The post Best Fit Line in Linear Regression appeared first on The Data Monk.

]]>The best fit line in linear regression is the one which tries to minimize the Residual sum of squares.

It is the line which is supposed to give the best predictions on the unseen data depending on the training

data on which it is built..

In simple regression with on independent variable that coefficient is the slope of the line of best fit

In regression with 2 Independent variables the slope is a mix of the two COEFFICIENTS

The constant in regression eqation is is the y intercept of the line of best fit

The eqation for simple or linear regression

Y= a+bx +e

Y is the dependent VARIABLE

x is independent variable

b is the slope of regression line or fit line predictor or estimator

e error

A line of fit is a straight line that is the best approximation of the given set of data

A more accurate method of finding the line of best is the least sqare method

- A regression model fits the data well if the differences between observations and predicted values are small and in biased
- You can trust the results
- VALUE OF R^2 sqare of CORRELATION coefficient
- R^2 is called COEFFICIENT of Determination is the %of dependent variable variation that a linear model explains
- R^2 value always lie between 0to100%
- Larger the R^2 VALUE the better the regression model fits data
- Scatter plot or scatter graph depicts the visual picture of regression points and out liers based on the regression line

If you can explain the concept of Best Fit line in a better/simplified way, then please answer it here

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]]>Regression Line vs Line of Best Fit

The regression line (curve) consists of the expected values of a variable (Y) when given the values of an explanatory variable (X). In other words it is defined as E[Y|X = x]. To actually compute this line we need to know the joint distribution of X and Y, which in many cases we don’t know.

The line of best fit can be thought of as our estimate of the regression line. “Best fit” is not a precise term, since there are many ways to define it (ie using a least squares criterion, minimizing the absolute values of the residuals etc.).

One desirable property for the line of best fit to have is for it to converge to the regression line as our number of observations increase. And in the case of the variables X and Y having a bivariate normal distribution (which is often assumed) and selecting the ordinary least squares line as best fitted can be proven to occur.

The above answer was shared by Michael Zahir.

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]]>The post How can you avoid the overfitting your model? appeared first on The Data Monk.

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]]>The post Data Science Model with high accuracy in training dataset but low in testing dataset appeared first on The Data Monk.

]]>Data Science model interview question

Answer by Swapnil

It means the model is getting trained to the noise in the data and trying to fit exactly to the training data rather than generalizing it well over many different data sets. So, the model is suffering from high variance in the test set and the solution is to introduce a little bit of bias in the model so that it reduces the variance in the test set. This is also called as overfitting in technical terms.

Answer by Shubham Bhatt

“The model has high accuracy in Training dataset but low in testing dataset” means overfitting.

When a model gets trained with so much of data, it starts learning from the noise and inaccurate data entries in our data set. Then the model does not categorize the data correctly, because of too many details and noise. The causes of overfitting are the non-parametric and non-linear methods because these types of machine learning algorithms have more freedom in building the model based on the dataset and therefore they can really build unrealistic models. A solution to avoid overfitting is using a linear algorithm if we have linear data or using the parameters like the maximal depth if we are using decision trees.

It suggests “High variance and low bias”.

Techniques to reduce overfitting :

1. Increase training data.

2. Reduce model complexity.

3. Early stopping during the training phase (have an eye over the loss over the training period as soon as loss begins to increase stop training).

4. Ridge Regularization and Lasso Regularization

5. Use dropout for neural networks to tackle overfitting.

Answer by SMK – The Data Monk user

Data Science model interview question

1) This is a case of overfitting a model. It happens when a model learns the detail and noise in the training data to the extent that it negatively impacts the performance of the model on new data

2) Overfitting is more likely with nonparametric and nonlinear models that have more flexibility when learning a target function. For example, decision trees are a nonparametric machine learning algorithm that is very flexible and is subject to overfitting training data. We can prune a tree after it has learned in order to remove some of the detail it has picked up

3) Techniques to limit overfitting:

a) Use a resampling technique to estimate model accuracy

– k-fold cross-validation: We partition the data into k subsets, called folds. Then, we iteratively train the algorithm on k-1 folds while using the remaining fold as the test set (called the “holdout fold”).

