Predictions using the regression model are most reliable within the age range of the collected data, 21 to 61 years, making it appropriate for 53- and 36-year-olds but not for a 65-year-old. Extrapolation for a 19-year old can still be reasonable.
When determining whether it is appropriate to use a regression model for prediction, it is important to consider the range of the independent variable, in this case, age, over which the data was collected. The given data ranges from 21 to 61 years old. Therefore, predictions using the regression model ŷ = -4.21x + 344.07 would be more reliable for ages within this range.
It is not appropriate to use this model to predict weekly entertainment expenses for a 65-year-old adult, as this age is outside the range of the collected data and would constitute extrapolation.
It is appropriate to use this model to predict weekly entertainment expenses for a 53-year-old adult, as this age is within the range of collected data.
It is appropriate to use this model to predict weekly entertainment expenses for a 36-year-old adult, as this age is within the range of collected data.
It is appropriate to use this model to predict weekly entertainment expenses for a 19-year-old adult, although this age is slightly below the range, the prediction is likely to be reasonably accurate as it is close to the range of the collected data.
The probable question may be:
The data below shows age (x, in years) and weekly entertainment expenses (y, in dollars) for a random sample of ten adults. The least squares regression model for this data is ŷ = -4.21x + 344.07. Select all valid statements regarding the use of this regression model.
This is a "select all that apply" question where multiple correct answer choice are possible. You must make a selection for each option. Click once to place a check mark for correct answers and click twice to empty the box for the wrong answers.
? It is appropriate to use this model to predict weekly entertainment expenses for a 65-year-old adult.
? It is appropriate to use this model to predict weekly entertainment expenses for a 53-year-old adult.
? It is appropriate to use this model to predict weekly entertainment expenses for a 36-year-old adult.
? It is appropriate to use this model to predict weekly entertainment expenses for a 19-year-old adult.
Age Entertainment expenses
21 242
23 265
27 275
30 192
33 215
42 98
45 164
47 128
55 159
61 85