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HW 8  MA 303 December 3, 2021  1

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HW 8 
MA 303 December 3, 2021 
1. Open the shared Sheets file .2020 NFL data". Use the variables x = points for/points allowed, and y = wins/losses. Add columns for your x and y. 
a) Define a parameter r. Put in an original guess for r that you think could best fit the data to y = e. 
b) Add a column for the power fit model's predicted y for each NFL teams win/loss ration, x. 
c) Add another column with the squared error between each teams predicted win/loss ratio and actual win/loss ratio. 
d) Use the Solver command in Excel to estimate the best parameter r that fits the model y = xr to the 2020 data. 
e) Based on our model, if a team has 400 points and 200 points al-lowed, how many games should the team win in a 16 game season? 
f) Based on our model, which team would you expect to improve the most in 2021 (have the greatest increase in wins)? Explain why. 
2. Data is listed below with hours studied and the test score for each student in a class. HoursStudied,x1 0 I 1 I 2 I 4 I 4 I 5 I 5  Test Score, y I 40 I 41 I 51 I 48 I 64 I 69 I 73 Hours Studied, x I 5 I 6 6  II  7 8 93 84 Test Score, y I 75 I 68 90 95 a) Using Sheets, find the line of best of fit (regression line) for the data y = ax + b. Plot the data and the trendline through the data. 
b) Calculate the standard squared error for the regression model. 
b) If you studied 6.5 hours, what would be the predicted test score? 
3. Open the shared Google Sheet "Heart Disease". Make a copy for yourself. The data has information on towns with their biking rates(xj), smoking rates(x2), and heart disease rates (y). We will create a multiple regression model for heart disease rates based on smoking rates and biking rates: 
y = wisi + w2x2 + b 
a) Before you begin creating the multiple regression equation, decide whether wi and w2 should be positive or negative. Explain why. 
b) Use the XL Miner Analysis ToolPak in Sheets to find the multiple re-gression equation. Are the coefficients the sign you thought they'd be? 
c) Use the regression equation to predict the heart disease rates in Allaire-vile, where 4% of the residents bike, and 10% of the residents smoke. 
d) What other independent variables might give as a better predictive model? Explain why.