Simple Linear Regression Analysis
1. Simple Regression
This can be done by regressing dependent variable to the independent variables. This concept is likely to be introduce during the JC H2 mathematics class.
2. The general notation of a simple regression model
y = B0 + B1x + u
Where,
- y is the dependent variable
- x is the independent variable
- B0 is the intercept
- B1 is the slope
3. Formula of calculating regression slope in simple regression
A regression slope can be calculated using ordinary least square method. This method is to obtain the regression slope that can minimize the sum of square between the predicted dependent variable and the true dependent variable.
Regression slope, beta = Covariance(x,y)/Variance(x)
Question
Determine the regression slope for the following datasets.
Question 1
| y1 | x1 |
| 0 | 3 |
| 5 | 1 |
| 2 | 1 |
| 5 | 3 |
| 0 | 3 |
| 2 | 2 |
| 3 | 4 |
| 4 | 0 |
| 0 | 1 |
| 1 | 4 |
| 4 | 0 |
| 1 | 1 |
| 4 | 5 |
| 3 | 1 |
Question 2
| y2 | x2 |
| 4 | 3 |
| 5 | 5 |
| 4 | 5 |
| 2 | 3 |
| 2 | 5 |
| 5 | 2 |
| 0 | 0 |
| 5 | 2 |
| 2 | 1 |
| 3 | 1 |
| 4 | 3 |
| 4 | 4 |
| 2 | 0 |
| 1 | 2 |
Question 3
| y3 | x3 |
| 5 | 4 |
| 1 | 3 |
| 0 | 4 |
| 4 | 1 |
| 4 | 5 |
| 4 | 1 |
| 3 | 0 |
| 4 | 1 |
| 1 | 4 |
| 1 | 3 |
| 2 | 4 |
| 5 | 1 |
| 3 | 2 |
| 4 | 4 |
Question 4
| y4 | x4 |
| 5 | 3 |
| 5 | 0 |
| 3 | 4 |
| 2 | 3 |
| 0 | 2 |
| 1 | 1 |
| 3 | 4 |
| 1 | 0 |
| 0 | 5 |
| 0 | 2 |
| 5 | 3 |
| 1 | 1 |
| 5 | 3 |
| 0 | 5 |
Question 5
| y5 | x5 |
| 1 | 0 |
| 1 | 4 |
| 2 | 0 |
| 1 | 4 |
| 0 | 1 |
| 4 | 5 |
| 4 | 0 |
| 4 | 0 |
| 3 | 4 |
| 4 | 1 |
| 0 | 0 |
| 2 | 0 |
| 0 | 3 |
| 0 | 0 |
Answer
- -0.134
- 0.442
- -0.342
- -0.077
- 0.064
Notes: There are other useful information can be determined when performing simple regression analysis such as the R-squared.
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