The regression model works on the constructive evaluation principle. We build a model, check from metrics, and then make improvements. And continue until we achieve a desirable accuracy. Evaluation metrics explain the performance of a model.

Model evaluation used in all type algorithms Linear Regression

### Evaluation matrics

- R-Squared
- Adjusted R-Squared
- RMSE
- VIF
- P-Value
- Residual.

**R-Squared**

R-squared is an evaluation metric. Through which we can measure, how good the model is higher the R-square better the accuracy.

For example:

Let say after evaluation we got R-squared = 0.81. This means we can explain 81% of the variance in data, also we can say the accuracy of a model is 81%.

We can compute the RSS (Residual sum squared) with the square sum of (actual — predicted).

In TSS (Total sum squared) we need to take squared sum of (predicted — mean value)

As we can see R2 = 1 which mean Residual is 0 R-Squared = 1

Best fit, as you can see as fit line getting poor the R-Squared value. Also, get reduce and become close to zero R-Squared lies between 0 to 1

0 < R-Squared <=1

**Model-1**

As you can see in the final model we got R-Squared = 0.839

This means we can explain 83% of the variance in data, also we can say the accuracy of a model is 83%.

**Adjusted R-Squared:**

Adjusted R-Squared Penalize the model which have too many feature or variable in that.

Let say if we have 2 model each with 3 features R-squared is 83.9% and adjusted-R-Squared 83.2%

Now if we add 3 more features in the first model R-Squared will get an increase. But adjusted-R-Squared will penalize the model. And it will tell I am giving you a lower value as you have added a new feature which could because of a problem in modeling.

The adjusted R-squared increases only if the new term improves in the model. Adjusted R-squared gives the percentage of variation explained by only those independent variables. That affects the dependent variable. Adjusted R-Squared also measures the goodness of the model.

As we can see in our final **Model-1** R-Squared and adjusted R-squared are very close.

R-Squared = 0.839

Adjusted R-Squared =0.832.

And with this, we assume none of the other variables need to add into the model as a predictor.

**P-Value and VIF**

The P-value will tell us how significant the variable. And VIF will tell multicollinearity between the independent variable. If VIF > 5, which means a high correlation.

The P-Value will tell the probability of the accepted Null Hypothesis. Which means the probability of failing to reject the Null Hypothesis.

Higher the P-value higher the probability of fail to reject a Null Hypothesis.

Lower the P-Value higher probability of the Null Hypothesis will reject.

Our Observation if we see the above final model. All variable has less the 0.05 P-value. Which means they are highly significant variables.

VIF value is less than 5 in our final model. We can say there is no correlation between the independent variable.

**RMSE: (Root mean Square)**

The most popular used metric RMSE. This will measure the differences between sample values predicted, and the values observed. Because Root Mean Square Error (RMSE) is a standard way to measure the error of a model in predicting quantitative data.

The RMSE is the standard deviation of the residuals (prediction errors). Residuals are a measure of how far from the regression line data points are.

It will evaluate the sum of mean squared error over the number of total sample observations.

In **Model-1** we calculated the RMSE: 0.08586514469292264. Lower the RMSE better the model performance.

**Durbin-Watson: **Durbin-Watson test evaluate the Autocorrelation it should lie between 0 to 4

In our above observation in final model we got Durbin-Watson: 2.132

**Summary:**

There is some disadvantage if we not consider that our evaluation metrics, which will increase the in-performance measurement. For all metrics, R-Squared, Adjusted R-Squared, RMSE, VIF, P-Value, Residual, Durbin-Watson, Will tell us how good the model is (best fit model) each metrics is important for model evaluation as I describe above.

In Linear Regression there are some assumption like:

- Linearity
- Outliers
- Autocorrelation
- Multicollinearity
- Heteroskedasticity

which we need to check while measuring the matrics.

- RMASE has a disadvantage RMSE will be affected by the outliers. If we have outliers in our data sample
- If the sample population is not linear RMSE will affect as there would be no trend and which means standard division will vary.
- Residual also affect by the outliers which will increase the residual squared sum.

**stroke, engine size, fuelsystem_idi, car_company_bmw, cylindernumber_two, car_company_subaru**

These are the driving factor as per the **Model-1** on which the pricing of cars depends.

### Observation

- I can see a good model with R-Square = 0.839
- I can see good-adjusted R-Squared = 0.832
- As R-Squared and adjusted R-Squared is very close, we can assume none of the other variable need to add into the model as a predictor.
- Model have Durbin-Watson:2.132 which is between 0 and 4, we can assume there is no Autocorrelation
- As we can see VIF<5 which means no Multicollinearity
- P-value is less 0.05 which means they are highly significant variables.

### Footnotes

**OK**, that’s it, we are done now. If you have any questions or suggestions, please feel free to reach out to me. I’ll come up with more Machine Learning topic soon.

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