Choosing the Best Model Answers

Data were recorded for the temperature of a cup of coffee over a 30-minute period. A regression analysis was completed and the computer output is given.

Data were recorded for the temperature of a cup of coffee over a 30 minute period. It is known that the temperature of hot coffee will cool to room temperature following an exponential model.Which of the following would linearize the data for temperature and minutes?

Data were recorded for the temperature, in degrees Celsius, of a cup of coffee over a 30-minute period. Given the regression equation, , what is the predicted temperature after 5 minutes?

Water is being poured into a large, cone-shaped cistern. The volume of water, measured in cm3, is reported at different time intervals, measured in seconds and is displayed in scatterplot A. Two transformations of the data are shown in the second and third graphs. Scatterplot B displays the relationship between time and the log of volume. Scatterplot C displays the relationship between the log of time and the log of volume. Which model best represents the relationship between time and volume?

Data were recorded for a car’s fuel efficiency, in miles per gallon (mpg), and the corresponding speed, in miles per hour (mph). A regression analysis was completed and the computer output is given.

When a stone is dropped in a pond, ripples are formed and travel in concentric circles away from where the stone was dropped. The relationship between the time and area of the circles was analyzed and is shown in the computer output.

Water is being poured into a large, cone-shaped cistern. The volume of water, measured in cm3, is reported at different time intervals, measured in seconds. A regression analysis was completed and is displayed in the computer output.

The regression equation for water being poured into a large, cone-shaped cistern is . What is the predicted volume for a time of 12 seconds?

The lengths and weights for 15 different-sized bluegill fish were measured and recorded. Scatterplot A displays the relationship between the length, in inches, and the weight, in ounces, for each fish. Two transformations of the data are shown in the scatterplots B and C. Scatterplot B displays the relationship between the length and the natural log of the weight. Scatterplot C displays the relationship between the natural log of the length and the natural log of the weight.Which model best represents the relationship between the bluegills’ lengths and weights?

The lengths, in inches, and corresponding weights, in ounces, for 15 different-sized bluegill fish were measured and recorded. Given the regression equation, , what is the expected weight for a bluegill fish that is 11 inches long?