ࡱ> |}tuy q` bjbjqPqP ::`bg8888;;;;8" .<;fv(000w\y\y\y\K\4`4,e$hh kPee;'''Pe8800f'8 0;0w\'w\_ D:;0j c<B &Mf0f kkLk;,`hT PePe^f'''';;;Dd;;;;;;888888 Chapter 10 simple linear regression and correlation (The template for this chapter is: Simple Regression.xls.) 10-1. A statistical model is a set of mathematical formulas and assumptions that describe some real-world situation. 10-2. Steps in statistical model building: 1) Hypothesize a statistical model; 2) Estimate the model parameters; 3) Test the validity of the model; and 4) Use the model. 10-3. Assumptions of the simple linear regression model: 1) A straight-line relationship between X and Y; 2) The values of X are fixed; 3) The regression errors, (, are identically normally distributed random variables, uncorrelated with each other through time. 10-4.  EMBED Equation.3 is the Y-intercept of the regression line, and  EMBED Equation.3  is the slope of the line. 10-5. The conditional mean of Y, E(Y | X), is the population regression line. 10-6. The regression model is used for understanding the relationship between the two variables, X and Y; for prediction of Y for given values of X; and for possible control of the variable Y, using the variable X. 10-7. The error term captures the randomness in the process. Since X is assumed nonrandom, the addition of ( makes the result (Y) a random variable. The error term captures the effects on Y of a host of unknown random components not accounted for by the simple linear regression model. 10-8. The equation represents a simple linear regression model without an intercept (constant) term. 10-9. The least-squares procedure produces the best estimated regression line in the sense that the line lies inside the data set. The line is the best unbiased linear estimator of the true regression line as the estimators  EMBED Equation.3  and  EMBED Equation.3  have smallest variance of all linear unbiased estimators of the line parameters. Least-squares line is obtained by minimizing the sum of the squared deviations of the data points from the line. Least squares is less useful when outliers exist. Outliers tend to have a greater influence on the determination of the estimators of the line parameters because the procedure is based on minimizing the squared distances from the line. Since outliers have large squared distances they exert undue influence on the line. A more robust procedure may be appropriate when outliers exist. 10-11. (Template: Simple Regression.xls, sheet: Regression) Simple RegressionIncomeWealthXYErrorQuantileZConfidence Interval for Slope1117.30.80.6670.4311-a(1-a) C.I. for b12223.6-3.020.167-0.96795%10.12+ or -2.779743340.23.460.8330.9674445.8-1.060.333-0.431Confidence Interval for Intercept5556.8-0.180.5000.0001-a(1-a) C.I. for b095%6.38+ or -9.21937 Regression Equation: Wealth Growth = 6.38 + 10.12 Income Quantile b1 = SSXY /SSX = 934.49/765.98 = 1.22 10-13. (Template: Simple Regression.xls, sheet: Regression) Thus, b0 = (3.057 b1 = 0.187 r20.9217Coefficient of DeterminationConfidence Interval for Sloper0.9601Coefficient of Correlation1-a(1-a) C.I. for b195%0.18663+ or -0.03609s(b1)0.0164Standard Error of SlopeConfidence Interval for Intercept1-a(1-a) C.I. for b095%-3.05658+ or -2.1372s(b0)0.97102Standard Error of InterceptPrediction Interval for Y1-aX(1-a) P.I. for Y given X95%10-1.19025+ or -2.8317s0.99538Standard Error of predictionPrediction Interval for E[Y|X]1-aX(1-a) P.I. for E[Y | X]+ or -ANOVA TableSourceSSdfMSFFcriticalp-valueRegn.128.3321128.332129.5254.844340.0000Error10.8987110.99079Total139.23112 