Simple Regression Calculator
Input
Summary
| Sum X | 434 |
|---|---|
| Sum Y | 445 |
| Sum XY | 22126 |
| Sum X2 | 22426 |
| n | 10 |
| Y mean | 44.5 |
| X mean | 43.4 |
| Intercept | 10.497 |
| Coef | 0.7835 |
Formulas and Output
\[Coefficient = \frac{\sum XY - (\sum X)(\sum Y)/n}{\sum X^2-\sum (X)^2/n}=\frac{\ 22126 - 434\times445/10}{ 22426 - 188356/10} = 0.7835\]
\[Intercept = \bar{y}- b \times\bar{x} = 44.5- (0.7835 \times 43.4) = 10.497\]
\[SSR = b\sum XY - (\sum X)(\sum Y)/n = 0.7835 \times 22126 \times 445 / 10 = 2203.9241
\]
\[SSE = SST - SSR = 2300.5 - 2203.9241 = 96.5759\]
\[SST = \sum Y^2 - (\sum Y)^2/n = 22103 - 445^2 / 10 = 2300.5
\]
\[MSR = SSR / 1 = 2203.9241\]
\[MSE = SSE / n-2 = 96.5759/(10-2) = 12.072\]
ANOVA
| ANOVA | df | Sum squares | Mean square | Fvalue | PR(>F) |
|---|---|---|---|---|---|
| 1 | 1 | 2203.9241 | 2203.9241 | 182.5651 | 0.0 |
| 2 | 8 | 96.5759 | 12.072 | ||
| 3 | 9 | 2300.5 |
Graph
Example
Robert E. Moritz wants to find out using a simple linear regression model if the accountants
age (X)
has an effect on the time (in minutes) to finish an accounting task (Y).
The following data is from a sample of 10 accountants:
X = [20 25 30 37 45 47 55 59 62 65]
Y = [15 17 25 32 51 43 60 65 58 68]
a) Find the intercept and the coefficient.
b) Set up the ANOVA table and test if the coefficient is significant at p=0.05.
Using this calculator you can find the answer to the questions above
on any simple regression dataset and the method used to find them.