Which of the Following Is True for Family Separation Allowances (Fsa)

Introduction

Linear Regression is still the most prominently used statistical technique in information science manufacture and in academia to explain relationships betwixt features.

A total of 1,355 people registered for this skill test. It was specially designed for you to examination your knowledge on linear regression techniques. If you are 1 of those who missed out on this skill exam, here are the questions and solutions. You missed on the real fourth dimension exam, but can read this article to find out how many could have answered correctly.

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Helpful Resource

Here are some resources to make it depth cognition in the subject.

• five Questions which can teach you Multiple Regression (with R and Python)

• Going Deeper into Regression Analysis with Assumptions, Plots & Solutions

• 7 Types of Regression Techniques yous should know!

Are yous a beginner in Car Learning? Practise you want to master the concepts of Linear Regression and Machine Learning? Here is a beginner-friendly course to assist you in your journey –

• Certified AI & ML Blackbelt+ Programme
• Applied Machine Learning Form

Skill test Questions and Answers

i) True-Imitation: Linear Regression is a supervised machine learning algorithm.

A) TRUE
B) False

Solution: (A)

Yes, Linear regression is a supervised learning algorithm considering it uses truthful labels for training. Supervised learning algorithm should have input variable (x) and an output variable (Y) for each example.

2) True-False: Linear Regression is mainly used for Regression.

A) TRUE
B) Faux

Solution: (A)

Linear Regression has dependent variables that accept continuous values.

3) True-False: It is possible to design a Linear regression algorithm using a neural network?

A) TRUE
B) FALSE

Solution: (A)

True. A Neural network can be used as a universal approximator, so information technology can definitely implement a linear regression algorithm.

iv) Which of the following methods practice we utilise to detect the best fit line for data in Linear Regression?

A) Least Square Mistake
B) Maximum Likelihood
C) Logarithmic Loss
D) Both A and B

Solution: (A)

In linear regression, nosotros try to minimize the least square errors of the model to place the line of best fit.

5) Which of the following evaluation metrics can exist used to evaluate a model while modeling a continuous output variable?

A) AUC-ROC
B) Accuracy
C) Logloss
D) Mean-Squared-Error

Solution: (D)

Since linear regression gives output as continuous values, so in such instance nosotros use mean squared error metric to evaluate the model performance. Remaining options are use in case of a nomenclature trouble.

six) True-Faux: Lasso Regularization tin can exist used for variable selection in Linear Regression.

A) True
B) Fake

Solution: (A)

True, In case of lasso regression we use accented penalisation which makes some of the coefficients nada.

7) Which of the post-obit is true virtually Residuals ?

A) Lower is amend
B) College is better
C) A or B depend on the situation
D) None of these

Solution: (A)

Residuals refer to the error values of the model. Therefore lower residuals are desired.

8) Suppose that we take N independent variables (X1,X2… Xn) and dependent variable is Y. Now Imagine that you are applying linear regression past fitting the all-time fit line using least square error on this information.

You found that correlation coefficient for one of information technology's variable(Say X1) with Y is -0.95.

Which of the post-obit is true for X1?

A) Relation between the X1 and Y is weak
B) Relation between the X1 and Y is strong
C) Relation betwixt the X1 and Y is neutral
D) Correlation tin can't judge the human relationship

Solution: (B)

The absolute value of the correlation coefficient denotes the strength of the relationship. Since  absolute correlation is very high it ways that the relationship is stiff between X1 and Y.

ix) Looking at above two characteristics, which of the post-obit selection is the correct for Pearson correlation betwixt V1 and V2?

If you are given the 2 variables V1 and V2 and they are following below 2 characteristics.

1. If V1 increases then V2 also increases

2. If V1 decreases then V2 behavior is unknown

A) Pearson correlation will be close to one
B) Pearson correlation volition exist shut to -1
C) Pearson correlation volition be close to 0
D) None of these

Solution: (D)

We cannot comment on the correlation coefficient by using only statement ane.  We demand to consider the both of these ii statements. Consider V1 as x and V2 as |10|. The correlation coefficient would not be shut to 1 in such a example.

10) Suppose Pearson correlation between V1 and V2 is zip. In such case, is it right to conclude that V1 and V2 do non take whatsoever relation betwixt them?

A) Truthful
B) Fake

Solution: (B)

Pearson correlation coefficient between 2 variables might exist nothing fifty-fifty when they have a human relationship betwixt them. If the correlation coefficient is goose egg, information technology only means that that they don't move together. We tin have examples similar y=|ten| or y=x^2.

eleven) Which of the following offsets, do we utilize in linear regression'due south least square line fit? Suppose horizontal axis is independent variable and vertical axis is dependent variable.