10-14. b1 = SSXY /SSX = 2.11 b0 =  EMBED Equation.3  ( b1 EMBED Equation.3  = 165.3 ( (2.11)(88.9) = (22.279 10-15. Simple RegressionInflationReturnXYError11-3-20.0642223617.9677312.612-16.2944-10.3-8-14.124750.515336.410262.03-2-20.06137-1.8183.6464885.793210.298795.87242.22121 Inflation & return on stocksr20.0873Coefficient of DeterminationConfidence Interval for Sloper0.2955Coefficient of Correlation1-a(1-a) C.I. for b195%0.96809+ or -2.7972s(b1)1.18294Standard Error of SlopeConfidence Interval for Intercept1-a(1-a) C.I. for b095%16.0961+ or -17.3299s(b0)7.32883Standard Error of Intercepts20.8493Standard Error of predictionANOVA TableSourceSSdfMSFFcriticalp-valueRegn.291.1341291.1340.669745.591460.4401Error3042.877434.695Total33348  EMBED Excel.Chart.8 \s  There is a weak linear relationship (r) and the regression is not significant (r2, F, p-value) 10-16. Simple RegressionYearValueXYError11960180000840002197040000-720003198060000-6800041990160000160005200020000040000 Average value of Aston Martinr20.1203Coefficient of DeterminationConfidence Interval for Sloper0.3468Coefficient of Correlation1-a(1-a) C.I. for b195%1600+ or -7949.76s(b1)2498Standard Error of SlopeConfidence Interval for Intercept1-a(1-a) C.I. for b095%-3040000+ or -1.6E+07s(b0)4946165Standard Error of Intercepts78993.7Standard Error of predictionANOVA TableSourceSSdfMSFFcriticalp-valueRegn.2.6E+0912.6E+090.4102610.1280.5674Error1.9E+1036.2E+09Total2.1E+104  EMBED Excel.Chart.8 \s  There is a weak linear relationship (r) and the regression is not significant (r2, F, p-value). Limitations: sample size is very small. Hidden variables: the 70s and 80s models have a different valuation than other decades possibly due to a different model or style. 10-17. Regression equation is: Credit Card Transactions = 39.6717 + 0.06129 Debit Card Transactions r20.9624Coefficient of DeterminationConfidence Interval for Sloper0.9810Coefficient of Correlation1-a(1-a) C.I. for b195%0.6202+ or -0.17018s(b1)0.06129Standard Error of SlopeConfidence Interval for Intercept1-a(1-a) C.I. for b095%177.641+ or -110.147s(b0)39.6717Standard Error of InterceptPrediction Interval for Y1-aX(1-a) P.I. for Y given X+ or -s56.9747Standard Error of predictionPrediction Interval for E[Y|X]1-aX(1-a) P.I. for E[Y | X]+ or -ANOVA TableSourceSSdfMSFFcriticalp-valueRegn.3323661332366102.3897.708650.0005Error12984.543246.12Total3453515 There is no implication for causality. A third variable influence could be increases in per capital income or GDP Growth. 10-18. SSE =  EMBED Equation.3  Take partial derivatives with respect to b0 and b1:  EMBED Equation.3  = (2 EMBED Equation.3   EMBED Equation.3  = (2 EMBED Equation.3  Setting the two partial derivatives to zero and simplifying, we get:  EMBED Equation.3  = 0 and  EMBED Equation.3  = 0. Expanding, we get:  EMBED Equation.3  (nb0 (  EMBED Equation.3  = 0 and  EMBED Equation.3  -  EMBED Equation.3  = 0 Solving the above two equations simultaneously for b0 and b1 gives the required results. 10-19. 99% C.I. for  EMBED Equation.3 : 1.25533  EMBED Equation.3  2.807(0.04972) = [1.1158, 1.3949]. The confidence interval does not contain zero. 10-20. MSE = 7.629 From the ANOVA table for Problem 10-11: ANOVA TableSourceSSdfMSRegn.1024.1411024.14Error22.88837.62933Total1047.034 10-21. From the regression results for problem 10-11 s(b0) = 2.897 s(b1) = 0.873 s(b1)0.87346Standard Error of Slopes(b0)2.89694Standard Error of Intercept 10-22. From the regression results for problem 10-11 Confidence Interval for Slope 1-a(1-a) C.I. for b195%10.12+ or -2.77974Confidence Interval for Intercept1-a(1-a) C.I. for b095%6.38+ or -9.21937 95% C.I. for the slope: 10.12 2.77974 = [7.34026, 12.89974] 95% C.I. for the intercept: 6.38 9.21937 = [-2.83937, 15.59937] 10-23. s(b0) = 0.971 s(b1) = 0.016; estimate of the error variance is MSE = 0.991. 