \( \log(y)\) (log of circulation) is roughly linear and the residual plot (which is not shown here but is a key assumption based on the problem - solving logic for regression models) shows no distinct pattern, an exponential model is appropriate.
• A linear model is not sufficient as we are dealing with a transformation (\(\log\) of the response variable). A power model \( y = ax^{b}\) would have \( \log(y)=\log(a)+b\log(x)\), but here the independent variable is years (not a variable that we took the \( \log\) of).

Answer:

An exponential model is appropriate because the scatterplot of years and the log of circulation is roughly linear and the residual plot shows no distinct pattern.