R Linear Model

How can you fit a simple linear regression model in R using the lm() function if 'y' is the response variable and 'x' is the predictor variable?

• lm(y ~ x)

• linear(y, x)

• fit.model(y, x)

• regression(y, x)

What does the 'summary()' function display when applied to the result of a linear model fit in R?

• Coefficients and p-values

• Model formula and data summary

• Confidence intervals for predictors

• Residuals and fitted values

In a multiple linear regression model, how do you include both 'x1' and 'x2' as predictors?

• lm(y ~ x1/x2)

• lm(y ~ x1 * x2)

• lm(y ~ cbind(x1, x2))

• lm(y ~ x1 + x2)

In a linear regression model in R, what does the term "residuals" refer to?

• Predicted values

• Differences between observed and predicted values

• Coefficients of the model

• Sum squares error (SSE)

What is the purpose of the 'anova()' function in the context of linear models in R?

• Computes analysis of variance for the residuals

• Performs analysis of variance for predictor variables

• Conducts analysis of variance for the entire model

• Calculates the average of residuals

When interpreting the coefficients of a linear regression model in R, what does a negative coefficient indicate?

• A negative relationship between the predictor and the response variable

• A positive relationship between the predictor and the response variable

• No relationship between the predictor and the response variable

• An error in the model

What is the purpose of the 'predict()' function when working with linear regression models in R?

• To calculate the residuals of the model

• To make predictions using the model

• To calculate the coefficients of the model

• To calculate the analysis of variance for the model

How can you include interaction terms in a linear regression model in R?

• lm(y ~ x1/x2)

• lm(y ~ x1 * x2)

• lm(y ~ x1 + x2 + x1:x2)

• Both B and C are correct

What does the 'confint()' function display when applied to the result of a linear model fit in R?

• Coefficient estimates and their confidence intervals

• Model formula and data summary

• Residuals and fitted values

• Analysis of variance table

How can you include fit a second-order model (i.e., a model with the squared term of 'X')?

• lm(Y ~ X^2)

• lm(Y ~ X + X^2)

• lm(Y ~ X + I(X^2))

• All are correct