Final answer:
To find the implied regression coefficients in PCR, perform PCA on predictors, use the principal components in a regression model, and calculate the coefficients. Interpret the coefficient of determination and check residuals for outliers.
Step-by-step explanation:
To find the implied regression coefficients in Principal Component Regression (PCR), you must first perform a Principal Component Analysis (PCA) on the predictor variables to obtain the principal components. Then, you use these principal components as predictors in a linear regression model. Here's a step-by-step explanation:
- Standardize the predictor variables if they are on different scales.
- Carry out PCA on the standardized variables to obtain the principal components.
- Select a number of principal components based on their eigenvalues or the cumulative variance they explain.
- Use the selected principal components as new predictor variables in a linear regression model instead of the original data.
- Calculate the regression coefficients for these principal components.
- Transform these coefficients back to the original variable space, if required, to interpret them in terms of the original variables.
Additionally, you should calculate and interpret the coefficient of determination (R-squared), which explains the proportion of the variance in the dependent variable that is predictable from the independent variables (principal components in this case). To check for outliers, you can analyze the residuals from your regression model and identify any points that do not fit well with the regression model.