Math Problem Statement

A convenience store manager notices that sales of soft drinks are higher on hotter days. The table provides data on the high temperature (°F) and the number of cans sold. Create a scatter plot, find and graph a linear regression equation, and predict sales at 95°F.

Solution

(b) Linear Regression Equation:

The equation of the regression line is: y=16.42x621.83y = 16.42x - 621.83 where yy is the number of cans sold and xx is the temperature in °F.

(c) Prediction for 95°F:

Using the regression model, the predicted number of cans sold at 95°F is approximately: 937.72 cans937.72 \text{ cans}

Would you like further details or explanations? Here are a few related questions you might find interesting:

  1. How does the slope of the regression line affect the prediction?
  2. What is the interpretation of the y-intercept in this context?
  3. How can we assess the accuracy of the linear regression model?
  4. Could another model (e.g., polynomial) provide a better fit for this data?
  5. How would you test the validity of the prediction for 95°F?

Tip: In regression analysis, the coefficient of determination (R²) is a key metric to evaluate how well the model fits the data.

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Math Problem Analysis

Mathematical Concepts

Linear Regression
Scatter Plot
Prediction

Formulas

y = mx + b (Equation of a Line)

Theorems

Least Squares Method

Suitable Grade Level

Grades 9-12