This set of R Programming Language Multiple Choice Questions & Answers (MCQs) focuses on “Linear Regression – 2”.

1. In practice, Line of best fit or regression line is found when _____________

a) Sum of residuals (∑(Y – h(X))) is minimum

b) Sum of the absolute value of residuals (∑|Y-h(X)|) is maximum

c) Sum of the square of residuals ( ∑ (Y-h(X))2) is minimum

d) Sum of the square of residuals ( ∑ (Y-h(X))2) is maximum

View Answer

Explanation: Here we penalize higher error value much more as compared to the smaller one, such that there is a significant difference between making big errors and small errors, which makes it easy to differentiate and select the best fit line.

2. If Linear regression model perfectly first i.e., train error is zero, then _____________________

a) Test error is also always zero

b) Test error is non zero

c) Couldn’t comment on Test error

d) Test error is equal to Train error

View Answer

Explanation: Test Error depends on the test data. If the Test data is an exact representation of train data then test error is always zero. But this may not be the case.

3. Which of the following metrics can be used for evaluating regression models?

i) R Squared

ii) Adjusted R Squared

iii) F Statistics

iv) RMSE / MSE / MAE

a) ii and iv

b) i and ii

c) ii, iii and iv

d) i, ii, iii and iv

View Answer

Explanation: These (R Squared, Adjusted R Squared, F Statistics, RMSE / MSE / MAE) are some metrics which you can use to evaluate your regression model.

4. How many coefficients do you need to estimate in a simple linear regression model (One independent variable)?

a) 1

b) 2

c) 3

d) 4

View Answer

Explanation: In simple linear regression, there is one independent variable so 2 coefficients (Y=a+bx+error).

5. In a simple linear regression model (One independent variable), If we change the input variable by 1 unit. How much output variable will change?

a) by 1

b) no change

c) by intercept

d) by its slope

View Answer

Explanation: For linear regression Y=a+bx+error. If neglect error then Y=a+bx. If x increases by 1, then Y = a+b(x+1) which implies Y=a+bx+b. So Y increases by its slope.

6. Function used for linear regression in R is __________

a) lm(formula, data)

b) lr(formula, data)

c) lrm(formula, data)

d) regression.linear(formula, data)

View Answer

Explanation: lm(formula, data) refers to a linear model in which formula is the object of the class “formula”, representing the relation between variables. Now this formula is on applied on the data to create a relationship model.

7. In syntax of linear model lm(formula,data,..), data refers to ______

a) Matrix

b) Vector

c) Array

d) List

View Answer

Explanation: Formula is just a symbol to show the relationship and is applied on data which is a vector. In General, data.frame are used for data.

8. In the mathematical Equation of Linear Regression Y = β1 + β2X + ϵ, (β1, β2) refers to __________

a) (X-intercept, Slope)

b) (Slope, X-Intercept)

c) (Y-Intercept, Slope)

d) (slope, Y-Intercept)

View Answer

Explanation: Y-intercept is β1 and X-intercept is – (β1 / β2). Intercepts are defined for axis and formed when the coordinates are on the axis.

9. What plot(s) are used to view the linear regression?

a) Scatterplot

b) Box plot

c) Density plot

d) Scatterplot, Boxplot, Density plot

View Answer

Explanation: Each plot has its own importance of highlighting a specific feature. Scatter plot is used to visualise the relationship between the variables, Box plot is used to spot the outliers which effect line of best fit.

10. Common Metrics which are used to select linear model are ____________

a)

R-Squared Lower the better F-Statistic Higher the better

b)

R-Squared Lower the better F-Statistic Lower the better

c)

R-Squared Higher the better F-Statistic Higher the better

d)

R-Squared Higher the better F-Statistic Lower the betterView Answer

Explanation: For choosing linear regression model it is always advised to have more R-squared and lower F-Statistic. It ensures the best fit for the given data.

11. In lm(response ~ terms), terms specification of the form “first*second” is same as __________

a) first+second

b) first:second

c) first+second+first:second

d) first:second+second:first

View Answer

Explanation: A terms specification of the form “first + second” indicates all the terms in first together with all the terms in second with duplicates removed.

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