## Regression Algorithms I Objective Type Questions

**1. Regression can be performed for which kind of variables:**

a) Continuous

b) Discrete

c) Categorical

d) All of the above

**Answer: d) All of the above**

### Regression Algorithms I Class 12 Questions and Answer

**2. Which of the following statement is false?**

a) Regression can be done for only two variables.

b) Regression is a supervised learning technique.

c) Regression can be done for categorical variables.

d) None of the above

**Answer: a) Regression can be done for only two variables.**

**3. Which of the following are used for regression?**

a) K-NN

b) Linear Regression

c) Both of the above

d) None of the above

**Answer: b) Linear Regression**

**4. The value of RSME is usually greater than the value of MAE**

a) True

b) False

**Answer: b) False**

**5. MEA considers the direction of the residuals**

a) True

b) False

**Answer: b) False**

### Regression Algorithms I Class 12 Questions and Answer

### Standard Questions

### 1. In your own words, write down the steps to create a line of best fit.

### Steps for Establishing the Ideal Line of Best Fit:

In order to find your optimal line of best fit, follow these steps.

**Step-1:** Extract data pairs (x,y) from your dataset.

**Step-2:**Convert points into scatter plots.

**Step-3:** Examine the general trend of data.

**Step-4:** Calculate the equation of a straight line that represents your trend: (y = mx + b).

**Step-5:**Adjust the slope (m) and y-intercept (b) so as to decrease the vertical distance between the line and data points.

**Step-6:** Use statistical methods like least squares regression to identify an optimal line that best represents your data.

### Regression Algorithms I Class 12 Questions and Answer

### 2. What is the application of root mean square deviation?

### Applications of Root Mean Square Deviation:

Root mean square deviation is widely utilized across a range of fields including statistics, physics, and engineering. In terms of statistics it measures dispersion or variation from the mean of data points while for physics it helps analyze errors in measurements as well as quantify any differences between predicted and observed values.

Within engineering it serves to assess model accuracy through climate modeling or signal processing by comparing simulation data against real world measurements – useful when testing models against data generated through climate simulation or signal processing simulation.

### 3. Write a short note on mean absolute error.

### Mean Absolute Error (MAE):

MAE is an analytical metric designed to evaluate the accuracy of predictive models. It calculates the average of absolute differences between predicted and actual values; lower MAE values represent better model performance due to smaller deviations between predictions and real outcomes.

Furthermore, unlike squared error metrics which give equal weighting across errors (making outliers less noticeable), MAE gives equal weightage across errors making it less sensitive than squared error metrics to outliers and is therefore widely utilized across fields like machine learning economics and finance to evaluate accuracy of regression models.

It has also proven its use extensively across fields such as machine learning economics finance when used alongside squared error metrics when measuring regression models accuracy for this evaluation purpose.

### Regression Algorithms I Class 12 Questions and Answer

### Higher Order Thinking Skills(HOTS)

### 1. Which is a better metric – Mean Absolute Error or Root Mean Square Deviation? Discuss.

Decisions between Mean Absolute Error (MAE) and Root Mean Square Deviation (RMSD) depend on the specific context and priorities of a problem at hand. Here’s an overview of their characteristics:

MAE is easier to interpret since it represents the average absolute difference between predicted and actual values, making it suitable for situations in which outliers have significant impacts. Due to its absolute value nature, it provides greater resilience against outliers while not penalizing large errors as severely as RMSD (which squares errors) would. However, in certain circumstances this might be undesirable.

RMSD assigns greater weight to large errors through squaring, making it more sensitive to outliers and outlier events. Furthermore, its relationship to standard deviation can prove useful in certain statistical analyses; however, squared errors might amplify outlier effects further making this approach less suitable for datasets with extreme values.

MAE provides an accurate representation of overall accuracy while being more robust to outliers and larger errors, without amplifying them further. If, on the other hand, you wish to penalize large errors more heavily while considering variance in errors more heavily then RMSD may be more suitable.

### 2. What are some of the drawbacks of using linear regression?

### Drawbacks of linear regression:

Linear regression assumes a linear relationship between predictor variables and response, so if it turns out not to be strictly linear, its predictions could prove inaccurate.

**Sensitivity to Outliers:** Linear regression can be especially sensitive to outliers due to the way its squared error loss function weights extreme values disproportionately, giving an unfair amount of weighting for extreme values that appear outside its predicted parameters and overall fit. As such, outliers can significantly alter model parameters and alter overall fit.

**Multicollinearity:** When predictor variables are highly correlated, multicollinearity issues arise that make it challenging to ascertain the individual impact of each variable on response; potentially diminishing interpretability of the model.

**Overfitting:** Linear regression may become overfitted if its model is too complex and its number of predictors exceeds its number of observations, leading to subpar generalization for new data sets.

**Assumptions Regarding Residuals:** Linear regression relies on certain assumptions regarding residuals (errors), including normality, constant variance and independence. Any deviation from this may compromise the model’s reliability in its predictions.

**Linear Regression Model Only:** As its name implies, linear regression only models linear relationships between variables in your data set. As such, it may fail to capture complex non-linear patterns present within it.

Although linear regression has its drawbacks, it remains an invaluable and widely employed technique across various fields due to its ease of use, interpretability and ability to shed insight into relationships among variables. However, it is essential to be mindful of its limitations and consider other advanced techniques if linear regression’s assumptions cannot be fulfilled.