Understanding Linear Models, Interpolation, and Extrapolation

The video tutorial introduces linear models, explaining interpolation and extrapolation. It uses examples to demonstrate how to estimate or predict answers using these models. The first example involves estimating marriage ages over time, while the second example focuses on predicting smoking rates among pregnant women. The tutorial emphasizes understanding trends in data and applying linear models to make predictions.

What is the primary purpose of using a linear model?

• To describe a trend in data using a line

• To calculate the exact values of data points

• To create a non-linear representation of data

• To eliminate outliers from data

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CCSS.HSF.LE.B.5

What does interpolation help us estimate?

• The maximum value in a dataset

• The average of all data points

• Future data points beyond the given data

• Data points between two known data points

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CCSS.RL.9-10.7

CCSS.RL.11-12.7

CCSS.RI.9-10.7

CCSS.RI.8.7

CCSS.RL.8.7

In the early 20th century, how did the median age of marriage for males and females compare?

• Males married significantly younger than females

• Females married significantly younger than males

• Males and females married at similar ages

• There was no data available for comparison

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CCSS.RL.11-12.7

CCSS.RI.8.7

CCSS.RI.9-10.7

CCSS.RI.11-12.7

CCSS.RL.9-10.7

What trend was observed in the median age of marriage around the 1960s?

• It increased significantly

• It decreased to a minimum point

• It fluctuated without a clear trend

• It remained constant

How do you fit a line by hand to data before 1970 to estimate the age at marriage for females in 1946?

• By drawing a line that passes through all data points

• By drawing a line that gets as close to all data points as possible

• By ignoring outliers in the data

• By using a curve that fits the data

What is the estimated age at marriage for females in 1984 using data from 1970 onwards?

• 22.5 years

• 20.5 years

• 24.5 years

• 23.2 years

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CCSS.8.EE.C.7B

What method is used to estimate the age at marriage for males in 1995?

• Polynomial fitting

• Non-linear regression

• Linear interpolation

• Linear extrapolation

What was the trend in the percentage of pregnant smokers from 1990 to 2004?

• It decreased significantly

• It fluctuated without a clear trend

• It remained constant

• It increased significantly

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CCSS.8.EE.C.7B

How is linear extrapolation different from interpolation?

• Extrapolation predicts beyond the known data points

• Extrapolation uses non-linear models

• Extrapolation ignores the trend of data

• Extrapolation estimates between known data points

What is the estimated percentage of pregnant smokers in 2006 using extrapolation?

• 7.5%

• 9.5%

• 10.5%

• 8.5%