In television's early years, most commercials were 60 seconds long. Now, however, commercials can be any length. The objective of commercials remains the same-to have as many viewers as possible remember the product in a favorable way and eventually buy it. In an experiment to determine how the length of a commercial is related to people's memory of it, 60 randomly selected people were asked to watch a 1-hour television program. In the middle of the show, a commercial advertising a brand of toothpaste appeared. Some viewers watched a commercial that lasted for 20 seconds, others watched one that lasted for 24 seconds, 28 seconds, ..., 60 seconds. The essential content of the commercials was the same. After the show, each person was given a test to measure how much he or she remembered about the product. The commercial times and test scores (on a 30-point test) were recorded.
a. Draw a scatter diagram of the data to determine whether a linear model appears to be appropriate.
b. Determine the least squares line.
c. Interpret the coefficients.