A Aa~ Ap v ? = va = v A v DVAv E Styles Styles Dictate Pane AAAEC 2401-01 Fall 2022 Homework 2 Least Squares Regression The due date for this assignment is October 14, 11:59pm. Submit through Blackboard 1) excel file with regression output, correlation coefficient, and scatterplot and 2) word file/scanned picture of your hand calculations and interpretations. There are nine (9) questions in total. PLEASE REMEMBER TO ATTEMPT ALL QUESTIONS. Name Feedlot Cattle Cost of Gain and Mortality - Feedlot mortality measures the percent of cattle that die while in the feedlot. Feedlot mortality is an important factor that affects cost of feeding cattle and cost of gain. Data are shown below for this assignment (from a sample of 20 pens of fed cattle) on feedlot mortality and cost of gain. The objective of the exercise is to estimate a simple regression model to relate cost of gain to mortality. Part 1 (hand calculations): Calculate estimates for the intercept (bo) and slope (bi) of the least-squares regression line with COST of GAIN as the dependent variable (y) and MORTALITY as the independent variable (x). Use hand calculations and show all your work using the following formulas. (Refer to the table in the Homework 2 Practice Problem on Blackboard. You can estimate x2 and x*y in the table using excel but make sure you plug in the numbers in the formulas below by hand). (1) b , Exy - nxy [x2 - n(x)? (2) bo = y -b,x Part 2 (use Excel): Use Excel to estimate a linear regression between the dependent variable, COST, and the independent variable MORTALITY. This can be accomplished by following these steps. In Excel select Data tab, then select Data Analysis from the menu. In the Data Analysis select Regression option. (Refer to Excel Examples folder on Blackboard for a video on how to perform regression in excel). a) Find the least-squares estimates for bo and bi on the Excel output. Write the least-squares regression equation in the form COST = bo + bj * MORTALITY. Check: Do the hand-calculated values for bo and bi from Part 1 match the Excel values from the Excel spreadsheet? - If not, go back and find the mistake in your hand calculations. b) Is it appropriate to interpret the intercept coefficient (bo) in the regression equation? - Why or why not? Interpret bo, if appropriate. Interpret means to write 1 to 2 sentences to c) Interpret the slope coefficient (bi) in your regression equation. explain the item in the question. d) Can you use this model to predict cost of gain when mortality is 2%. If yes, what is the cost of gain? If no, explain why not? e) Can you use this model to predict cost of gain when mortality is 10%? If yes, what is the cost of gain? If no, explain why not? f) Find the coefficient of determination (R') in the Excel output. Interpret R. nited States) Focus OCT 13 o quit tv AADVA v E E E IEV Styles Styles Dictate Pane g) Calculate the correlation coefficient based on the R? value. Then calculate the correlation coefficient using excel using the 'CORREL' function and compare with your original answer. Are the two correlation coefficients identical? Interpret the correlation coefficient. h) Draw a scatterplot with MORTALITY on the x-axis and COST of GAIN on the y-axis. Add the axes titles. What does the plot look like? (Refer to Excel Examples folder on Blackboard for a video on how to plot a scatterplot in excel). This data is also provided in an Excel file. Cost of gain % Pen (S per cwt) Mortality 65.25 2.4 WN- 49.00 0.0 70.50 4.2 62.80 3.5 74.50 5.8 54.90 3.3 69.75 4.6 10 00 71.35 6.1 55.20 2.4 10 64.30 4.3 11 67.00 5.3 12 61.50 4.8 13 75.10 6.1 14 49.85 2.4 15 57.60 4.0 16 62.70 4.3 17 61.00 3.1 18 66.18 5.6 19 48,10 1.1 20 63.30 4.0 Source: Estimating the Effects of Animal Health on the Performance of Feedlot Cattle, by Irsik, Langemeier, Schroeder, Spire, and Roder, The Bovine Practitioner, vol. 40, no. 2, Summer 2006. United States) Focus OCT 13 tv 4