Part 1 In this assignment, you will be working with a very small data set. You need to build a regression from the ground up. I want you to focus on understanding the least-squares method, which is the method used to derive the regression equation/line. Y X 2 4 6 . 11 10 10 Show all your work 1. Getto Microsoft Excel, open HW, parttal, and gatimate the bivirate regression equation Thea+ix Write out the estimated regression equation. That is what are the estimated values of wintercept and the regression coefficient p Meet the merce" and the regression coefficient hok 1 5 6 7 2. Using the regression equation that you estimated previously in [1], predict the value of Y for each observation (i.e., calculate Y^ in column 3 below). Note that in this small dataset, we have five (5) observations. Then calculate the deviation of the actual values of Y (column 2) from the predicted values of Y. This deviation is called the error of the regression (i.e., error =Y-Y^ in column 4). Square these errors and obtain the sum, which we call the error sum of squares (SSE) in column 5. SSE is the sum of the five squared errors in column 5. (6 points) (1) (2) (3) (4) X YA error=Y-YA (5) error (squared errors) 2 1 4 5 6 6 8 7 10 11 SSE = 2 error= Note: Y for each observation is derived by plugging the actual values of X in the regression equation you estimated in [1]. a) What is the value of the error sum of squares (SSE)? b) is it still possible to derive a regression line with SSE = 3.5? Why or Why not? points) (2 points) (2 c) Is it possible to identify a regression line with SSE= 3.7? Why or why not? (2 points) 3. Interpret the R-square (R) of the regression equation you estimated in [1]. That is, what does R say about the explanatory power or strength of the regression model? (2 points) Part 1 In this assignment, you will be working with a very small data set. You need to build a regression from the ground up. I want you to focus on understanding the least-squares method, which is the method used to derive the regression equation/line. Y X 2 4 6 . 11 10 10 Show all your work 1. Getto Microsoft Excel, open HW, parttal, and gatimate the bivirate regression equation Thea+ix Write out the estimated regression equation. That is what are the estimated values of wintercept and the regression coefficient p Meet the merce" and the regression coefficient hok 1 5 6 7 2. Using the regression equation that you estimated previously in [1], predict the value of Y for each observation (i.e., calculate Y^ in column 3 below). Note that in this small dataset, we have five (5) observations. Then calculate the deviation of the actual values of Y (column 2) from the predicted values of Y. This deviation is called the error of the regression (i.e., error =Y-Y^ in column 4). Square these errors and obtain the sum, which we call the error sum of squares (SSE) in column 5. SSE is the sum of the five squared errors in column 5. (6 points) (1) (2) (3) (4) X YA error=Y-YA (5) error (squared errors) 2 1 4 5 6 6 8 7 10 11 SSE = 2 error= Note: Y for each observation is derived by plugging the actual values of X in the regression equation you estimated in [1]. a) What is the value of the error sum of squares (SSE)? b) is it still possible to derive a regression line with SSE = 3.5? Why or Why not? points) (2 points) (2 c) Is it possible to identify a regression line with SSE= 3.7? Why or why not? (2 points) 3. Interpret the R-square (R) of the regression equation you estimated in [1]. That is, what does R say about the explanatory power or strength of the regression model? (2 points)
