Section 1.3: Simple Linear Regression Model with Distribution of Error Terms Unspecified

1. State the model for simple linear regression when the distribution of the error terms is unspecified except for their means, variances, and covariances.
2. Explain which part of the simple linear regression model is “signal” and which part is “noise.”
3. State the mean and variance of the response in the simple linear regression model.
4. Relate the estimators for the population slope and intercept to the ordinary least squares solutions.

Section 1.6: Estimation of Regression Functions

1. State the ordinary least squares solutions for the slope and intercept of a simple linear regression.
2. Compute the ordinary least squares solutions for the slope and intercept of a simple linear regression given the relevant sample statistics for \(X\) and \(Y\).
3. State the objective function that is minimized to find the ordinary least squares solutions for the slope and intercept.

Section 1.7: Estimation of Error Terms Variance \(\sigma^{2}\)

1. State the estimator for the noise variance \(\sigma^{2}[\epsilon] = \sigma_{\epsilon}^{2}\).

Section 1.8: Normal Error Regression Model

1. Recognize “Gaussian” as a synonym for “normal”.
2. Recognize the acronym “SLRGN” for “simple linear regression with Gaussian noise”
3. State the population parameters of the SLRGN model.
4. Draw a (rough) schematic of the SLRGN model given values for the population parameters.
5. Compute the probability that the response will fall within an interval, given the population parameters of the SLRGN model and a value for the predictor.

R

1. Use lm to fit a simple linear regression.
2. Use makeFun from the mosaic package to turn an output from lm into a callable function.
3. Extract the estimate of the noise variance from an output from lm.
4. Use pnorm to compute probabilites for a Gaussian (“normal”) random variable.