95% C.I. for  EMBED Equation.3 : 0.187 + 2.201(0.016) = [0.1518, 0.2222]. Zero is not a plausible value at  EMBED Equation.3 = 0.05. Confidence Interval for Slope1-a(1-a) C.I. for b195%0.18663+ or -0.03609s(b1)0.0164Standard Error of SlopeConfidence Interval for Intercept1-a(1-a) C.I. for b095%-3.05658+ or -2.1372s(b0)0.97102Standard Error of Intercept 10-24. s(b0) = 85.44 s(b1) = 0.1534 Estimate of the regression variance is MSE = 8122 95% C.I. for b1: 1.5518 ( 2.776 (0.1534) = [1.126, 1.978] Zero is not in the range. Confidence Interval for Slope1-a(1-a) C.I. for b195%1.55176+ or -0.42578s(b1)0.15336Standard Error of SlopeConfidence Interval for Intercept1-a(1-a) C.I. for b095%-255.943+ or -237.219s(b0)85.4395Standard Error of Intercept 10-25. s 2 gives us information about the variation of the data points about the computed regression line. 10-26. In correlation analysis, the two variables, X and Y, are viewed in a symmetric way, where no one of them is dependent and the other independent, as the case in regression analysis. In correlation analysis we are interested in the relation between two random variables, both assumed normally distributed. 10-27. From the regression results for problem 10-11: r0.9890Coefficient of Correlation 10-28. r = 0.960 r0.9601Coefficient of Correlation 10-29. t(5) =  EMBED Equation.3  = 0.640 Accept H0. The two variables are not linearly correlated. Yes. For example suppose n = 5 and r = .51; then: t =  EMBED Equation.3  = 1.02 and we do not reject H0. But if we take n = 10,000 and r = 0.04, giving t = 14.28, this leads to strong rejection of H0. 10-31. We have: r = 0.875 and n = 10. Conducting the test: t (8) =  EMBED Equation.3  =  EMBED Equation.3  = 5.11 There is statistical evidence of a correlation between the prices of gold and of copper. Limitations: data are time-series data, hence not dependent random samples. Also, data set contains only 10 points. 10-34. n= 65 r = 0.37 t (63) =  EMBED Equation.3  = 3.16 Yes. Significant. There is a correlation between the two variables.  EMBED Equation.3  =  EMBED Equation.3 ln [(1 + r)/(1 5)] =  EMBED Equation.3 ln (1.37/0.63) = 0.3884  EMBED Equation.3  =  EMBED Equation.3 ln [(1 +  EMBED Equation.3 )/(1  EMBED Equation.3 )] =  EMBED Equation.3 ln (1.22/0.78) = 0.2237  EMBED Equation.3  = 1/ EMBED Equation.3  = 1/ EMBED Equation.3  = 0.127 z = ( EMBED Equation.3  (  EMBED Equation.3 )/ EMBED Equation.3  = (0.3884 0.2237)/0.127 = 1.297. Cannot reject H0. Using TINV((,df) function in Excel, where df = n-2 = 52: =TINV(0.05,52) = 2.006645 And TINV(0.01, 52) = 2.6737 Reject H0 at 0.05 but not at 0.01. There is evidence of a linear relationship at  EMBED Equation.3 = 0.05 only. 10-37. t (16) = b1/s(b1) = 3.1/2.89 = 1.0727. Do not reject H0. There is no evidence of a linear relationship using any  EMBED Equation.3 . 10-38. Using the regression results for problem 10-11: critical value of t is: t( 0.05, 3) = 3.182 computed value of t is: t = b1/s(b1) = 10.12 / 0.87346 = 11.586 Reject H0. There is strong evidence of a linear relationship. 10-39. t (11) = b1/s(b1) = 0.187/0.016 = 11.69 Reject H0. There is strong evidence of a linear relationship between the two variables. 