Math Problem Statement

Find the linear model that best fits the data using regression, predict weekly demand for $205, and set the price for a demand of 179,400 units.

Solution

The linear regression model that best fits the data has the equation:

s=T(p)=0.38p+268s = T(p) = -0.38p + 268

Where:

  • ss is the weekly demand in thousands.
  • pp is the price in dollars.

Additional Results:

  • Predicted weekly demand for p=205p = 205: 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:

  1. How does the squared correlation coefficient r2r^2 assess the model fit?
  2. Can this model predict demands for prices outside the provided range?
  3. How would you interpret the negative slope in this context?
  4. Could a quadratic model provide a better fit for this data?
  5. 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)