Simple Linear Regression - Creating a Model

In this activity, you are to analyze two variables of your choosing and develop a least squares equation. Be creative.

Example:
As an example, I looked at home sales in the newspaper and randomly selected several homes in a particular neighborhood to compare their prices to the number of square feet of living space. Below is a graph and the Regression Readout from Excel:

Home Prices | Square Footage
-------------|----------------
... | ...

From the readout, there appears to be a significant relationship between the cost of a home and the square feet. For B (\(3 \times 10^{16}\) which is approximately 0.405), the formula for estimating the cost of a home given the number of square feet is:

\[ \text{Cost} = 3816 \times \text{SOFEET} - 1804 \]

The \(R^2\) value looks good - 82.9% of the total sample variability around the mean cost of the sampled homes is explained by the linear relationship between the cost and the square feet. A good fit. As an example in using the equation, a home in this neighborhood with 3300 square feet would be estimated to cost:

\[ \text{Cost} = 3816 \times 3300 - 1804 = 1,383,795 \]

Your Task:
Pick two variables, collect data, graph the data, follow the instructions below, and answer the questions. Your project should be interesting and meaningful. Do something different than what's in the book or my examples:

1. Explain what your project is about.
2. How did you collect your data? Why do you feel that your data is a good representation of the relationship between the two variables?
3. Use Excel to create a least squares equation.
4. Use Excel to generate a regression readout. Is there a relationship between the variables? Explain.
5. What is the slope of your least squares equation and what does it tell you?
6. What is the 95% confidence interval given in the Excel readout for your independent variable? What does it tell you?
7. Find the \( R^2 \) value. What does this value tell you?
8. Show one example using your least squares equation to calculate and predict a value for the dependent variable. This is similar to what I did in my example when I used the equation to predict the cost for a home with \( x = 3500 \text{ ft} \).
9. For the value in number 8, create a 95% confidence interval for the mean value of \( y \) and a 95% prediction interval for an individual new value of \( y \). Interpret these intervals. You will need the formulas to do this.