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Determine the regression equation
Price = ___________ + ________________ screen size

To determine the regression equation that predicts the Price based on the Screen size, we need to calculate a simple linear regression equation in the form:

\[
\text{Price} = a + b \times \text{Screen size}
\]

Where:
- \( a \) is the intercept (the price when the screen size is zero).
- \( b \) is the slope (the change in price for each additional inch in screen size).

I'll outline the steps to calculate this regression equation:
1. Calculate the mean of the Screen size (\( \bar{X} \)) and the mean of Price (\( \bar{Y} \)).
2. Compute the slope \( b \) using the formula:
   \[
   b = \frac{\sum (X - \bar{X})(Y - \bar{Y})}{\sum (X - \bar{X})^2}
   \]
3. Calculate the intercept \( a \) using:
   \[
   a = \bar{Y} - b \times \bar{X}
   \]

Would you like me to perform these calculations step-by-step or summarize the results directly? Alternatively, I can guide you through using software or a calculator for this regression. 

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Here are five relevant questions for further exploration:
1. What is the purpose of using regression analysis in this context?
2. How does the manufacturer (Sharp, Sony, Samsung) affect the Price prediction?
3. Can we extend this model to a multiple regression model by including manufacturer as a variable?
4. How does the range of screen sizes influence the accuracy of the regression model?
5. What does the slope in the regression equation imply about the price change per inch?

**Tip:** For linear regression, always check if the data meets linearity assumptions. Scatter plots are useful to visualize relationships between variables.

Determine the regression equation Price = ___________ + ________________ screen size

Learn how to determine the regression equation to predict Price based on Screen size. This guide covers calculating the slope and intercept of a linear regression model, with sample data provided. Ideal for college-level statistics students.

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