Final answer:
The question asks for the regression equation, Pearson correlation, SS residual, and standard error of the estimate. These statistics are found through linear regression analysis and understanding the relationships among the regression line, coefficient of determination, and Pearson correlation coefficient.
Step-by-step explanation:
The question involves finding the regression equation for predicting y from x, calculating the Pearson correlation, and using r² and SSY to compute SS residual and the standard error of estimate. To answer this question, we need to use statistical methods including linear regression analysis and understanding of the correlation coefficient and coefficients of determination.
The least-squares regression line is the best-fit line that minimizes the sum of the squared errors (SSE). The coefficient of determination, r², when expressed as a percentage, indicates the percentage of variation in the dependent variable y that can be explained by variation in the independent variable x using the regression line. The Pearson correlation coefficient, r, ranges from -1 to +1 and measures the strength of the linear relationship between x and y.
If we had a situation where a regression equation is given along with its correlation coefficient, as seen in the provided options, we could calculate the residual sum of squares (SS residual) by first obtaining the coefficient of determination (r²) from the correlation coefficient (r), then multiplying this by SSY to arrive at the SSE. Using the SSE, we can further determine the standard error of the estimate (SE).
.