Results

Linear Regression

Actual vs Predicted

This scatter plot shows the relationship between the actual and predicted values. Each point on the plot represents one data point in the test set, and the position of the point indicates the actual and predicted values for that data point. Ideally, the points will fall along a straight line, indicating that the predicted values are close to the actual values. From the graph, the points follow roughly a straight line.

Residual Plot

The residual plot is a graph of the residuals (the differences between the observed values and the predicted values) against the predicted values. The ideal output for a residual plot would be a random scatter of points around the horizontal line at zero. The above result indicates that the linear regression model is not a good fit for the data since the residuals are distributed randomly and not evenly around zero.

Density plot

The ideal output for a density plot of the residuals would be a symmetric, bell-shaped curve centred around zero.

Since the density plot is skewed to the left, this may indicate that the residuals are not normally distributed. This can be problematic because many statistical tests assume normality and non-normal residuals may affect the validity of the statistical inference.

Performance metrics

R^2 value of 0.54 indicates that approximately 54% of the variance in the dependent variable can be explained by the independent variable(s) in the model. An MAE of 3.84 indicates that, on average, the model's predictions are off by about 3.84 units and n RMSE of 7.06 indicates that, on average, the model's predictions are off by about 7.06 units. Thus, the accuracy is above 90%.

multiple Linear Regression

Actual vs Predicted

This scatter plot shows the relationship between the actual and predicted values. Each point on the plot represents one data point in the test set, and the position of the point indicates the actual and predicted values for that data point. Ideally, the points will fall along a straight line, indicating that the predicted values are close to the actual values. From the graph, the points follow roughly a straight line.

Residual Plot

The residual plot is a graph of the residuals (the differences between the observed values and the predicted values) against the predicted values. The ideal output for a residual plot would be a random scatter of points around the horizontal line at zero. The above result, it indicates that the linear regression model is a good fit for the data and that the residuals are distributed randomly and evenly around zero.

coefficient plot

A coefficient plot can be useful for visualizing the relative importance of the independent variables in the model and can help to identify which variables have the strongest relationships with the dependent variable. The plot suggests that the dependent variable is strongly influenced by the intercept term and less so by the independent variables included in the model.

Performance metrics

R^2 value of 0.54 indicates that approximately 54% of the variance in the dependent variable can be explained by the independent variable(s) in the model. An MAE of 3.66 indicates that, on average, the model's predictions are off by about 3.66 units and RMSE of 7.15 indicates that, on average, the model's predictions are off by about 7.15 units. Thus, the accuracy is above 90%.