b) Hold back a validation dataset – A validation dataset is simply a subset of your training data that you hold back from your algorithms until the very end of your project. After you have tuned your algorithms on your training data, you can evaluate the learned models on the validation dataset to get a final objective idea of how the models might perform on unseen data

c) Remove irrelevant input features (Feature selection)

d) Early Stopping: Up until a certain number of iterations, new iterations improve the model. After that point, however, the model’s ability to generalize can weaken as it begins to overfit the training data. Early stopping refers to stopping the training process before the learner passes that point. Deep Learning uses this technique.

Answer by Harshit Goyal

Data Science model interview question

The model’s high accuracy in the training dataset but low in the testing dataset is due to overfitting.

Overfitting is a modeling error that occurs when a function is too closely fit to a limited set of data points.

In reality, the data often studied has some degree of error or random noise within it. Thus, attempting to make the model conform too closely to slightly inaccurate data can infect the model with substantial errors and reduce its predictive power.

Therefore, the model fails to fit additional data or predict future observations reliably.

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]]>The post Missing Value Treatment by mean, mode, median, and KNN Imputation | Day 5 appeared first on The Data Monk.

]]>One of the most important technique in any Data Science model is to replace missing values with some numbers/values.

We can’t afford to remove the rows with missing values as there will be a lot of columns and every column might have some missing values. Removing all the missing rows will drastically reduce the data volume. That’s why we use Missing Value treatment

Explore all the answers from our users – http://thedatamonk.com/question/explain-missing-value-treatment-by-meanmode-median-and-knn-imputation/

Missing Value Treatment by mean, mode, median, and KNN Imputation

Many real-world datasets may contain missing values for various reasons. They are often encoded as NaNs, blanks or any other placeholders. Training a model with a dataset that has a lot of missing values can drastically impact the machine learning model’s quality. Some algorithms such as scikit-learn estimators assume that all values are numerical and have and hold meaningful value.

One way to handle this problem is to get rid of the observations that have missing data. However, you will risk losing data points with valuable information. A better strategy would be to impute the missing values. In other words, we need to infer those missing values from the existing part of the data. **There are three main types of missing data:Missing completely at random (MCAR)Missing at random (MAR)Not missing at random (NMAR)**

However, in this article, I will focus on 6 popular ways for data imputation for cross-sectional datasets ( Time-series dataset is a different story ).

That’s an easy one. You just let the algorithm handle the missing data. Some algorithms can factor in the missing values and learn the best imputation values for the missing data based on the training loss reduction (ie. XGBoost). Some others have the option to just ignore them (ie. LightGBM — use_missing=false). However, other algorithms will panic and throw an error complaining about the missing values (ie. Scikit learn — LinearRegression). In that case, you will need to handle the missing data and clean it before feeding it to the algorithm.

This works by calculating the mean/median of the non-missing values in a column and then replacing the missing values within each column separately and independently from the others. It can only be used with numeric data.

Easy and fast.

Works well with small numerical datasets.

Doesn’t factor the correlations between features. It only works on the column level.

Will give poor results on encoded categorical features (do NOT use it on categorical features).

Not very accurate.

Doesn’t account for the uncertainty in the imputations.

**Mean/Median Imputation****3- Imputation Using (Most Frequent) or (Zero/Constant) Values:**

Most Frequent is another statistical strategy to impute missing values and YES!! It works with categorical features (strings or numerical representations) by replacing missing data with the most frequent values within each column.**Pros:**

Works well with categorical features.**Cons:**

It also doesn’t factor the correlations between features.

It can introduce bias in the data.

