This set of Machine Learning Multiple Choice Questions & Answers (MCQs) focuses on “Polynomial Regression”.

1. Who coined the term regression?

a) Andrey Markov

b) Alexey Chervonenkis

c) Vladimir Vapnik

d) Francis Galton

View Answer

Explanation: Galton introduced the idea of regression in the 19

^{th}century. Vapnik and Chervonenkis established the VC dimension. Markov was best known for his work on stochastic processes. He introduced the Markov model.

2. Polynomial regression and multivariate regression are the same.

a) True

b) False

View Answer

Explanation: In multivariate regression, there must be at least two independent variables. In polynomial regression, even one variable is enough. Different degrees of indices or products of features can be used.

3. The learner is trying to predict the price of a house based on the length and width of the house.

x_{1} = length and x_{2} = width. What is a better hypothesis?

a) h(X) = t_{0} + t_{1}x_{1}

b) h(X) = t_{0} + t_{1}x_{1} + t_{2}x_{2}

c) h(X) = t_{0} + t_{2}x_{2}

d) h(X) = t_{0} + t_{1}X, where area of the house: X = x_{1} * x_{2}

View Answer

Explanation: To predict the price of the house, the size is a better parameter. It can be determined by the area of the house which is length multiplied by width. So, instead of using the two features separately, a better third feature can be used.

4. h(X) = t_{0} + t_{1}x + t_{2}x^{2} + t_{3}x^{3}. What type of regression is this?

a) Polynomial regression

b) Univariate linear regression

c) Logistic regression

d) Multivariate linear regression

View Answer

Explanation: The expression has only one feature x, so it is not a multivariate linear regression. There is more than one term containing a feature, so it is also not a univariate linear regression. The features are expressed as a polynomial, so it is a polynomial regression.

5. h(x) = t_{0} + t_{1}x + t_{2}x^{2}. t_{0} = t_{1} = t_{2} = 1. X is the size of the house. For what value of x, h(x) is minimum?

a) -1

b) 0

c) 0 or -1

d) 1

View Answer

Explanation: h(x) = t

_{0}+ t

_{1}x + t

_{2}x

^{2}

= 1 + x + x

^{2}

Since x cannot be negative, the minimum value of h(x) is 1.

6. h(x) = t_{0} + t_{1}x + t_{2}x^{2}. t_{0} = 0, t_{1} = t_{2} = 1. X is the size of the house. For what value of x, h(x) is minimum?

a) -1

b) 0

c) 0 or -1

d) 1

View Answer

Explanation: h(x) = t

_{0}+ t

_{1}x + t

_{2}x

^{2}

= x + x

^{2}

h(x) will be minimum if the expression (x + x

^{2}) is minimum i.e. 0 (size of house cannot be negative)

x + x

^{2}= 0

or, x(x + 1) = 0

Since, x cannot be negative, the value of x is 0.

7. There are two features. One is of higher priority. What can be done to improve the hypothesis?

a) Increase the power to which the feature with higher priority is raised

b) Remove the feature with lower priority

c) Depends on the dataset

d) Nothing can be done

View Answer

Explanation: One of the advantages of polynomial regression is that of handling features with a different priority. If a feature with higher priority is encountered, its power can be raised to give it higher priority in the hypothesis.

8. A drawback of Polynomial Regression is handling of features with a different priority.

a) True

b) False

View Answer

Explanation: Polynomial Regression can handle features with varying priority very well. One of its drawbacks is that it is sensitive to outliers. Overfitting may or may not occur.

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