AnswersStatisticsChoosing the Best Model

Choosing the Best Model Answers

1 verified answers1 views
1
Free Preview

Online entertainment streaming services have gained in popularity in recent years as an alternative to traditional television. One such company has seen steady growth in each period of 3 months, called a quarter, over the past 4 years. The scatterplot shows the relationship between the number of quarters passed since January 2014 and the number of members to the streaming service. A least-squares equation that summarizes this relationship is , with a value for r of 0.991.

Question illustration
A
A linear model is appropriate because the value of r is close to 1.
B
A linear model is appropriate because the residual plot is curved.
C
A linear model is not appropriate because the residual plot shows a clear pattern.
D
A linear model is not appropriate because the scatterplot relating time and subscribers shows a clear pattern.
2
Free Preview

A small technology company started offering shares of stock to investors in 1987. At that time, the price of one share of stock was $0.39. Since then, the company has experienced rapid growth. Twenty-two years later, the price of a single share of stock has risen to over $110. One scatterplot shown summarizes the number of years since the initial stock offering in 1987 and the price of the stock, while the other compares years since 1987 to the log of stock price.

Question illustration
A
A linear model is appropriate because the scatterplot of the transformed data is roughly linear.
B
An exponential model is appropriate because the scatterplot of time and log price is increasing.
C
An exponential model could be appropriate because the scatterplot of time versus log price is roughly linear.
D
A power model is appropriate because the scatterplot of time and price shows a curved relationship.
3

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 226,000 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.

Question illustration
A
A linear model is appropriate because the residual plot does not show a clear pattern.
B
A power model is appropriate because the scatterplot of years and the log of circulation is roughly linear.
C
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.
D
Both an exponential and a power model would be appropriate because the log of circulation was used to develop the model.
4

A forest management agency collects measurements from beech trees in a public park. The age of many of the trees is known, and the basal area—the area of land occupied by the trunks of the trees—is also measured. A least-squares equation that compares the basal area to the age of each tree is given by .

Question illustration
A
Because the residuals are centered about zero, a linear model is appropriate.
B
Because the residual plot does not show a clear pattern, a linear model is appropriate.
C
Because the residual plot shows a random a scatter of points, a linear model is not appropriate.
D
Because the residual plot does not appear linear, it is likely that tree age and basal area do not have a linear relationship.
5

One method used to measure the speed of supercomputers is the number of floating-point mathematical operations the computer can perform in one second. This is often referred to by the acronym FLOPS. For many years since 1992, the number of FLOPS performed by the largest supercomputer available that year was recorded.

Question illustration
A
A linear model, because the scatterplot of years and ln operations is roughly linear.
B
A power model, because the scatterplot of years and operations shows a steep curve.
C
An exponential model could be appropriate because the scatterplot of years and ln(operations) is roughly linear. The next step is to look at the residual plot.
D
A power model, because the scatterplot of ln(years) and ln(operations) shows the strongest linear relationship.

Did you find these answers helpful?

More from this Course

Quiz
10 verified answers

Calculating the Least-Squares Regression Line

Quiz
1 verified answers

Residuals

Quiz
2 verified answers

Transforming to Achieve Linearity

Choosing the Best Model Answers — Statistics