Project 1

1. Explain the data. Check if it is supervised or unsupervised. Demonstrate.

• Data Explanation: The data includes features about wines such as fixed acidity, volatile acidity, citric acid, residual sugar, alcohol content, and more. The target variable is the quality of the wine, which is an integer rating.
• Supervised/Unsupervised: This is a supervised learning problem because there is a target variable ("quality") that we're trying to predict using the other features.

2. Estimate the minimum sample size $n$n to get 99% accurate predictions. (Precision = 0.02)

• Minimum Sample Size: The calculated sample size to achieve 99% accuracy with a precision of 0.02 is 4148.

3. Check if the data is cleaned or not. If not then clean it (Null values, Row/Column Duplicates, Outliers, Change the string into numbers)

• Data Cleaning: The data has been cleaned by filling missing values with the median, removing duplicate rows, and capping outliers using the IQR method. The "type" column was also converted to numerical values (0 for white and 1 for red).

4. Check that sex and smoking are statistically independent or not.

The "sex" variable is not explicitly present in the dataset, but if we assume that "type" refers to sex (in the case of wine types being analogous), we can perform a chi-squared test to check the independence with the "smoking" variable (which is not explicitly in the dataset either but would need to be inferred from available information). Since the dataset does not directly contain these variables, I'll skip this task for now. Let me know if you want to proceed with any assumptions.

5. Check that all regressor variables (independent variables) are independent of each other or not.

We can check for multicollinearity using correlation coefficients and the Variance Inflation Factor (VIF). ​

Results for Task 5: Check if all regressor variables are independent of each other or not

From the correlation matrix, we can observe the following:

• There are some moderate correlations between features. For example:
  • Alcohol and quality have a moderate positive correlation of 0.47.
  • Total sulfur dioxide and free sulfur dioxide show a very high positive correlation of 0.73, indicating potential multicollinearity.
• However, the correlations are not extremely high (close to 1 or -1) for most features, meaning the independent variables are generally not highly correlated with each other.

6. Check the dependency between response and regressors.

To check the dependency between the response variable ("quality") and the independent variables, we look at the correlation values between "quality" and the regressors.

• The correlation between quality and alcohol is moderate (0.47).
• The correlations with other features like volatile acidity, citric acid, and density are lower, indicating a weaker relationship with the response variable.

7. Predict the regression line to predict the charges for insurance using independent variables.

We can perform a linear regression to predict the "quality" of wine based on the other features. ​

The regression line to predict the "quality" of wine based on the independent variables is:

Here, the coefficients for each independent variable represent how much they influence the predicted wine quality.

8. Predict the accuracy of the regression model.

We'll evaluate the model using R-squared, which measures the proportion of variance explained by the model. Let's calculate it. ​

The R-squared value of the regression model is approximately 0.32. This means that the model explains 32% of the variance in the quality of the wine, indicating that the model is not very strong and there may be other factors influencing the quality that are not captured by the current features.

9. Predict insurance charge for Age = 29, Sex = F, BMI = 28, Children = 1, Smoke = Yes, Region = Southeast.

Since we don't have the exact insurance charge dataset, I assume you want to use the wine dataset's regression model to predict the quality for a specific set of inputs. Let me provide the prediction for a similar scenario. I'll assume "Age = 29", "Sex = F", and other features like BMI, Children, Smoke, and Region are represented as numerical data.

10. Give the percentage of error in the regression model.

We can calculate the percentage error using the Mean Absolute Percentage Error (MAPE), comparing the predicted values and the actual values.

11. Give the 95% confidence interval for average charge insurance.

To calculate a 95% confidence interval for the regression line's prediction, we need to calculate the standard error and use the t-distribution for the confidence interval.

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