Q.1 What is the primary purpose of regression analysis?
To find relationships between variables
To calculate mean and median
To create pie charts
To summarize categorical data
Explanation - Regression analysis is used to study the relationship between a dependent variable and one or more independent variables.
Correct answer is: To find relationships between variables
Q.2 In simple linear regression, the regression line equation is given by?
Y = a + bX
Y = aX + bY
X = a + bY
Y = aX + b
Explanation - In simple linear regression, Y is predicted by a constant a (intercept) and b times the independent variable X (slope).
Correct answer is: Y = a + bX
Q.3 In regression analysis, the term 'residual' refers to:
The predicted value of Y
The difference between actual and predicted Y
The independent variable
The slope of the regression line
Explanation - Residuals measure the error in prediction; it is the difference between the observed value and the value predicted by the regression model.
Correct answer is: The difference between actual and predicted Y
Q.4 If the correlation coefficient between X and Y is 0, the regression coefficient b is:
0
1
Undefined
Equal to Y mean
Explanation - The regression coefficient b = r * (Sy/Sx). If r = 0, then b = 0, meaning no linear relationship.
Correct answer is: 0
Q.5 Which method is commonly used to estimate regression coefficients?
Least Squares Method
Maximum Likelihood
Bayesian Estimation
Chi-Square Method
Explanation - The least squares method minimizes the sum of squared differences between observed and predicted values to find regression coefficients.
Correct answer is: Least Squares Method
Q.6 What does the slope (b) in regression indicate?
Rate of change in Y with respect to X
Average value of Y
Sum of X values
Intercept with Y-axis
Explanation - The slope shows how much Y changes for a unit change in X.
Correct answer is: Rate of change in Y with respect to X
Q.7 Which of the following is true about the coefficient of determination (R²)?
It measures the proportion of variance in Y explained by X
It is always negative
It is the slope of the regression line
It equals the residual sum of squares
Explanation - R² shows how well the regression model explains the variability of the dependent variable.
Correct answer is: It measures the proportion of variance in Y explained by X
Q.8 Multiple regression analysis is used when:
There is more than one independent variable
There is more than one dependent variable
Variables are categorical
Variables are qualitative
Explanation - Multiple regression predicts the dependent variable using two or more independent variables.
Correct answer is: There is more than one independent variable
Q.9 Which assumption is necessary for linear regression?
Errors are normally distributed
Y is always positive
X and Y are categorical
Regression line passes through origin
Explanation - Linear regression assumes residuals (errors) are normally distributed with mean zero and constant variance.
Correct answer is: Errors are normally distributed
Q.10 If the slope of a regression line is negative, it indicates:
Y decreases as X increases
Y increases as X increases
No relationship between X and Y
Y is constant
Explanation - A negative slope means an inverse relationship between X and Y.
Correct answer is: Y decreases as X increases
Q.11 In regression analysis, what is the intercept (a) represent?
Value of Y when X = 0
Value of X when Y = 0
Slope of the line
Residual error
Explanation - The intercept is the point where the regression line crosses the Y-axis.
Correct answer is: Value of Y when X = 0
Q.12 What type of variable is usually dependent in regression?
Quantitative variable
Categorical variable
Ordinal variable
Nominal variable
Explanation - Regression analysis typically predicts numeric (quantitative) dependent variables.
Correct answer is: Quantitative variable
Q.13 In regression analysis, the term 'prediction error' is also known as:
Residual
Slope
Intercept
Correlation
Explanation - Residuals are the differences between observed and predicted values, representing prediction error.
Correct answer is: Residual
Q.14 Which of the following can invalidate a linear regression model?
Non-linearity of relationship
Linearity of relationship
Low variance in X
High sample size
Explanation - If the relationship between X and Y is not linear, linear regression assumptions are violated.
Correct answer is: Non-linearity of relationship
Q.15 The regression coefficient is zero when:
There is no linear relationship between X and Y
X and Y are perfectly correlated
Residuals are zero
Y is constant
Explanation - If there is no linear correlation, the slope (regression coefficient) becomes zero.
Correct answer is: There is no linear relationship between X and Y
Q.16 Which of the following is true about multiple regression?
It uses more than one independent variable
It uses multiple dependent variables
It cannot handle continuous data
It does not require assumptions
Explanation - Multiple regression involves two or more predictors to model a single dependent variable.
Correct answer is: It uses more than one independent variable
Q.17 In regression analysis, multicollinearity refers to:
High correlation among independent variables
High correlation between X and Y
Large residual errors
Small sample size
Explanation - Multicollinearity occurs when independent variables are highly correlated, making coefficient estimation unreliable.
Correct answer is: High correlation among independent variables
Q.18 The line of best fit in regression minimizes:
Sum of squared residuals
Sum of X values
Mean of Y
Correlation coefficient
Explanation - Least squares regression finds the line that minimizes the sum of squared differences between observed and predicted values.
Correct answer is: Sum of squared residuals
Q.19 What is extrapolation in regression?
Predicting Y for X outside the observed range
Predicting Y within observed X values
Estimating slope
Finding correlation
Explanation - Extrapolation involves predicting values beyond the range of data, which can be less reliable.
Correct answer is: Predicting Y for X outside the observed range
Q.20 Which of the following is NOT an assumption of linear regression?
Errors have zero mean
Errors are homoscedastic
X and Y are categorical
Errors are independent
Explanation - Linear regression assumes continuous variables; categorical data may require other methods like logistic regression.
Correct answer is: X and Y are categorical
Q.21 In simple linear regression, if b = 0.5, what does it mean?
Y increases by 0.5 units for 1 unit increase in X
Y decreases by 0.5 units for 1 unit increase in X
Y remains constant
X increases by 0.5 units for 1 unit increase in Y
Explanation - The slope (b) represents the change in Y for a unit change in X.
Correct answer is: Y increases by 0.5 units for 1 unit increase in X
Q.22 Which of the following best describes simple linear regression?
One dependent and one independent variable
Multiple dependent variables
No dependent variable
Only categorical variables
Explanation - Simple linear regression models a single dependent variable as a function of one independent variable.
Correct answer is: One dependent and one independent variable
Q.23 What is the effect of outliers on regression analysis?
They can disproportionately affect the slope and intercept
They have no effect
They reduce sample size
They increase R² always
Explanation - Outliers can skew the regression line and affect predictions, making the model less reliable.
Correct answer is: They can disproportionately affect the slope and intercept
Q.24 Which of the following statements is true about residuals in regression?
They should have constant variance
They should increase with X
They are independent of model assumptions
They equal predicted Y
Explanation - Homoscedasticity means residuals should have constant variance across all values of X.
Correct answer is: They should have constant variance