Math Problem Statement
Solution
The linear regression model that best fits the data has the equation:
Where:
- is the weekly demand in thousands.
- is the price in dollars.
Additional Results:
- Predicted weekly demand for : The model predicts approximately 190,600 (nearest 100) units.
- Price for a weekly demand of 179,400 units: The price should be set at approximately $235 (nearest $1).
Would you like more details or have any other questions?
Here are 5 related questions you might explore:
- How does the squared correlation coefficient assess the model fit?
- Can this model predict demands for prices outside the provided range?
- How would you interpret the negative slope in this context?
- Could a quadratic model provide a better fit for this data?
- What would happen if the price increased to $270 according to the model?
Tip: When using regression models, always check the residuals to ensure the model assumptions hold.
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Math Problem Analysis
Mathematical Concepts
Linear Regression
Correlation Coefficient
Prediction in Regression
Formulas
Linear regression formula: y = mx + b
Correlation coefficient formula: r^2 = SSR / SST
Theorems
Least Squares Regression Theorem
Suitable Grade Level
Grades 10-12 (or undergraduate level for statistics)
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