GRR NEAR REGRESSION Name: INSTRUCTIONS; |. DO ALL THE ACTIVITIES AND TASKS AND ALSO ANSWER ALL THE QUESTIONS IN THIS PROJECT on separate sheets of paper. You may altach these sheets as your 'cover pages\". 2. While all the activities and tasks in this project require the use of Microsoft EXCEL, you are to copy and/or print your work and attach ALL to this project sheets. 3. This Project is DUE in elass on Friday, October 17%, 2025. 4. WRITE YOUR OWN WORK AND DO NOT COPY FROM OTHERS'! 5. In this project you will: * Explore and learn about linear regression and its link to linear function and graphing. Find a regression line and plot it on a seatterplot. * Examine the effect of \"outliers\" on the regression line. Use the regression line to make predictions and evaluate how reliable these predictions are. In real-world applications we often encounter numerical data in the form ofa table. The powerful mathematical tool Regression Analysis is a process for finding a function that provides a useful model for a set of data points. One uses computer software to create a graph (a scatter plot) of the set of points and find the function of best fit. The function can then be used to predict values of the dependent variable y for any given value of the independent variable x. Let's try the following example before starting the assignment. TASK 1: Study this Example Prices for round-shaped diamonds taken from an online trader are given in TABLE | below. Weight is the independent variable x and price is the dependent variable y. We will analyze this data in the computer. TABLE 1. Prices for round-shaped diamonds Weight (carats) Price (8) 0.5 27900 0.6 3191 0.7 3694 0. ALA 09 5018 Lo 5898 For Excel, enter chart into the Help menu to find out how to create charts, and enter trend into the Help menu to find detailed instructions on creating and manipulating trendlines for data series. In Excel, you can adjust the precision in the trendline equations by clicking on the trendline equation. Enter the data into a spreadsheet (including the header Weight and Price). Create a scatter plot of the data. Note that the scatter plot for this data appears roughly linear. Compute the linear regression equation( trendline). The trendline will be y = ax + 5 for some values of a and 5. Adjust the minimum/maximum values on the axes of the graph to 0.4 and 1.2 for the weight and 2000 and 6500 for the price to make the graph look nice. AP FP A sample of the output created on (Mac) Numbers is given below. The regression equation y = 6137.4x 478.9 is on the graph. To predict the price of a diamond weighing 0.85 carats, calculate price by plugging in x = 0.85 into the regression equation y= 6137.4(0.85) 478.9 = $4737.89. Diamond Prices for round-shaped diamonds Weight Price (5) Diamond prices (carats) OS $2,790.00 A y = 6137.4x - 478.9 oe $3,191.00 + OF $9,694.00 og $4,154.00 $5,375.00 og $5,018.00 1.0 $5,898.00 $4,250.00 + $3,125.00 $2,000.00 $A A O4 0.6 OB 1 12 + Weight (carats) = Price Pradicted price for 0.85 carat diamond: '$4,737.89 TASK 2: Analysis 1 'Complete the following exercises in Excel or similar software. Save your work often. Your work can be submitted any time before the due date. TABLE 2 contains price-supply data and price-demand data for soybeans: * Enter the data into a spreadsheet. = Create the scatter plots for the price-supply, where x is the supply (in billions of bushels) and y is the price (in dollars). De the same for price-demand. * Adjust the minimum and maximum of the axes of each plot to slightly below and slightly above the data values. * Compute the regression equations for supply and for demand using linear regression on each of the plots. The trendline will be = ax + for some values of a and 6. Round a and b two 3 decimal places. * Use the trendlines to find the equilibrium price for soybeans. (Hint: The supply model will be an increasing linear function. The price model will be a decreasing linear function. Set the two equations equal to each other and solve for the equilibrium value x, and then find the corresponding value for y equilibrium price.) TABLE 2. Supply and demand for soybeans. Supply (billion bu) Price ($/bu) Demand (billion bu) 2.60 2.40 2.18 2.05 1.95 LBS 1.55 1.86 NOTE: Refer to hups://www.ablebits.com/office-addins-blog/linear-regression-analysis-excel/ for a great tutorial on \"Linear regression analysis in Excel\