A) Vertical starting time
B) Perpendicular offset
C) Both, depending on the state of affairs
D) None of higher up

Solution: (A)

We always consider residuals as vertical offsets. We calculate the direct differences between actual value and the Y labels. Perpendicular first are useful in case of PCA.

12) True- False: Overfitting is more likely when you lot have huge amount of data to train?

A) TRUE
B) FALSE

Solution: (B)

With a small training dataset, it's easier to find a hypothesis to fit the grooming data exactly i.e. overfitting.

xiii) Nosotros tin can also compute the coefficient of linear regression with the assist of an analytical method chosen "Normal Equation". Which of the post-obit is/are true well-nigh Normal Equation?

1. Nosotros don't accept to choose the learning charge per unit
2. It becomes irksome when number of features is very large
3. Thers is no need to iterate

A) 1 and 2
B) 1 and 3
C) 2 and 3
D) 1,2 and three

Solution: (D)

Instead of slope descent, Normal Equation can besides be used to find coefficients. Refer this commodity for read more near normal equation.

14) Which of the following statement is true about sum of residuals of A and B?

Beneath graphs show two fitted regression lines (A & B) on randomly generated information. Now, I want to detect the sum of residuals in both cases A and B.

Note:

1. Scale is same in both graphs for both axis.
2. X axis is independent variable and Y-centrality is dependent variable.

A) A has higher sum of residuals than B
B) A has lower sum of residuum than B
C) Both have aforementioned sum of residuals
D) None of these

Solution: (C)

Sum of residuals will always be zero, therefore both have same sum of residuals

Question Context 15-17:

Suppose you lot take fitted a complex regression model on a dataset. Now, you are using Ridge regression with penality x.

15) Choose the choice which describes bias in best mode.
A) In example of very large x; bias is depression
B) In case of very big x; bias is high
C) Nosotros can't say about bias
D) None of these

Solution: (B)

If the penalty is very large it means model is less circuitous, therefore the bias would be high.

16) What volition happen when yous utilise very large penalty?

A) Some of the coefficient volition become absolute zero
B) Some of the coefficient will approach zero but not absolute zero
C) Both A and B depending on the state of affairs
D) None of these

Solution: (B)

In lasso some of the coefficient value get zero, but in case of Ridge, the coefficients get shut to zero simply not zero.

17) What will happen when y'all apply very big penalty in example of Lasso?
A) Some of the coefficient will become nothing
B) Some of the coefficient will be approaching to nothing merely not absolute zero
C) Both A and B depending on the situation
D) None of these

Solution: (A)

As already discussed, lasso applies absolute penalty, so some of the coefficients will get goose egg.

xviii) Which of the following argument is true about outliers in Linear regression?

A) Linear regression is sensitive to outliers
B) Linear regression is not sensitive to outliers
C) Can't say
D) None of these

Solution: (A)

The slope of the regression line will modify due to outliers in near of the cases. So Linear Regression is sensitive to outliers.

19) Suppose you plotted a scatter plot betwixt the residuals and predicted values in linear regression and you lot plant that there is a relationship betwixt them. Which of the post-obit conclusion practise y'all make almost this situation?

A) Since the in that location is a relationship means our model is not skillful
B) Since the there is a relationship ways our model is practiced
C) Can't say
D) None of these

Solution: (A)

There should non be any relationship betwixt predicted values and residuals. If at that place exists whatever relationship betwixt them,it ways that the model has not perfectly captured the information in the data.

Question Context xx-22:

Suppose that you take a dataset D1 and you lot blueprint a linear regression model of degree 3 polynomial and you institute that the training and testing mistake is "0" or in some other terms it perfectly fits the data.

twenty) What will happen when you fit degree 4 polynomial in linear regression?
A) In that location are loftier chances that degree 4 polynomial will over fit the data
B) In that location are high chances that degree 4 polynomial will under fit the information
C) Tin't say
D) None of these

Solution: (A)

Since is more caste 4 will exist more complex(overfit the information) than the degree 3 model so it will over again perfectly fit the data. In such example grooming fault will be zero but test mistake may not be zero.

21) What will happen when you fit degree 2 polynomial in linear regression?
A) It is high chances that degree 2 polynomial will over fit the data
B) Information technology is high chances that caste 2 polynomial will under fit the data
C) Can't say
D) None of these

Solution: (B)

If a degree three polynomial fits the data perfectly, it's highly likely that a simpler model(degree 2 polynomial) might under fit the data.

