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Linear Regression Pro

Advanced statistical analysis with comprehensive features

5 points

My Dataset

1
(1.00, 2.00)
2
(2.00, 4.00)
3
(3.00, 5.00)
4
(4.00, 4.00)
5
(5.00, 5.00)

REGRESSION EQUATION

y = 0.6000x + 2.2000

SLOPE

0.6000

INTERCEPT

2.2000

R² SCORE

0.6000

60.0% variance

RMSE

0.6928

MSE

0.4800

MAE

0.6400

MODEL QUALITY

✓ Good Fit

Single Prediction

Batch Predictions

Display Settings

Confidence Level:

Detailed Calculation Steps

1
Step 1: Given n=5n = 5 data points: (1,2)(1, 2), (2,4)(2, 4), (3,5)(3, 5), (4,4)(4, 4), (5,5)(5, 5)
2
Step 2: Calculate the necessary sums:
∑X=15.00,∑Y=20.00\sum X = 15.00, \quad \sum Y = 20.00
3
Step 3: Calculate products and squares:
∑XY=66.00,∑X2=55.00,∑Y2=86.00\sum XY = 66.00, \quad \sum X^2 = 55.00, \quad \sum Y^2 = 86.00
4
Step 4: Calculate the slope using the formula:
m=n∑XY−∑X⋅∑Yn∑X2−(∑X)2=5⋅66.00−15.00⋅20.005⋅55.00−(15.00)2m = \frac{n\sum XY - \sum X \cdot \sum Y}{n\sum X^2 - (\sum X)^2} = \frac{5 \cdot 66.00 - 15.00 \cdot 20.00}{5 \cdot 55.00 - (15.00)^2}
m=0.6000m = 0.6000
5
Step 5: Calculate the intercept using the formula:
b=∑Y−m⋅∑Xn=20.00−0.6000⋅15.005b = \frac{\sum Y - m \cdot \sum X}{n} = \frac{20.00 - 0.6000 \cdot 15.00}{5}
b=2.2000b = 2.2000
6
Step 6: The regression equation is:
y=0.6000x+2.2000\boxed{y = 0.6000x + 2.2000}
7
Step 7: Calculate the coefficient of determination:
R2=1−SSresSStot=0.6000R^2 = 1 - \frac{SS_{res}}{SS_{tot}} = 0.6000
8
Step 8: Model quality: The model explains 60.00%60.00\% of the variance in the data.
9
Step 9: Error metrics: - MSE (Mean Squared Error) = 0.48000.4800 - RMSE (Root Mean Squared Error) = 0.69280.6928 - MAE (Mean Absolute Error) = 0.64000.6400

Related Topics & Algorithms

Explore these related algorithms and concepts to deepen your understanding and discover complementary techniques.

Classification

Logistic Regression

Binary classification using sigmoid function for categorical outcomes

Optimization

Gradient Descent

Optimization algorithm used to minimize cost functions in regression

Deep Learning

Neural Networks

Advanced models that can learn complex non-linear relationships

Ensemble Learning

Random Forest

Ensemble method combining multiple decision trees for better predictions

Model Evaluation

Cross Validation

Technique to evaluate model performance and prevent overfitting

Preprocessing

Feature Engineering

Transform and create features to improve model performance

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