For Problem 1, open a new spreadsheet and put the usual heading on it. On the Baseball.xlsx sheet copy columns a through f and place them on your new spreadsheet. Delete columns b, d and e. Make columns a through l a width of 15 units. On d5, put your hypothesis, namely Ho: ρ = 0, no significant correlation Ha: ρ ≠ 0, significant correlation α = .05 (ρ is the small Greek letter rho, the population parameter for Pearson’s Product Moment Correlation Coefficient, for a sample we use r.) Now go to the ribbon and click on “Data” and go to “Data Analysis” and highlight “Regression”. The y-values—the response variable—are the wins column, and the x-values—the explanatory variable—are the runs. We are determining if runs are correlated with wins. If you included the titles, check the “labels” box. Check the “output” box and put in d8. Initiate. Excel will provide many statistics for us to utilize. We are only looking for the p-value for runs. Compare this to α. Write your conclusion in statistical language and write the regression equation in the cell beneath it. Excel provide the equation in slope/intercept form with the coefficient of the equation under “coefficients”. You will have an equation that looks like mx + b = y-hat. The slope m is the coefficient of runs and b, the y intercept, is the coefficient of wins. To find the correlation coefficient for this data to the ribbon and click on “Data” and go to “Data Analysis” and highlight “correlation”. The input is g8:h38. Your output may be g8. Initiate. The decimal you see next to runs is the correlation coefficient, which by itself can only have significance if we know the number in our sample, which we do, and examining a Pearson’s table. The coefficient of determination is this value squared and tells us how good a predictor of wins that runs will be. Lastly, put 800 runs into the regression equation and estimate the number of wins a team would have. In Problem 2, we will use the same procedures. Namely, open a new spreadsheet by going to the bottom left of the one you already created and pressing the + sign. Set up the widths of the columns like on the last problem. On the Baseball.xlsx sheet copy columns a through w starting on a5. Keep columns a, c and w, delete the rest. On d5 write your hypothesis, the same one as the last problem. Perform a regression analysis like the last problem with the results on d8. You have the information you need to answer the problems. Do not forget to find the correlation coefficient and the coefficient of determination. For Problem 3, we are going to take a short-cut. A complete step-wise procedure would require us to add and subtract one variable at a time, compare each regression equation determining significant variables and then repeating the process for additional values until we obtained the variables that are most significant. We will do this entire process using just one step. Open a new spreadsheet and copy the Baseball.xlsx sheet onto it starting in cell a5. Delete the column of variables that are not asked for in finding the predicted wins for the variables given. This should fill columns a through i. Perform a regression analysis, making sure you sweep your row including the labels; i.e., row 5 and put your output on a37. Then, looking at the p-values, you will see that the only significant variables are runs and ERA, at an α equal to .05. So, if you were a recruiter, you would concentrate on obtaining a great pitcher and players that score runs. Write the regression equation on a62. On a64 make a prediction with the given data. Great fun don’t you think?