**Most Frequent Imputation**

Zero or Constant imputation — as the name suggests — it replaces the missing values with either zero or any constant value you specify**4- Imputation Using k-NN:**

The k nearest neighbours is an algorithm that is used for simple classification. The algorithm uses ‘feature similarity’ to predict the values of any new data points. This means that the new point is assigned a value based on how closely it resembles the points in the training set. This can be very useful in making predictions about the missing values by finding the k’s closest neighbours to the observation with missing data and then imputing them based on the non-missing values in the neighbourhood. Let’s see some example code using Impyute library which provides a simple and easy way to use KNN for imputation:

**KNN Imputation for California Housing DatasetHow does it work?**

It creates a basic mean impute then uses the resulting complete list to construct a KDTree. Then, it uses the resulting KDTree to compute nearest neighbours (NN). After it finds the k-NNs, it takes the weighted average of them.

Can be much more accurate than the mean, median or most frequent imputation methods (It depends on the dataset).

Computationally expensive. KNN works by storing the whole training dataset in memory.

This type of imputation works by filling the missing data multiple times. Multiple Imputations (MIs) are much better than a single imputation as it measures the uncertainty of the missing values in a better way. The chained equations approach is also very flexible and can handle different variables of different data types (ie., continuous or binary) as well as complexities such as bounds or survey skip patterns.

This method works very well with categorical and non-numerical features. It is a library that learns Machine Learning models using Deep Neural Networks to impute missing values in a dataframe. It also supports both CPU and GPU for training.

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]]>The post Guesstimate – Annual income of a beggar in Bangalore appeared first on The Data Monk.

]]>Guesstimate is asked in an interview to understand the analytical understanding of the candidate as well as to check his thought/approach diversity.

Guesstimates can range from finding the number of ‘Red’ Cars in Delhi to the number of trees in Bangalore.

In one such interview, the candidate was asked to estimate the income of a beggar in Bangalore. We received 22 responses on this question, you can read their diverse approach or can write your own

Link to question – http://thedatamonk.com/question/how-much-is-the-annual-income-of-a-beggar-in-bangalore/

Annual income of a beggar in Bangalore

Link to the question with all the approach – http://thedatamonk.com/question/how-much-is-the-annual-income-of-a-beggar-in-bangalore/

If you have a different approach then please add your answer, else upvote the one which you like

First Approach – Ognish Banerjee

Assumption :

1. A beggar meets 100 people per day out of that chance of converting is 50%

2. The beggar knows where to search for people , let’s say near offices or tech park to have a better conversion rate

3. The beggar knows the peak time of the day as well as the peak time during the evening

4. The beggar starts his day from 10 am in the morning till 10 pm till night

5. Average income from a person is Rs 20

Now to go about this.

I’m categorizing the daily hour for wekkdays

10 am to 1 pm – peak time

1 pm to 5 pm – medium

5pm to 8 pm – peak

8pm to 10 pm – medium

Number of people he meets in these hours

10 am to 1 pm – 40 people

1 pm to 5pm – 10 people

5pm to 8pm – 40 people

8pm to 10pm – 10 people

On average expected income would be

(40*20) + (10*20) + (40*20) + (10*20) = 2000

5 days for weekdays = 10000

50% conversion rate = 5000

On weekdays in a month his income is = 5000 * 4 ( 4 weeks in a month) = 20000

Now taking the week ends. His strategy would be different. The beggar won’t be roaming near the offices, rather he would roam near the neighborhood during day and shopping mall/theatre during night.

If I go with similar calculation (not mentioned here) his evening income is way higher, peak time 6pm – 11pm

He meets 50 people with 20 rs each – 1000

50% conversion – 500

Number of weekends 8 – 500*8 = 4000

Total monthly income = 24000

Total annual income : 24000 * 12 around (3 lacs ) taking holidays, special events all around the year.

I’m a Mu Sigman also, during my first year I also earned the same like a beggar!!! Wow

Second Approach – Nilanjan Kumar

In the 24 hours time, let’s assume that a beggar sleeps 5 hours a day and also assume 5 hours he is busy doing other pieces of stuff like eating, playing cards on the roadside, etc. so that makes our time as: –

24-5-5 = 14 hours.