10-40. b1/ s(b1) = 1600/2498 = 0.641 Do not reject H0. There is no evidence of a linear relationship. 10-41. t (58) = b1/s(b1) = 1.24/0.21 = 5.90 Yes, there is evidence of a linear relationship. Using the Excel function, TDIST(x,df,#tails) to estimate the p-value for the t-test results, where x = 1.51, df = 585692 2 = 585690, #tails = 2 for a 2-tail test: TDIST(1.51, 585690,2) = 0.131. The corresponding p-value for the results is 0.131. The resgression is not significant even at the 0.10 level of significance. 10-43. t (211) = z = b1/s(b1) = 0.68/12.03 = 0.0565 Do not reject H0. There is no evidence of a linear relationship using any  EMBED Equation.3 . (Why report such results?) 10-44. b1 = 5.49 s(b1) = 1.21 t (26) = 4.537 Yes, there is evidence of a linear relationship. The coefficient of determination indicates that 9% of the variation in customer satisfaction can be explained by the changes in a customers materialism measurement. 10-46 a. The model should not be used for prediction purposes because only 2.0% of the variation in pension funding is explained by its relationship with firm profitability. b. The model explains virtually nothing. c. Probably not. The model explains too little. 10-47. In Problem 10-11 regression results, r 2 = 0.9781. Thus, 97.8% of the variation in wealth growth is explained by the income quantile. r20.9781Coefficient of Determination 10-48. In Problem 10-13, r 2 = 0.922. Thus, 92.2% of the variation in the dependent variable is explained by the regression relationship. 10-49. r 2 in Problem 10-16: r 2 = 0.1203 10-50. Reading directly from the MINITAB output: r 2 = 0.962 r20.9624Coefficient of Determination 10-51. Based on the coefficient of determination values for the five countries, the UK model explains 31.7% of the variation in long-term bond yields relative to the yield spread. This is the best predictive model of the five. The next best model is the one for Germany, which explains 13.3% of the variation. The regression models for Canada, Japan, and the US do not predict long-term yields very well. 10-52. From the information provided, the slope coefficient of the equation is equal to -14.6. Since its value is not close to zero (which would indicate that a change in bond ratings has no impact on yields), it would indicate that a linear relationship exists between bond ratings and bond yields. This is in line with the reported coefficient of determination of 61.56%. 10-53. r 2 in Problem 10-15: r 2 = 0.873 r20.8348Coefficient of Determination 10-54.  EMBED Equation.3  =  EMBED Equation.3  =  EMBED Equation.3  =  EMBED Equation.3  +  EMBED Equation.3  But:  EMBED Equation.3  =  EMBED Equation.3  = 0 because the first term on the right is the sum of the weighted regression residuals, which sum to zero. The second term is the sum of the residuals, which is also zero. This establishes the result:  EMBED Equation.3  10-55. From Equation (10-10): b1 = SSXY/SSX. From Equation (10-31): SSR = b1SSXY. Hence, SSR = (SSXY /SSX)SSXY = (SSXY) 2/SSX 10-56. Using the results for problem 10-11: F = 134.238 F(1,3) = 10.128 Reject H0. FFcriticalp-value134.23810.1280.0014 10-57. F (1,11) = 129.525 t (11) = 11.381 t 2 = 11.3812 = the F-statistic value already calculated. FFcriticalp-value129.5254.844340.0000 10-58. F(1,4) = 102.39 t (4) = 10.119 t 2 = F (10.119)2 = 102.39 FFcriticalp-value102.3897.708650.0005 10-59. F (1,7) = 0.66974 Do not reject H0. F (1,102) = MSR/MSE =  EMBED Equation.3  = 701.8 There is extremely strong evidence of a linear relationship between the two variables. 