ÐÏà¡±á>þÿ =?þÿÿÿ<}ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿì¥Á[à ø¿h$bjbj ægpa!\pa!\hÿÿÿÿÿÿ·¤¤ÿÿÿÿ00004d\0 14À$ääääÛÛÛŸ0¡0¡0¡0¡0¡0¡0$T2¶ 5‚Å0:AšÛ::Å0ää]Ú0’ ’ ’ :ääŸ0’ :Ÿ0’ ’ ž-˜?0äÿÿÿÿ€«.ÕîÏÿÿÿÿPî¯/H‹0ð00 1÷/HŒ5>*Œ5?0Œ5?0LÛL'6’ ],‰±ÛÛÛÅ0Å0h*ÛÛÛ 1::::ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿŒ5ÛÛÛÛÛÛÛÛÛ¤>â: AP Statistics Ch 6-8 Review Name ___________________________________________________ Part I - Multiple Choice (Questions 1-10) - Circle the answer of your choice. Foresters use regression to predict the volume of timber in a tree using easily measured quantities such as diameter. Let y be the volume of timber in cubic feet and x be the diameter in feet (measured at 3 feet above ground level). One set of data gives y = -30 +60x. The predicted volume for a tree of 18 inches is: 1050 cubic feet 600 cubic feet 105 cubic feet 90 cubic feet 60 cubic feet Consider the following scatterplot of midterm and final exam scores for a class of 15 students. Which of the following are true statements? The same number of students scored 100 on the midterm exam as scored 100 on the final exam. Students who scored higher on the midterm exam tended to score higher on the final exam. The scatterplot shows a moderate negative correlation between midterm and final exam scores. I and II I and III II and III I, II, and III None of the above gives the complete set of complete true responses. Data are obtained for a group of college freshman examining their SAT scores (math plus verbal) from their senior year of high school and their GPAs during their first year of college. The resulting regression equation is: EMBED Equation.DSMT4 with EMBED Equation.DSMT4 , and EMBED Equation.DSMT4 What percentage of the variation in GPAs can be explained by looking at SAT scores? 0.161% 16.1% 39.9% 63.2% This value cannot be computed from the information given. Suppose the correlation between two variables is r = 0.23. What will the new correlation be if 0.14 is added to all values of the x-variable, every value of the y-variable is doubled, and the two variables are interchanged? 0.23 0.37 0.74 -0.23 -0.74 Given the least-squares regression line: [Cost of a Monopoly Property] = 67.3 + 6.78 * [Spaces From GO], determine the residual for Reading Railroad which costs $200 and is 5 spaces from GO. –98.8 –9.88 98.8 –1418.3 A residual has no meaning since one of the variables is categorical. A study of the fuel economy for various automobiles plotted the fuel consumption (in liters of gasoline used per 100 kilometers traveled) vs. speed (in kilometers per hour). A least-squares regression line was fitted to the data and the residual plot is displayed to The right. What does the pattern of the residuals tell you about the linear model? The evidence is inconclusive. The residual plot confirms the linearity of the data. The residual plot suggests a different line would be more appropriate. The residual plot clearly contradicts the linearity of the data. None of the above. The coefficient of determination of the data described in the scatterplot is: 0.35 0.65 -0.80 0.88 use the calculator to determine. 0 With regard to regression, which of the following statements about outliers are true? Outliers have large residuals. A point may not affect the regression equation even though its x-value is displaced in the x-direction and its y-value is an outlier in the y direction. Removal of an outlier affects the regression line in a meaningful way. I and II I and III II and III I, II, and III None of the above gives the complete set of true responses. As reported in the Journal of the American Medical Association (June 13, 1990), for a study of ten nonagenarians, the following tabulation shows a measure of strength versus a measure of functional mobility Strength (kg)7.5611.510.59.51841293Walk time (s)184682525722121048 What does the slope of the least-squares regression line signify? The sign is positive, signifying a direct cause-and-effect relationship between strength and mobility. The sign is positive, signifying that the greater the strength, the greater the functional mobility. The sign is negative, signifying that the relationship between strength and functional mobility is weak. The sign is negative, signifying that the greater the strength, the less the functional mobility. The slope is close to zero, signifying that the relationship between strength and functional mobility is weak. Consider the three points (2,11), (3,17), (and (4,29). Given any straight line, we can calculate the sum of the squares of the three vertical distances from these points to the line. What is the smallest possible value this sum can be? 6 9 29 57 cannot be determined Part II – Free Response (Questions 11-13) – Show your work and explain your results clearly. (a) Find the equation of the least-squares regression line of the data represented in the scatterplot at the right. EMBED Equation.DSMT4 Use the calculator to determine the LSRL equation. Draw in the LSRL on the scatterplot using two points on either extreme of the scatterplot. Record these points below. Plot (0, 1.5) and (5, 4), then draw LSRL Calculate r and EMBED Equation.DSMT4 . What does EMBED Equation.DSMT4 describe? r = .5, r2 = .25 25 percent of the variation in the y – variable is explained by the variation in the x – variable. An analysis of the relationship between the number of telephones in a household (x) and the annual family income(y) revealed the following statistics: EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 Determine the least-squares regression line. EMBED Equation.DSMT4 (b) Determine coefficient of determination. Explain what this index means. EMBED Equation.DSMT4 r2 = .4225 42.25% of the variation in annual family income is explained by the variation in the number of telephones in the household.. 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. EMBED Equation.DSMT4 r = 0.88 (a) Is a line an appropriate model to use for these data? What information tells you this? A straight line model is appropriate because there is a random pattern of residuals in the plot. There is no curved pattern. (b) What is the value of the slope of the least squares regression line? Interpret the slope in the context of this situation. b = slope = 233.517 There is an increase of 233.517 flights for each year from 1990, on average. (c) What is the value of the intercept of the least squares regression line? Interpret the intercept in the context of this situation. y – intercept = 2939.93 The model predicts 2939.93 flights occurring in 1990. (d) What is the predicted number of commercial aircraft flying in 1992? (2, 3406.964) or 3407 flights. What was the actual number of commercial aircraft flying in 1992? The residual at 2 (1992) is 40, so….. 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