Chapter_3_Packet_Stats

# Part ii free response show your work and explain your

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Part II Free Response (Questions 11-13) Show your work and explain your results clearly. 11. (a) Find the equation of the least-squares regression line of the data represented in the scatterplot at the right. (b) Draw in the LSRL on the scatterplot using two points on either extreme of the scatterplot. Record these points below. (c) Calculate r and 2 r . What does 2 r describe? 12. An analysis of the relationship between the number of telephones in a household (x) and the annual family income(y) revealed the following statistics: 3.8 x 65,000 y 26 n 1.2 x s 15,500 y s 0.65 r (a) Determine the least-squares regression line. (b) Determine coefficient of determination. Explain what this index means. Y 0 1 2 3 4 5 X 0 1 2 3 4 5 Data Scatter Plot

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14 Residuals -50 -30 -10 10 30 50 Years_Since_1990 1 2 3 4 5 6 7 8 9 Aircraft Scatter Plot 13. Lydia and Bob were searching the Internet to find information on air travel in the United States. They found data on the number of commercial aircraft flying in the United States during the years 1990-1998. The dates were recorded as years since 1990. Thus, the year 1990 was recorded as year 0. They fit a least squares regression line to the data. The graph of the residuals and part of the computer output for their regression are given below. ^ 2939.93 233.517 y x r = 0.88 (a) Is a line an appropriate model to use for these data? What information tells you this? (b) What is the value of the slope of the least squares regression line? Interpret the slope in the context of this situation. (c) What is the value of the intercept of the least squares regression line? Interpret the intercept in the context of this situation. (d) What is the predicted number of commercial aircraft flying in 1992? (e) What was the actual number of commercial aircraft flying in 1992?
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