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 types of algorithms Linear Regression

### Evaluation metrics

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

**R-Squared**

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

For example:

Let’s 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 the squared sum of (predicted — mean value)

R2 = 1, Residual is 0 and R-Squared = 1

Best fit, as you can see as the fit line getting poor the R-Squared value. Also, gets reduced and becomes 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 that has too many features or variables.

Let’s say we have 2 models 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. It will tell you I am giving you a lower value as you have added a new feature which could be 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.

With this, we assume none of the other variables need to be added to the model as a predictor.

**P-Value and VIF**

The P-value will tell us how significant the variable is. And VIF will tell multicollinearity between the independent variable. If VIF > 5, it 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.

The higher the P-value higher the probability of failure to reject a Null Hypothesis.

The lower the P-value higher the probability that the Null Hypothesis will be rejected.

Our Observation is 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 is 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. Lowering the RMSE better the model performance.

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

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

**Summary:**

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

In Linear Regression there are some assumptions:

- Linearity
- Outliers
- Autocorrelation
**Multicollinearity**- Heteroskedasticity

which we need to check while measuring the metrics.

- 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 be affected as there would be no trend which means standard division will vary.
- Residual is also affected 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 factors 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 are very close, we can assume none of the other variables need to be added to the model as a predictor.
- The model has 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 than 0.05 which means they are highly significant variables.

### Footnotes

If you have any questions or suggestions, please feel free to reach out to me. I’ll come up with more Machine Learning topics soon.

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