9-3 Textbook Assignment: Homework Problems

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Mathematics

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Complete the Chapter 14 textbook homework assigned by your instructor. Please check the announcements area for information on this assignment.

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Chapter 14 14-10. Amazon.com has become one of the most successful online merchants. Two measures of its successful sales and net income/loss figures (all figures in $million). These values for the years 1995-2007 are shown as follows. Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 Net Income/Loss -0.3 -5.7 -27.5 -124.5 -719.9 -1,411.2 -567.3 -149.1 35.3 588.5 359 190 476 Sales 0.5 15.7 147.7 609.8 1639.8 2,761.9 3,122.9 3,933 5,263.7 6,921 8,490 10,711 14,835 a. Produce a scatter plot for Amazon’s net income/loss and sales figures for the period 1995 to 2007. Does there appear to be a linear relationship between these two variables? Explain your response. b. Calculate the correlation coefficient between Amazon’s net income/loss and sales figures for the period 1995 to 2007. c. Conduct a hypothesis test to determine if a positive correlation exists between Amazon’s net income/loss and sales figures. Use a significance level of 0.05 and assume that these figures form a random sample. 14-18. You given the following sample data for variables x and y: x (independent) 1 7 3 8 11 5 4 y (dependent) 16 50 22 59 63 46 43 a. Construct a scatter plot for these data and describe what, if any, relationship appears to exist. b. Compute the regression equation based on these sample data and interpret the regression coefficients. c. Based on the sample data, what percentage of the total variation in the dependent variable can be explained by the independent variable? d. Test the significance of the overall regression model using a significance level of 0.01. e. Test to determine whether the true regression slope coefficient is equal to 0. Use a significance level of 0.01. 14-20. Consider the following sample data for the variables y and x: x y 30.3 14.6 4.8 27.9 15.2 17.6 24.9 15.3 8.6 19.8 20.1 13.2 a. Calculate the linear regression equation for these data. b. Determine the predicted y-value when x =10. 9.3 25.6 11.2 19.4 c. Estimate the change in the y variable resulting from the increase in the x variable of 10 units. d. Conduct a hypothesis test to determine if an increase of 1 unit in the x variable will result in the decrease of the average value of the y variable. Use a significance of 0.025. 14.34. You are given the following sample data: x 10 6 9 3 2 8 3 y 3 7 3 8 9 5 7 a. Develop a scatter plot for these data. b. Determine the regression equation for the data. c. Develop a 95% confidence interval estimate for the true regression slope and interpret this interval estimate. d. Provide a 95% prediction interval estimate for a particular y, given 𝑥𝑝 = 7.
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