Step 1: Make a chart of your data, filling in the columns in the same way as you would fill in the chart if you were finding the Pearson’s Correlation Coefficient.
| SUBJECT | AGE X | GLUCOSE LEVEL Y | XY | X2 | Y2 |
|---|---|---|---|---|---|
| 1 | 43 | 99 | 4257 | 1849 | 9801 |
| 2 | 21 | 65 | 1365 | 441 | 4225 |
| 3 | 25 | 79 | 1975 | 625 | 6241 |
| 4 | 42 | 75 | 3150 | 1764 | 5625 |
| 5 | 57 | 87 | 4959 | 3249 | 7569 |
| 6 | 59 | 81 | 4779 | 3481 | 6561 |
| Σ | 247 | 486 | 20485 | 11409 | 40022 |
From the above table, Σx = 247, Σy = 486, Σxy = 20485, Σx2 = 11409, Σy2 = 40022. n is the sample size (6, in our case).
Step 2: Use the following equations to find a and b.
a = 65.1416
b = .385225
Find a:
- ((486 × 11,409) – ((247 × 20,485)) / 6 (11,409) – 2472)
- 484979 / 7445
- =65.14
Find b:
- (6(20,485) – (247 × 486)) / (6 (11409) – 2472)
- (122,910 – 120,042) / 68,454 – 2472
- 2,868 / 7,445
- = .385225
Step 3: Insert the values into the equation.
y’ = a + bx
y’ = 65.14 + .385225x
That’s how to find a linear regression equation by hand!