Understanding Linear Models and Trends

Lesson 11 focuses on using linear models in a data context. It revisits concepts from the previous lesson, such as dependent and independent variables, and the meaning of the slope. The lesson uses examples like Old Faithful's eruptions and Olympic race times to illustrate how to fit a line to data and interpret the results. It emphasizes understanding the relationship between variables and making predictions using linear models.

What is the primary focus of lesson 11 in module 6?

• Understanding quadratic models

• Exploring linear models in a data context

• Studying exponential growth

• Analyzing geometric sequences

In the Old Faithful example, what is the dependent variable?

• Amount of water

• Height of eruption

• Length of eruption

• Temperature of water

What does the slope represent in the Old Faithful linear model?

• Minutes per gallon

• Minutes per eruption

• Gallons per eruption

• Gallons per minute

Why might the y-intercept not make sense in the context of the Old Faithful model?

• It indicates the average water output

• It predicts the maximum water output

• It shows the minimum water output

• It predicts water output when there is no eruption

In the Olympic race data, what trend is observed over the years?

• Times fluctuate randomly

• Times remain constant

• Times are decreasing

• Times are increasing

How does the linear model help in predicting future Olympic race times?

• By ignoring past data

• By considering only the fastest times

• By calculating the average of past times

• By using past trends to estimate future times

What does a negative slope indicate in the context of the Olympic race data?

• Times are getting slower

• Times are getting faster

• Times are unpredictable

• Times are constant

What is the significance of the y-intercept in the Olympic race model?

• It predicts the time in the year zero

• It represents the fastest time ever

• It indicates the average time over all years

• It shows the slowest time recorded

What adjustment can be made to the Olympic model to make the y-intercept more meaningful?

• Change the year numbering to start from a specific year

• Use a different slope

• Ignore the y-intercept

• Use a quadratic model instead

How does the linear model from the Olympic data support the prediction of time decrease?

• It shows a consistent decrease per year

• It shows an increase per year

• It shows no change per year

• It shows random changes per year