1. A fisherman has collected data about the length in inches, L, and weight in ounces, w, of fish he has caught. The resulting line of best fit for the data is w=−37.1+3.2L. What is the predicted weight in ounces for a fish that is 22 inches long?(1 point)
a.107.5 ounces
b.18.5 ounces
c.70.4 ounces
d.33.3 ounces
2. A biology student is investigating the claim that the temperature can be predicted by counting cricket chirps. She has found a linear regression equation T=42.2+0.21r, where T is the temperature in degrees Fahrenheit and r is the number of chirps per minute. What is the predicted temperature for 90 chirps per minute?(1 point)
a.227.6 degrees
b.23.3 degrees
c.61.1 degrees
d.18.9 degrees
3. A fisherman has collected data about the length in inches, L, and weight in ounces, w, of fish he has caught. The resulting line of best fit for the data is w=−37.1+3.2L. Would predicting the weight of a 26-inch fish be interpolation or extrapolation? Explain.
L 13 14 15 16 18 21 23 23
w 3 10 10 15 20 35 38 45
a.Using the model to predict the weight of a 26-inch fish is interpolation because 26 inches is inside the range of the lengths in the data.
b.Using the model to predict the weight of a 26-inch fish is extrapolation because 26 inches is outside the range of the lengths in the data.
c.Using the model to predict the weight of a 26-inch fish is interpolation because 26 inches is outside the range of the lengths in the data.
d. Using the model to predict the weight of a 26-inch fish is extrapolation because 26 inches is inside the range of the lengths in the data.
4. A biology student is investigating the claim that the temperature can be predicted by counting cricket chirps. She has collected the data in the table below and come up with the regression equation T=42.2+0.21r, where T is the temperature in degrees Fahrenheit and r is the number of chirps per minute. Would using this model to predict the temperature for 100 chirps per minute be an example of interpolation or extrapolation? Explain.
r 66 73 81 95 116 120 138 138
T 59 55 60 67 64 68 71 73
a.Using the model to predict the temperature for a chirp rate of 100 chirps per minute is extrapolation because 100 chirps per minute is inside the range of the values of r in the data set.
b.Using the model to predict the temperature for a chirp rate of 100 chirps per minute is interpolation because 100 chirps per minute is inside the range of the values of r in the data set.
c.Using the model to predict the temperature for a chirp rate of 100 chirps per minute is interpolation because 100 chirps per minute is outside the range of the values of r in the data set.
d.Using the model to predict the temperature for a chirp rate of 100 chirps per minute is extrapolation because 100 chirps per minute is outside the range of the values of r in the data set.
5. A real estate agent has developed a linear model for the price of a house, P, in dollars in terms of the area, A, in square feet for the homes in a certain neighborhood. The data set had areas ranging from 1,000 square feet to 4,500 square feet. Would predicting the prices of a home that is 4,900 square feet be interpolation or extrapolation? Explain.(1 point)
Responses
a.Using the model to predict the price of a 4,900 square foot home is interpolation because 4,900 square feet is inside the range of the areas in the data.
b.Using the model to predict the price of a 4,900 square foot home is extrapolation because 4,900 square feet is outside the range of the areas in the data.
c.Using the model to predict the price of a 4,900 square foot home is interpolation because 4,900 square feet is outside the range of the areas in the data.
d.Using the model to predict the price of a 4,900 square foot home is extrapolation because 4,900 square feet is inside the range of the areas in the data.
1. 33.3
2. 61.1
3.Using the model to predict the weight of a 26-inch fish is extrapolation because 26 inches is outside the range of the lengths in the data.
4.Using the model to predict the temperature for a chirp rate of 100 chirps per minute is interpolation because 100 chirps per minute is inside the range of the values of r in the data set.
5. Using the model to predict the price of a 4,900 square foot home is extrapolation because 4,900 square feet is outside the range of the areas in the data.
thx
1. To find the predicted weight in ounces for a fish that is 22 inches long, we can use the given line of best fit equation: w = -37.1 + 3.2L.
Substitute L = 22 into the equation: w = -37.1 + 3.2*22
Simplify the equation: w = -37.1 + 70.4
Calculate the value: w = 33.3 ounces
So, the predicted weight in ounces for a fish that is 22 inches long is "d. 33.3 ounces".
2. To find the predicted temperature for 90 chirps per minute, we can use the given linear regression equation: T = 42.2 + 0.21r.
Substitute r = 90 into the equation: T = 42.2 + 0.21*90
Simplify the equation: T = 42.2 + 18.9
Calculate the value: T = 61.1 degrees
So, the predicted temperature for 90 chirps per minute is "c. 61.1 degrees".
3. To determine whether predicting the weight of a 26-inch fish using the given line of best fit equation is interpolation or extrapolation, we need to consider the range of lengths in the data.
Given data:
L: 13, 14, 15, 16, 18, 21, 23, 23
w: 3, 10, 10, 15, 20, 35, 38, 45
The lengths range from 13 to 23 inches. Since 26 inches falls within this range, predicting the weight of a 26-inch fish using the model is interpolation as it is within the range of the lengths in the data.
Therefore, the correct answer is "a. Using the model to predict the weight of a 26-inch fish is interpolation because 26 inches is inside the range of the lengths in the data."
4. To determine whether using the given model to predict the temperature for 100 chirps per minute is interpolation or extrapolation, we need to consider the range of values of r in the data.
Given data:
r: 66, 73, 81, 95, 116, 120, 138, 138
T: 59, 55, 60, 67, 64, 68, 71, 73
The chirp rates range from 66 to 138. Since 100 chirps per minute falls within this range, predicting the temperature for 100 chirps per minute using the model is interpolation as it is within the range of the values of r in the data.
Therefore, the correct answer is "b. Using the model to predict the temperature for a chirp rate of 100 chirps per minute is interpolation because 100 chirps per minute is inside the range of the values of r in the data set."
5. To determine whether predicting the price of a 4,900 square foot home using the given linear model is interpolation or extrapolation, we need to consider the range of areas in the data.
Given that the data set had areas ranging from 1,000 square feet to 4,500 square feet. Since 4,900 square feet is outside this range, predicting the price of a 4,900 square foot home using the model is extrapolation as it is outside the range of the areas in the data.
Therefore, the correct answer is "b. Using the model to predict the price of a 4,900 square foot home is extrapolation because 4,900 square feet is outside the range of the areas in the data."
1. c. 70.4 ounces
2. c. 61.1 degrees
3. a. Using the model to predict the weight of a 26-inch fish is interpolation because 26 inches is inside the range of the lengths in the data.
4. a. Using the model to predict the temperature for a chirp rate of 100 chirps per minute is extrapolation because 100 chirps per minute is inside the range of the values of r in the data set.
5. b. Using the model to predict the price of a 4,900 square foot home is extrapolation because 4,900 square feet is outside the range of the areas in the data.