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CHAPTER 8 Curve Fitting, Regression, and Correlation
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Generalized correlation coefficient
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8.83. Find the standard error of estimate of z on x and y for the data of Problem 8.71. 8.84. Compute the coefficient of multiple correlation for the data of Problem 8.71.
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Rank correlation
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8.85. Two judges in a contest, who were asked to rank 8 candidates, A, B, C, D, E, F, G, and H, in order of their preference, submitted the choice shown in Table 8-40. Find the coefficient of rank correlation and decide how well the judges agreed in their choices. Table 8-40 Candidate First Judge Second Judge A 5 4 B 2 5 C 8 7 D 1 3 E 4 2 F 6 8 G 3 1 H 7 6
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8.86. Find the coefficient of rank correlation for the data of (a) Problem 8.67, (b) Problem 8.76. 8.87. Find the coefficient of rank correlation for the data of Problem 8.82.
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Sampling theory of regression
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8.88. On the basis of a sample of size 27 a regression equation y on x was found to be y 25.0 2.00x. If sy.x 1.50, sx 3.00, and x 7.50, find (a) 95%, (b) 99%, confidence limits for the regression coefficient. # 8.89. In Problem 8.88 test the hypothesis that the population regression coefficient is (a) as low as 1.70, (b) as high as 2.20, at a 0.01 level of significance. 8.90. In Problem 8.88 find (a) 95%, (b) 99%, confidence limits for y when x 6.00.
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8.91. In Problem 8.88 find (a) 95%, (b) 99%, confidence limits for the mean of all values of y corresponding to x 6.00. 8.92. Referring to Problem 8.76, find 95% confidence limits for (a) the regression coefficient of y on x, (b) the blood pressures of all women who are 45 years old, (c) the mean of the blood pressures of all women who are 45 years old.
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8.93. A correlation coefficient based on a sample of size 27 was computed to be 0.40. Can we conclude at a significance level of (a) 0.05, (b) 0.01, that the corresponding population correlation coefficient is significantly greater than zero 8.94. A correlation coefficient based on a sample of size 35 was computed to be 0.50. Can we reject the hypothesis that the population correlation coefficient is (a) as small as r 0.30, (b) as large as r 0.70, using a 0.05 significance level 8.95. Find (a) 95%, (b) 99%, confidence limits for a correlation coefficient that is computed to be 0.60 from a sample of size 28.
CHAPTER 8 Curve Fitting, Regression, and Correlation
8.96. Work Problem 8.95 if the sample size is 52. 8.97. Find 95% confidence limits for the correlation coefficient computed in Problem 8.76.
8.98. Two correlation coefficients obtained from samples of sizes 23 and 28 were computed to be 0.80 and 0.95, respectively. Can we conclude at a level of (a) 0.05, (b) 0.01, that there is a significant difference between the two coefficients
Miscellaneous results
8.99. The sample least-squares regression lines for a set of data involving X and Y are given by 2x 5x 8y 2. Find the linear correlation coefficient. 5y 3,
8.100. Find the correlation coefficient between the heights and weights of 300 adult males in the United States as given in the Table 8-41. Table 8-41 HEIGHTS x (inches) 59 62 90 109 WEIGHTS y (pounds) 110 129 130 149 150 169 170 189 190 209 210 229 2 7 5 2 63 66 1 8 15 12 7 2 4 22 63 28 10 1 2 7 19 32 20 4 1 5 12 7 2 67 70 71 74 75 78
8.101. (a) Find the least-squares regression line of y on x for the data of Problem 8.100. (b) Estimate the weights of two men whose heights are 64 and 72 inches, respectively. 8.102. Find (a) sy.x, (b) sx.y for the data of Problem 8.100. 8.103. Find 95% confidence limits for the correlation coefficient computed in Problem 8.100. 8.104. Find the correlation coefficient between U.S. consumer price indexes and wholesale price indexes for all commodities as shown in Table 8-42. The base period 1947 1949 100. Table 8-42 Year Consumer Price Index Wholesale Price Index 1949 101.8 99.2 1950 102.8 103.1 1951 111.0 114.8 1952 113.5 111.6 1953 114.4 110.1 1954 114.8 110.3 1955 114.5 110.7 1956 116.2 114.3 1957 120.2 117.6 1958 123.5 119.2