MATH 302 STATISTICS Week 7 Test Prep Knowledge Check Homework Practice Questions and Answers

Week 7 Knowledge Check Homework Practice Questions Part 1 of 9 - Linear Regression and Correlation Question 1 of 20 Due to erosion, a river shoreline is losing several thousand pounds of soil each year. A linear equation that expresses the total amount of soil lost per year is y = 12,000x. How many pounds of soil does the shoreline lose in a year? Round to a whole number. Don't use any commas or decimals. Answer: 12000 Answer Key: 12000 Feedback: The slope is 12,000. The change in the slope impacts the linear equation. Since the slope is 12,000 and this is the change in the line, the shoreline will lose 12,000 pounds of soil each year. Question 2 of 20 Which of the following equations are linear? • A. 4y=8 • B. y2=6x3+8 • C. 3y=6x+5y2 • D. y-x=8x2 Answer Key: A Feedback: A linear equation is a linear line. If a problem has a squared or a cubed term, it isn't linear. It is a quadratic equation. Part 2 of 9 - Multiple Linear Regression Question 3 of 20 You move out into the country and you notice every Spring there are more and more Deer Fawns that appear. You decide to try and predict how many Fawns there will be for the up coming Spring. You collect data to, to help estimate Fawn Count for the upcoming Spring season. You collect data on over the past 10 years. x1 = Adult Deer Count x2 = Annual Rain in Inches x3 = Winter Severity • Where Winter Severity Index: o 1 = Warm o 2 = Mild o 3 = Cold o 4 = Freeze o 5 = Severe Find the estimated regression equation which can be used to estimate Fawn Count when using these 3 variables are predictor variables. See Attached Excel for Data. Deer 10 KB • A. Fawn Count = -5.5591 + 0.3071(Adult Count) + 0.3978(Annual Rain) + 0.2493(Winter Severity) • B. Fawn Count = -6.4320 + 3.5626(Adult Count) + 4.3813(Annual Rain) + 4.3878(Winter Severity) • C. Fawn Count = 0.9661 + 0.9886(Adult Count) + 0.9774(Annual Rain) + 0.1105(Winter Severity) • D. Fawn Count = 0.8643 + 0.0853(Adult Count) + 0.0908(Annual Rain) + 0.0568(Winter Severity) Answer Key: A Feedback: You can run a Multiple Linear Regression Analysis using the Data Analysis ToolPak in Excel. Data - Data Analysis - Scroll to Regression Highlight Fawn Count for the Y Input: Highlight columns Adult Count to Winter Severity for the X Input: Make sure you click on Labels and Click OK If done correctly then you look under the Coefficients for the values to write out the Regression Equation Coefficients Intercept -5. Adult Count 0. Annual Rain in Inches 0. Winter Severity 0. Fawn Count = -5.5591 + 0.3071(Adult Count) + 0.3978(Annual Rain) + 0.2493(Winter Severity) Question 4 of 20 You are thinking about opening up a Starbucks in your area but what to know if it is a good investment. How much money do Starbucks actually make in a year? You collect data to help estimate Annual Net Sales, in thousands, of dollars to know how much money you will be making? You collect data on 27 stores to help make your decision. 1 = Rent in Thousand per month x2 = Amount spent on Inventory in Thousand per month x3 = Amount spent on Advertising in Thousand per month x4 = Sales in Thousand per month x5= How many Competitors stores are in the Area Estimate the Annual Net Sales of a Starbucks when Rent = 2.5, Inventory = 430, Advertising =7.75, Sales = 9.89 and Number of Competitors = 8. See Attached Excel for Data. Starbuck Sales 9 KB • A. 280.81 • B. 274.65 • C. 275.79 • D. 270.77 Answer Key: C Feedback: You can run a Multiple Linear Regression in Excel using the Data Analysis ToolPak. Data - Data Analysis - Scroll to Regression Highlight Annual Net Sales for the Y Input: Highlight all 5 columns from Rent to Competitor for the X Input: Make sure you click on Labels and Click OK If done correctly then you look under the Coefficients for the values to write out the Regression Equation Coefficients Intercept -49. Rent/$1000 15. Inventory/$1000 0. Advertising/$1000 12. Sales per month /$1000 14. # Competior Stores in Area -2. Annual Net Sales = -49.0449 + 15.1571(Rent) + 0.1744(Inventory) + 12.1779(Advertising) + 14.2972(Sales) - 2.9766(Competitor) Plug in, Rent = 2.5, Inventory = 430, Advertising = 7.75, Sales = 9.89 and Number of Competitors = 8 Annual Net Sales = -49.0449 + 15.1571(2.5) + 0.1744(430) + 12.1779(7.75) + 14.2972(9.89) - 2.9766(8)