You are given a dataset of housing prices and the size of houses in square
feet. You want to build a simple linear regression model to predict housing
prices based on the size of the houses. The data is as follows:
Size (saft)
1200
1400
1600
1900
2100
Price
200000
220000
250000
300000
320000
Use the regression line to predict the price of a house with a Size of 1500
sqft?

To solve this problem, we need to determine the equation of the simple linear regression line, which is in the form:

\[
\text{Price} = m \times \text{Size} + b
\]

Where:
- \( m \) is the slope of the line.
- \( b \) is the y-intercept.

### Step 1: Calculate the Slope (\( m \))
The formula for the slope \( m \) is:

\[
m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}
\]

Where:
- \( x \) is the size of the house.
- \( y \) is the price of the house.
- \( n \) is the number of data points.

### Given Data
\[
\begin{array}{|c|c|}
\hline
\text{Size (sqft)} & \text{Price} \\
\hline
1200 & 200000 \\
1400 & 220000 \\
1600 & 250000 \\
1900 & 300000 \\
2100 & 320000 \\
\hline
\end{array}
\]

### Step 2: Calculate the Summations

\[
\sum x = 1200 + 1400 + 1600 + 1900 + 2100 = 8200
\]

\[
\sum y = 200000 + 220000 + 250000 + 300000 + 320000 = 1290000
\]

\[
\sum xy = (1200 \times 200000) + (1400 \times 220000) + (1600 \times 250000) + (1900 \times 300000) + (2100 \times 320000) 
\]

\[
\sum x^2 = 1200^2 + 1400^2 + 1600^2 + 1900^2 + 2100^2 
\]

I'll calculate these sums and the slope \(

Learn how to predict housing prices based on house size using a simple linear regression model. Calculate the slope and intercept of the regression line with step-by-step guidance. Suitable for Grades 10-12.

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