Making Predictions Answers

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5

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6

Compare and contrast interpolations and extrapolations based on a scatterplot.

Answer:

Interpolations and extrapolations are both methods used to make predictions based on a scatterplot's line of best fit. An interpolation is a prediction that lies within the range of the existing data points (the cluster), while an extrapolation is a prediction for a value that lies outside the range of the observed data. Consequently, interpolations are considered more reliable, whereas extrapolations carry more risk because they assume that the observed trend will continue indefinitely.

7

Kardal used the trend line to predict that a man 72 inches tall would wear about a size 10.5 shoe. What can be concluded about this prediction? Check all that apply.

A
The prediction is not reasonable.
B
The prediction is an interpolation.
C
No data is given in the scatterplot for a height of 72 inches, but a shoe size can still be predicted.
D
A prediction cannot be made without the linear regression equation.
E
A 72-inch tall man will wear a size 11.5 shoe.
9

Ramona determined that her answer was incorrect because a man who is –17.52 inches tall does not make any sense. What was Ramona’s mistake?

A
She substituted the 8.5 for the wrong variable.
B
She should have added .444 and 8.5.
C
The value for y should be positive.
D
The solution of –17.52 should be the shoe size.
10

Explain how to use the regression calculator to make a reasonable prediction given a data table.

Answer:

To use a regression calculator for predictions, first identify the independent (x) and dependent (y) variables in the data table. Enter the data pairs into the calculator to generate the regression equation. Then, substitute a known value into this equation and simplify to calculate the predicted value for the other variable.

11

Which did your explanation include? Check all that apply.

A
An interpolation is more reliable than an extrapolation.
B
An interpolation is based on data within the range of data for the scatterplot.
C
An extrapolation is based on data outside the range of data for the scatterplot.

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