1. Tentukanlah nilai error dan nilai mutlak eror dari data di bawah ini, serta gambarkan error garis
regresinya?
X Y Ŷ
Error Nilai mutlak
error
2 1 3 …… ……
4 4 4 …… ……
7 5 6 …… ……
9 7 10 …… ……
10 11 8 …… ……
13 12 9 …… ……
2. Data X Y
1 2 60
2 4 80
3 6 100
12 240
Berikut ini merupakan tabel data nilai ulangan ( Y) dan masa lama belajar siswa (X). Tentukan dan
hitunglah besaran nilai persamaan regresi dugaan!
3. Tentukanlah nilai koefficient dari tabel di bawah ini serta signifikansinya? selanjutnya tentukan persamaan
regresi dugaan dari tabel berikut.!
Coefficientsa
Model
Unstandardized
Coefficients
Standardized
Coefficients t Sig
B Std.Error Beta
1 (Constant) 3.919 2.418 1.621 0.149
 X1 2.491 0.703 1.024 3.544 0.009
 X2 - .466 1.016 -0.133 -.459 0.660

Let's break down your queries step by step.

### 1. Error Calculation and Regression Line
Given the dataLet's break down your queries step by step.

### 1. Error Calculation and Regression Line
Given the 

| X  | Y  | Ŷ  |
|----|----|----|
| 2  | 1  | 3  |
| 4  | 4  | 4  |
| 7  | 5  | 6  |
| 9  | 7  | 10 |
| 10 | 11 | 8  |
| 13 | 12 | 9  |

**Error** is calculated as \( \text{Error} = Y - \hat{Y} \).

**Absolute Error** is calculated as \( |\text{Error}| \).

Now, let's compute these values:

| X  | Y  | Ŷ  | Error (Y - Ŷ) | Absolute Error |
|----|----|----|----------------|-----------------|
| 2  | 1  | 3  | -2             | 2               |
| 4  | 4  | 4  | 0              | 0               |
| 7  | 5  | 6  | -1             | 1               |
| 9  | 7  | 10 | -3             | 3               |
| 10 | 11 | 8  | 3              | 3               |
| 13 | 12 | 9  | 3              | 3               |

### 2. Regression Equation
For the second dataset:

| X  | Y  |
|----|----|
| 1  | 2  |
| 2  | 4  |
| 3  | 6  |
| 12 | 240|

You can calculate the regression coefficients using the formulas for linear regression. The formula for the regression line is \( Y = a + bX \).

Let's calculate \( b \) (slope) and \( a \) (intercept):

1. Calculate the means of X and Y.
2. Use the formula for slope \( b = \frac{N(\sum XY) - (\sum X)(\sum Y)}{N(\sum X^2) - (\sum X)^2} \).
3. Calculate \( a \) using \( a = \bar{Y} - b\bar{X} \).

The calculations will yield the regression equation.

### 3. Coefficients and Significance
For the regression table you provided:

| Coefficientsa           |          |
|-------------------------|----------|
| Model                   | Unstandardized Coefficients | Standardized Coefficients | t      | Sig   |
|                         | B      | Std.Error | Beta      |        |       |
| (Constant)              | 3.919  | 2.418     |          | 1.621  | 0.149 |
| X1                      | 2.491  | 0.703     | 1.024    | 3.544  | 0.009 |
| X2                      | -0.466 | 1.016     | -0.133   | -0.459 | 0.660 |

- The **significance** of coefficients can be checked using the p-values (Sig). Typically, a p-value < 0.05 indicates significance.
- The regression equation can be written as:
  \[ Y = 3.919 + 2.491X1 - 0.466X2 \]

### Summary of Results:
1. **Error and Absolute Error:**
   - Error calculated for each data point.
   - Absolute error calculated as well.

2. **Regression Equation:**
   - Find slope and intercept for the second dataset.

3. **Coefficients and Significance:**
   - Constant and coefficients from the regression output.
   - Check significance using p-values.

If you need detailed calculations or explanations for any step, feel free to ask!

### Questions for Further Exploration:
1. How do you interpret the slope and intercept of a regression line?
2. What methods can be used to evaluate the goodness of fit for a regression model?
3. How can multicollinearity affect the interpretation of regression coefficients?
4. What are potential reasons for a high error in regression predictions?
5. How can you visualize the regression line and errors graphically?

### Tip:
Always check for outliers in your data, as they can significantly affect regression results and errors.

Tentukanlah nilai error dan nilai mutlak eror dari data di bawah ini, serta gambarkan error garis regresinya? X Y Ŷ Error Nilai mutlak error. Data X Y 1 2 60 2 4 80 3 6 100 12 240. Berikut ini merupakan tabel data nilai ulangan ( Y) dan masa lama belajar siswa (X). Tentukan dan hitunglah besaran nilai persamaan regresi dugaan! Tentukanlah nilai koefficient dari tabel di bawah ini serta signifikansinya? selanjutnya tentukan persamaan regresi dugaan dari tabel berikut.

Explore how to calculate errors and absolute errors in regression analysis with step-by-step examples. This guide includes error calculations for provided data, regression equations, and coefficients significance analysis. Ideal for high school students studying statistics.

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