The beggar divided his time as below(5 days of working) : –

Time Interaction with People(per day) Conversion rate

6 a.m – 10 a.m 50 80%

12 p.m – 4 p.m 30 50%

6 p.m – 10 p.m 40 70%

11 p.m – 1 a.m 25 30%

Reasons for taking the conversion rate like this:

6 a.m. to 10 a.m – People in a good mood going to start their day by offering something to needy people.

12 p.m to 4 p.m. – People will be in a hurry as they have got limited time from the office.

6 p.m to 10 p.m – Back from work if a day went well they will offer to make each day good.

11 p.m to 1 a.m – End of the day.

If on average they get Rs. 5 from a single person, then: –

Time People offering money(per day) Amount(avg Rs 5 per person)

6 a.m – 10 a.m 40 200

12 p.m – 4 p.m 15 75

6 p.m – 10 p.m 28 140

11 p.m – 1 a.m 10 50

Total = Rs 465 per day

This 465 per day will be for 5 days a week as on weekends the time between 12 p.m. to 4 p.m and 6 p.m to 10 p.m will have conversion rates more. But on the contrary morning conversion rate will be less. So taking that situation into count, this Rs. 465 per day will increase to Rs. 500 per day (considering an average increase of Rs. 35 ).

Hence, Calculating for per week: –

(465*5)+(500*2) = Rs. 3325

A month has 4 weeks, hence income in 1 month = Rs. 3325*4 = Rs. 13,300

For annual income, 12 months, Hence, 12* 13300 = Rs. 1,59,600/-

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]]>The post Order of Execution of SQL commands appeared first on The Data Monk.

]]>Why do we need to optimize our queries?

When you are dealing with a dummy dataset then you don’t actually care about optimizing your queries, but once you start hitting real-time data with millions of rows then each query you trigger costs some dollar to your company. The more optimized your query is, the lesser is its cost to the company.

To start optimizing your queries, you need to understand the flow of execution. And this is why it’s one of the most asked question in any Analytics interview (between 0 to 5 years of experience)

Order of Execution of SQL commands

Each SQL query starts with finding the data first and then moves to filter it based on conditions specified. Below is the order of execution of SQL commands

1. From and Joins : since these two forms the basis of the query

2. Where : Filters out the rows

3. Group By : Grouping values based on the column specified in the Group By clause

4. Having : Filters out the grouped rows

5. Select

6. Distinct : Rows with duplicate values in the column marked as Distinct are discarded

7. Order By : Rows are sorted based on Order By clause

8. Limit, Offset : Finally the limit or offset is applied

Query order of execution

1. FROM and JOINs

The FROM clause, and subsequent JOINs are first executed to determine the total working set of data that is being queried. This includes subqueries in this clause, and can cause temporary tables to be created under the hood containing all the columns and rows of the tables being joined.

2. WHERE

Once we have the total working set of data, the first-pass WHERE constraints are applied to the individual rows, and rows that do not satisfy the constraint are discarded. Each of the constraints can only access columns directly from the tables requested in the FROM clause. Aliases in the SELECT part of the query are not accessible in most databases since they may include expressions dependent on parts of the query that have not yet executed.

3. GROUP BY

The remaining rows after the WHERE constraints are applied are then grouped based on common values in the column specified in the GROUP BY clause. As a result of the grouping, there will only be as many rows as there are unique values in that column. Implicitly, this means that you should only need to use this when you have aggregate functions in your query.

4. HAVING

If the query has a GROUP BY clause, then the constraints in the HAVING clause are then applied to the grouped rows, discard the grouped rows that don’t satisfy the constraint. Like the WHERE clause, aliases are also not accessible from this step in most databases.

5. SELECT

Any expressions in the SELECT part of the query are finally computed.

6. DISTINCT

Of the remaining rows, rows with duplicate values in the column marked as DISTINCT will be discarded.

7. ORDER BY

If an order is specified by the ORDER BY clause, the rows are then sorted by the specified data in either ascending or descending order. Since all the expressions in the SELECT part of the query have been computed, you can reference aliases in this clause.

8. LIMIT / OFFSET

Finally, the rows that fall outside the range specified by the LIMIT and OFFSET are discarded, leaving the final set of rows to be returned from the query.

