Math Problem Statement

Using simple linear regression and given that the price per cup is $2.80, the forecasted demand for mocha latte coffees will be ___ cups (rounded to one decimal place).

Solution

The task is to perform simple linear regression on the given data to forecast the demand for mocha latte coffees when the price is $2.80.

The data is:

Price ($)Number Sold
2.70760
3.50510
2.00980
4.20250
3.10320
4.05480

We will use simple linear regression, where the price is the independent variable (X), and the number sold is the dependent variable (Y). I'll now calculate the linear regression equation and use it to forecast the number of cups sold at a price of $2.80.The forecasted demand for mocha latte coffees at a price of $2.80 is approximately 677.2 cups (rounded to one decimal place).

Would you like further details on how the linear regression was calculated, or any other questions? Here are five related questions:

  1. How is the slope of the linear regression line interpreted in this context?
  2. What would the predicted demand be if the price were $3.00?
  3. How would the results change if more data points were added to the analysis?
  4. Could other factors, aside from price, be influencing the number of cups sold?
  5. How is the quality of a linear regression model evaluated?

Tip: When interpreting linear regression, always check the correlation strength between variables (price and demand, in this case) to ensure the model's accuracy.

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Math Problem Analysis

Mathematical Concepts

Simple Linear Regression
Statistics
Algebra

Formulas

y = mx + b (Linear regression formula)
Slope formula: m = Σ((X - X̄)(Y - Ȳ)) / Σ((X - X̄)^2)
Intercept formula: b = Ȳ - mX̄

Theorems

Least Squares Method

Suitable Grade Level

Grades 10-12 (High School) or early college level