Understanding Linear Regression Concepts

What is the general form of the linear regression equation?

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CCSS.8.SP.A.2

• Both are slope coefficients

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CCSS.8.SP.A.2

What is the population regression line in comparison to the least squares line?

• They are the same

• The population regression line represents the true relationship; the least squares line estimates this using observed data

• The least squares line represents the true relationship; the population regression line is an estimate

• The population regression line is more accurate than the least squares line

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CCSS.8.SP.A.2

Which of the following is a key assumption of linear regression?

• The relationship between the variables is quadratic

• The residuals are normally distributed

• The independent variable is categorical

• The dependent variable is binary

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CCSS.HSS.ID.B.6B

In the context of linear regression, what is multicollinearity?

• When the dependent variable is correlated with the error term

• When two or more independent variables are highly correlated

• When the residuals are not normally distributed

• When the model has a high R-squared value

What is the purpose of the least squares method in linear regression?

• To maximize the sum of the residuals

• To minimize the sum of the squared residuals

• To maximize the correlation between variables

• To minimize the number of independent variables

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CCSS.8.SP.A.2

Which of the following is a measure of the goodness of fit in a linear regression model?

• P-value

• R-squared

• T-statistic

• F-statistic

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CCSS.HSS.ID.B.6B

What does a high R-squared value indicate in a linear regression model?

• The model is overfitting the data

• The model explains a large proportion of the variance in the dependent variable

• The independent variables are not significant

• The residuals are not normally distributed

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What is the null hypothesis in the context of testing the significance of a regression coefficient?

• The coefficient is equal to zero

• The coefficient is greater than zero

• The coefficient is less than zero

• The coefficient is equal to one

What is multicollinearity, and why is it a concern in regression?

• It refers to correlation between the response variables.

• It refers to high correlation between predictors, which can inflate variance estimates and affect model interpretation.

• It is when predictors have no relationship to the response variable.

• It refers to errors in the model residuals.

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