There are a few more answers to this question, you can add your approach as well on this link – http://thedatamonk.com/question/what-is-the-order-of-execution-of-sql-commands/#comments

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]]>The post Explain type 2 error in simple terms appeared first on The Data Monk.

]]>Confusion Matrix is one of those concepts which is a bit confusing but is also asked to candidates in order to check their clarity of concepts.

There could be questions like,”Explain a model which is 99% accurate but still of no use to the company”

The answer lies to the understanding of the concepts of confusion matrix

Type 2 error in simple terms

You will encounter this error while solving a Classification problem.

You will always produce a confusion matrix while solving a classification problem,

irrespective of the algorithm you use.

A confusion matrix is a 2*2 matrix consisting of True Positives, True Negatives, False Positives, False Negatives.

Type 2 Error corresponds to False Negatives.

To say in layman terms, predicting something False when it is actually True.

For Example – Predicting a person will not default on the Loan when in reality has defaulted on the Loan.

The above has been contributed by the user **spawlaw007**

Username – **smk** has defined the above question in the following way

1) A statistically significant result cannot prove that a research hypothesis is correct (as this implies 100% certainty). Because a p-value is based on probabilities, there is always a chance of making an incorrect conclusion regarding accepting or rejecting the null hypothesis (H0)

2) Anytime we make a decision using statistics there are four possible outcomes, with two representing correct decisions and two representing errors

TYPE II ERROR:

1) A type II error is also known as a false negative and occurs when a researcher fails to reject a null hypothesis which is really false. Here a researcher concludes there is not a significant effect when actually there really is

2) You can decrease the risk of type II error by having a large sample size

TYPE I ERROR:

1)A type 1 error is also known as a false positive and occurs when a researcher incorrectly rejects a true null hypothesis

2) This means that your report that your findings are significant when in fact they have occurred by chance

3) The probability of making a type I error is represented by your alpha level (α), which is the p-value below which you reject the null hypothesis EXAMPLE: A p-value of 0.05 indicates that you are willing to accept a 5% chance that you are wrong when you reject the null hypothesis.

You can reduce your risk of committing a type I error by using a lower value for p. For example, a p-value of 0.01 would mean there is a 1% chance of committing a Type I error. However, using a lower value for alpha means that you will be less likely to detect a true difference if one really exists (thus risking a type II error)

There are 15+ users who have answered this questions, you can explore all the answers to have a clear understanding of Type-2 error

Link to question – http://thedatamonk.com/question/explain-type-2-error-in-simple-terms/

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]]>The post P-value in Linear Regression appeared first on The Data Monk.

]]>Suppose a child in the family goes to the school daily and one day, his teacher writes to his mother in the school diary that your son is very naughty and he was found fighting with another kid. This situation is quite common in schools and like any mother, this child’s mother says no my son is not naughty, it must have been the other kid who provoked him. Simple…agreed?

Now, if you wish to do a Hypothesis test whether this child is really naughty or not, you would presume that he is actually naughty (that would be your hypothesis of interest) but you would try to formulate another hypothesis opposite to this (i.e. your Null Hypothesis) that says that the child is not naughty.

So your two hypotheses would be:

Null: The child is not naughty

Alternative: The child is naughty

Then you would try to find evidence by collecting data and putting it to test.

Coming back to the story from the child’s school…

After some days, there is another complaint from the school of this child fighting with another kid and, again the mother of the kid in question does not accept the fault of her child.

The situation repeats itself again with this kid the third time with a third kid and now the mother becomes suspicious as to probably her child is really naughty.

Interestingly, this third instance in our example actually becomes what is Statistically called the Threshold of Significance (or the level of significance).

When the same child again is reported to fight with another kid, the mother has no other option but to accept that her child is really naughty and he finds ways to fight with other kids. This is actually when it is said that the evidence is “Statistically Significant”. This is accepted to be significant since it has occurred beyond the level of significance.

The above situation is purely hypothetical but could be a subject of a Statistical analysis somewhere.

Important Links to explore Data Science

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]]>