Intercept
The intercept of the least-squares line.
The formula:
Intercept = [∑(x²)∑(y) - ∑(x)∑(xy)]/[n∑(x²) - ∑(x)²]
Sample 1
Given the set of X and Y values where X and Y can represent any correlated values below:
| X | Y |
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 8 |
| 5 | 10 |
| 6 | 12 |
| 7 | 14 |
| 8 | 16 |
| 9 | 18 |
| 10 | 20 |
Sample table of correlated values
- Solve the parts of the formula.
Intercept = [∑(x²)∑(y) - ∑(x)∑(xy)]/[n∑(x²) - ∑(x)²]
n =count of items, equal to 10
∑(x²) = get the square of all x items and sum up the values. To square a number also means to multiply the number by itself.
1x1 + 2x2 + 3x3 + 4x4 + 5x5 + 6x6 + 7x7 + 8x8 + 9x9 + 10x10 = 385
∑(y) = sum of y items = 110
∑(x) = sum of x items = 55
∑(xy) = multiply all x and y items and get the sum = 770
1x2 + 2x4 + 3x6 + 4x8 + 5x10 + 6x12 + 7x14 + 8x16 + 9x18 + 10x20 = 770
∑(x)² = get the sum of all items in x and get the square = 55 * 55 or 3025
- Substitute the known values in the formula and compute for the intercept:
Intercept = [385(110) – 55(770)/[10(385) - 3025]
Intercept = [42350 – 42350]/[3850 – 3025]
Intercept = [0]/825]
Intercept = 0
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