Problem 16.6 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 remembering 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 20 seconds, others watched one that lasted 24 seconds, 28 seconds,…, 60 seconds. The essential content of the commercial 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 and are listed below. Test Length Type 24 52 1 20 40 2 16 36 2 11 28 1 10 44 3 4 16 1 24 48 1 18 52 2 16 60 3 15 44 2 14 36 1 15 44 2 24 60 3 10 24 3 1 32 1 8 40 3 9 24 1 0 32 3 17 52 2 9 36 3 26 60 2 28 56 1 15 20 1 8 40 3 2 48 1 0 20 2 11 24 3 8 36 3 24 60 1 10 44 1 15 52 2 7 28 3 26 56 1 11 20 3 18 52 2 16 16 2 8 20 3 12 40 1 10 16 3 14 44 1 19 32 2 8 20 3 11 56 3 24 56 1 15 60 2 9 24 3 18 48 2 14 16 2 14 32 1 11 16 3 15 40 2 11 24 3 27 36 2 5 28 3 17 56 2 8 32 1 15 28 1 8 48 1 24 28 2 21 48 2 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.
Problem 16.28 (continued in conjunction with problem 16.6) Refer to Exercise 16.6 above A. What is the standard deviation error of estimate? Interpret its value.
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