Q. In a linear regression model, what does a negative coefficient for an independent variable indicate?
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A.
A positive relationship with the dependent variable
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B.
No relationship with the dependent variable
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C.
A negative relationship with the dependent variable
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D.
The variable is not significant
Solution
A negative coefficient indicates that as the independent variable increases, the dependent variable tends to decrease.
Correct Answer:
C
— A negative relationship with the dependent variable
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Q. In linear regression, what does the term 'residual' refer to?
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A.
The predicted value of the dependent variable
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B.
The difference between the observed and predicted values
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C.
The slope of the regression line
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D.
The intercept of the regression line
Solution
A residual is the difference between the observed value and the predicted value in a regression model.
Correct Answer:
B
— The difference between the observed and predicted values
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Q. In the context of linear regression, what does the term 'homoscedasticity' refer to?
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A.
Constant variance of the residuals
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B.
Normal distribution of the errors
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C.
Independence of observations
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D.
Linearity of the relationship
Solution
Homoscedasticity refers to the condition where the variance of the residuals is constant across all levels of the independent variable.
Correct Answer:
A
— Constant variance of the residuals
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Q. What does the R-squared value indicate in a linear regression model?
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A.
The proportion of variance explained by the model
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B.
The slope of the regression line
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C.
The number of predictors in the model
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D.
The correlation between independent variables
Solution
R-squared indicates the proportion of variance in the dependent variable that can be explained by the independent variables.
Correct Answer:
A
— The proportion of variance explained by the model
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Q. What is the effect of adding more predictors to a linear regression model?
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A.
Always improves model accuracy
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B.
Can lead to overfitting
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C.
Reduces the complexity of the model
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D.
Eliminates multicollinearity
Solution
Adding more predictors can lead to overfitting, especially if the additional predictors do not contribute meaningful information.
Correct Answer:
B
— Can lead to overfitting
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Q. What is the primary assumption of linear regression regarding the relationship between the independent and dependent variables?
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A.
The relationship is quadratic
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B.
The relationship is linear
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C.
The relationship is exponential
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D.
The relationship is logarithmic
Solution
Linear regression assumes a linear relationship between the independent and dependent variables.
Correct Answer:
B
— The relationship is linear
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Q. What is the purpose of the F-test in the context of linear regression?
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A.
To test the significance of individual predictors
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B.
To test the overall significance of the regression model
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C.
To assess the normality of residuals
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D.
To evaluate multicollinearity
Solution
The F-test is used to determine the overall significance of the regression model.
Correct Answer:
B
— To test the overall significance of the regression model
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Q. Which of the following techniques can be used to address overfitting in linear regression?
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A.
Increasing the number of features
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B.
Using regularization techniques like Lasso or Ridge
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C.
Decreasing the size of the training dataset
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D.
Ignoring outliers
Solution
Regularization techniques like Lasso or Ridge can help to reduce overfitting in linear regression models.
Correct Answer:
B
— Using regularization techniques like Lasso or Ridge
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