22) In terms of bias and variance. Which of the following is true when y'all fit degree 2 polynomial?

A) Bias will exist loftier, variance volition exist high
B) Bias volition exist depression, variance volition be loftier
C) Bias will be high, variance will be depression
D) Bias will be low, variance will be low

Solution: (C)

Since a degree two polynomial will exist less complex as compared to degree three, the bias will be high and variance will be low.

Question Context 23:

Which of the post-obit is true about below graphs(A,B, C left to correct) between the cost part and Number of iterations?

23) Suppose l1, l2 and l3 are the three learning rates for A,B,C respectively. Which of the following is true most l1,l2 and l3?

A) l2 < l1 < l3

B) l1 > l2 > l3
C) l1 = l2 = l3
D) None of these

Solution: (A)

In instance of high learning rate, step will be loftier, the objective office will decrease quickly initially, only information technology will not notice the global minima and objective function starts increasing after a few iterations.

In instance of low learning charge per unit, the step will be small-scale. And then the objective function will subtract slowly

Question Context 24-25:

Nosotros accept been given a dataset with n records in which we have input attribute every bit x and output attribute as y. Suppose nosotros use a linear regression method to model this data. To test our linear regressor, we divide the data in training set and examination gear up randomly.

24) Now we increase the training set size gradually. As the training set size increases, what exercise y'all await volition happen with the mean grooming error?

A) Increase
B) Subtract
C) Remain abiding
D) Tin can't Say

Solution: (D)

Training error may increment or decrease depending on the values that are used to fit the model. If the values used to train contain more outliers gradually, then the error might simply increase.

25) What practice you await volition happen with bias and variance as you increase the size of training information?

A) Bias increases and Variance increases
B) Bias decreases and Variance increases
C) Bias decreases and Variance decreases
D) Bias increases and Variance decreases
E) Can't Say False

Solution: (D)

As we increase the size of the preparation data, the bias would increase while the variance would decrease.

Question Context 26:

Consider the following information where one input(X) and ane output(Y) is given.

26) What would be the root mean foursquare training mistake for this data if you run a Linear Regression model of the form (Y = A0+A1X)?

A) Less than 0
B) Greater than zero
C) Equal to 0
D) None of these

Solution: (C)

We can perfectly fit the line on the following data so hateful fault will be null.

Question Context 27-28:

Suppose you have been given the following scenario for preparation and validation error for Linear Regression.

Scenario	Learning Charge per unit	Number of iterations	Grooming Fault	Validation Fault
1	0.1	one thousand	100	110
2	0.2	600	90	105
three	0.3	400	110	110
iv	0.4	300	120	130
v	0.4	250	130	150

27) Which of the following scenario would requite yous the right hyper parameter?

A) 1
B) 2
C) 3
D) 4

Solution: (B)

Option B would be the ameliorate choice considering it leads to less training too as validation error.

28) Suppose y'all got the tuned hyper parameters from the previous question. Now, Imagine you desire to add a variable in variable infinite such that this added characteristic is important. Which of the post-obit thing would yous discover in such example?

A) Training Mistake will decrease and Validation error will increase

B) Training Error will increase and Validation fault will increment
C) Training Fault will increment and Validation error volition decrease
D) Preparation Mistake volition decrease and Validation mistake will subtract
Eastward) None of the above

Solution: (D)

If the added feature is important, the grooming and validation fault would subtract.

Question Context 29-xxx:

Suppose, y'all got a situation where you find that your linear regression model is nether fitting the information.

29) In such situation which of the following options would you consider?

1. Add together more variables
2. Start introducing polynomial caste variables
3. Remove some variables

A) 1 and 2
B) 2 and three
C) 1 and 3
D) i, 2 and 3

Solution: (A)

In instance of under fitting, you lot demand to induce more variables in variable infinite or yous can add some polynomial caste variables to make the model more complex to be able to fir the data better.

30) Now situation is same every bit written in previous question(under plumbing equipment).Which of following regularization algorithm would you prefer?

A) L1
B) L2
C) Any
D) None of these

Solution: (D)

I won't use any regularization methods because regularization is used in case of overfitting.

End Notes

I tried my all-time to brand the solutions equally comprehensive as possible just if you take any questions / doubts delight drop in your comments below. I would honey to hear your feedback about the skilltest. For more than such skilltests, cheque out our electric current hackathons.

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Source: https://www.analyticsvidhya.com/blog/2017/07/30-questions-to-test-a-data-scientist-on-linear-regression/

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