Questions and Answers
What is the definition of 'Interpreting a Linear Model'?
Workbook: 29.1
What does 2.8 represent in the function f(x)=2x+2.8?
For every 2.8 years of employment, employees can expect to get 1 additional vacation day.
What does 59.3 represent in the function f(x)=59.3x−58.3?
For each hour spent driving, the distance increases by 59.3 miles.
What is the definition of 'Predictions and Their Accuracy'?
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How accurate can Randall expect his prediction to be with a correlation coefficient of -0.95?
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If 50 items are sold, what is the predicted profit according to the line of fit f(x)=3x+20?
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Study Notes
Interpreting a Linear Model
- Linear models can illustrate relationships between two variables, such as employment duration and vacation days.
- The function f(x) = 2x + 2.8 indicates that 2.8 represents a baseline of vacation days employees receive at the start of employment.
Vacation Days and Employment
- The function f(x) = 2x + 2.8 suggests that for every 2.8 years of employment, an employee earns an additional vacation day.
- The relationship is linear, meaning the increase in vacation days is consistent as employment length increases.
Distance Traveled by a Car
- The scatter plot correlates driving time with distance traveled.
- The function f(x) = 59.3x - 58.3 indicates that the coefficient 59.3 shows the distance a car travels increases by 59.3 miles for each hour driven.
Predictions and Their Accuracy
- Correlation coefficient values range from -1 to 1; a value of -0.95 indicates a strong negative correlation.
- When the correlation coefficient is -0.95, predictions made with that model are expected to be very close to actual observed values.
Profit Prediction from Sales
- A linear equation f(x) = 3x + 20 models profits based on the number of items sold.
- If 50 items are sold, the predicted profit is calculated as 170, illustrating the predictive capability of linear models.
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Description
Test your knowledge with these flashcards covering Algebra Unit 6 Lesson 29. Focus on interpreting linear models and understanding scatter plots. These concepts are vital for analyzing data in various fields.
