What type of visualization tool is commonly used to initially assess the relationship between two continuous variables in linear regression?
Histogram
Scatter plot
Pie chart
Bar chart
A positive coefficient of the independent variable in a simple linear regression model indicates what?
As the independent variable increases, the dependent variable tends to increase.
The independent variable has no impact on the dependent variable.
There is no relationship between the independent and dependent variables.
As the independent variable increases, the dependent variable tends to decrease.
What does a pattern in the residual plot suggest?
The linear model is not a good fit for the data, and a non-linear model may be more appropriate.
The residuals are normally distributed.
The linear model is a good fit for the data.
What is a potential drawback of using a purely automated feature selection technique (like forward selection or backward elimination) without careful consideration?
It guarantees the most interpretable model.
It can sometimes overlook features that might be important in combination with others.
It can lead to models that are less accurate than using all available features.
It completely eliminates the need for domain expertise in model building.
Which of the following is NOT an assumption of linear regression?
Multicollinearity
Linearity
Normality of residuals
Homoscedasticity
If a Durbin-Watson test statistic is close to 2, what does it suggest about the residuals?
They are independent
They exhibit a linear pattern
They are normally distributed
They are homoscedastic
Which of the following is NOT a benefit of feature selection in linear regression?
Reduced computational cost
Improved model interpretability
Potential for better generalization to new data
Increased risk of overfitting
What does a high R-squared value indicate?
A large proportion of the variance in the dependent variable is explained by the independent variables.
The model is not a good fit for the data.
The independent variables are not correlated with the dependent variable.
The model is a perfect fit for the data.
Which assumption of linear regression ensures that the relationship between the independent and dependent variables is linear?
Normality of errors
Independence
Who is credited with developing the foundational principles of linear regression?
Marie Curie
Sir Francis Galton
Isaac Newton
Albert Einstein