Linear Regression – Do you know the basics?
Linear regression is considered to be the most basic element of Data Sciences. Whatever course you are going to attempt or problem you are going to solve, Linear regression can come in handy. This is a small quiz which is based on very basic fundamentals of Linear regression. Let’s see how much command do you have over Linear Regression.
Assume – we are talking about linear regression with cost function as residual sum of squares.
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Linear regression is one of the basic techniques in the field of data science. This quiz is focused on to let you know your understanding about Linear regression.
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Question 1 of 10
1. Question
Which of the following is(are) assumptions of a linear regression?
Correct
There are many assumptions of linear regression but the following four are considered to be the basic and the most important assumptions:
1) Linearity and Additivity
2) Statistical Independence of errors
3) Normality of error distributionIncorrect
There are many assumptions of linear regression but the following four are considered to be the basic and the most important assumptions:
1) Linearity and Additivity
2) Statistical Independence of errors
3) Normality of error distribution 
Question 2 of 10
2. Question
Consider the following fitted equation:
salary=4000+4.5(age)^{2}
Is this equation linear in nature?
Correct
Linearity means that the coefficients should be linear, it doesn’t depend on the actual variable itself.
Incorrect
Linearity means that the coefficients should be linear, it doesn’t depend on the actual variable itself.

Question 3 of 10
3. Question
Consider the following fitted line where we had Y as a dependent variable and X as an independent variable.
Y = 15 + 3X
Can we use the model fitted above to predicted x using y?
x = 5 + Y/3
Correct
It won’t be correct to estimate X from the fitted line for Y. When we tried to fit Y using X – Our objective was to reduce the errors in Y. Hence if we want to predict X from Y, we will have to use a different model altogether.
Incorrect
It won’t be correct to estimate X from the fitted line for Y. When we tried to fit Y using X – Our objective was to reduce the errors in Y. Hence if we want to predict X from Y, we will have to use a different model altogether.

Question 4 of 10
4. Question
Consider the following fitted line where we had Y as a dependent variable and X as an independent variable.
Y = 15 + 0.3X
Which of the following statements are true?
Correct
Incorrect

Question 5 of 10
5. Question
Consider ‘x’ as an independent variable and ‘y’ as dependent variable. Using these two – we fitted a linear regression line –
Yp = 5  2*x
Correlation between y and x is .58, what will be the correlation between y and Yp?
Correct
In simple linear regression, the correlation between dependent and independent variable is same as actual and predicted dependent variables.
Incorrect
In simple linear regression, the correlation between dependent and independent variable is same as actual and predicted dependent variables.

Question 6 of 10
6. Question
Consider ‘x’ as an independent variable and ‘y’ as dependent variable. Using these two – we fitted a linear regression line –
Yp = 5  2*x
Correlation between y and x is .6, what will be the Rsquare for the fitted model?
Correct
In the case of simple linear regression Rsquare is nothing but the square of the correlation between dependent and independent variables while in case of multilinear regression, it is going to be square of multicorrelation
Incorrect
In the case of simple linear regression Rsquare is nothing but the square of the correlation between dependent and independent variables while in case of multilinear regression, it is going to be square of multicorrelation

Question 7 of 10
7. Question
State whether the given statement is TRUE/ FALSE
Linear regression uses Maximum Likelihood Method to estimate the parameters.Correct
Linear regression uses OLS (Ordinary Least Square) method to estimate the parameters.
Incorrect

Question 8 of 10
8. Question
We fitted a linear regression with following parameters and got corresponding RSquare values:
Dependent Variable No. of Independent Variables R^{2} Y 3 R1 Y 6 R2 Y 9 R3 What will be relationship between R1, R2 & R3?
Correct
R^{2} always increases with the increase in number of independent variables. That is the reason we look into Adjusted RSquare along with RSquare.
Incorrect
R^{2} always increases with the increase in number of independent variables. That is the reason we look into Adjusted RSquare along with RSquare.

Question 9 of 10
9. Question
Which of the following statement is true about RSquare?
Correct
Incorrect

Question 10 of 10
10. Question
A paired data set has mean(x)=6, mean(y)=5 and slope of the regression line (predicted y using x) is 1.5. The intercept of the regression line is
Correct
A regression line always passes through mean of dependent and independent variables.
Incorrect
A regression line always passes through mean of dependent and independent variables.
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