Transforming to Achieve Linearity Answers

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?

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 and corresponding weights for 15 different-sized bluegill fish were measured and recorded. 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.

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?

Data were recorded for a car’s fuel efficiency, in miles per gallon (mpg), and corresponding speed, in miles per hour (mph). Scatterplot A displays the relationship between the car’s speed and fuel efficiency. Two transformations of the data are shown in scatterplots B and C. Scatterplot B displays the relationship between the car’s speed and the natural log of the fuel efficiency. Scatterplot C displays the relationship between the natural log of the car’s speed and the natural log of the fuel efficiency.Which scatterplot best represents the relationship between a car’s speed and its fuel efficiency?

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?

Water is 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 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?

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.