10-61.  EMBED Equation.3  = F (1,k) . Thus, F(1,20) = [b1/s(b1)]2 = (2.556/4.122)2 = 0.3845 Do not reject H0. There is no evidence of a linear relationship.  EMBED Equation.3  = [b1/s(b1)]2 =  EMBED Equation.3  [using Equations (10-10) and (10-15) for b1 and s(b1), respectively] =  EMBED Equation.3  =  EMBED Equation.3  =  EMBED Equation.3  =  EMBED Equation.3  =  EMBED Equation.3  = F (1,k) [because  EMBED Equation.3  = SSR by Equations (10-31) and (10-10)] 10-63. a. Heteroscedasticity. b. No apparent inadequacy. c. Data display curvature, not a straight-line relationship. 10-64. a. No apparent inadequacy. b. A pattern of increase with time. 10-65. a. No serious inadequacy. b. Yes. A deviation from the normal-distribution assumption is apparent. 10-66. Using the results for problem 10-11: Residual AnalysisDurbin-Watson statisticd3.39862 EMBED Excel.Chart.8 \s  Residual variance fluctuates; with only 5 data points the residuals appear to be normally distributed.  EMBED Excel.Chart.8 \s  10-67. Residuals plotted against the independent variable of Problem 10-14: No apparent inadequacy. Residual AnalysisDurbin-Watson statisticd2.0846  10-68. Residual AnalysisDurbin-Watson statisticd1.70855  Plot shows some curvature. In the American Express example, give a 95% prediction interval for x = 5,000:  EMBED Equation.3  = 274.85 + 1.2553(5,000) = 6,551.35. P.I. = 6,551.35  EMBED Equation.3 (2.069)(318.16) EMBED Equation.3  = [5,854.4, 7,248.3] 10-70. Given that the slope of the equation for 10-52 is 14.6, if the rating falls by 3 the yield should increase by 43.8 basis points. 10-71. For 99% P.I.: t .005(23) = 2.807 6,551.35  EMBED Equation.3 (2.807)(318.16) EMBED Equation.3  = [5,605.75, 7,496.95] 10-72. Point prediction:  EMBED Equation.3  The 99% P.I.: [28.465, 65.255] Prediction Interval for Y1-aX(1-a) P.I. for Y given X99%446.86+ or -18.3946 10-73. The 99% P.I.: [36.573, 77.387] Prediction Interval for Y1-aX(1-a) P.I. for Y given X99%556.98+ or -20.407 10-74. The 95% P.I.: [-142633, 430633] Prediction Interval for Y1-aX(1-a) P.I. for Y given X95%1990144000+ or -286633 10-75. The 95% P.I.: [-157990, 477990] Prediction Interval for Y1-aX(1-a) P.I. for Y given X95%2000160000+ or -317990 10-76. Point prediction:  EMBED Equation.3  10-77. a) simple regression equation: Y = 2.779337 X 0.284157 when X = 10, Y = 27.5092 InterceptSlopeb0b1-0.2841572.779337 b) forcing through the origin: regression equation: Y = 2.741537 X. InterceptSlopeb0b102.741537 When X = 10, Y = 27.41537 PredictionXY1027.41537 c) forcing through (5, 13): regression equation: Y = 2.825566 X 1.12783 InterceptSlopePredictionb0b1XY-1.127832.825566513 When X = 10, Y = 27.12783 PredictionXY1027.12783 d) slope ( 2: regression equation: Y = 2 X + 4.236 InterceptSlopeb0b14.2362 When X = 10, Y = 24.236 Using Excel function, TINV(x, df), where x = the p-value of 0.034 and df = 2058 2: TINV(0.034, 2056) = 2.121487. Since the slope coefficient = -0.051, t-value becomes negative, t = -2.121487. standard error of the slope:  EMBED Equation.3  Using an ( = 0.05, we would reject the null hypothesis of no relationship between the response variable and the predictor based on the reported p-value of 0.034. 10-79. Given the reported p-value, we would reject the null hypothesis of no relationship between neuroticism and job performance. Given the reported coefficient of determination, 19% of the variation in job performance can be explained by neuroticism. 10-80. The t-statistic for the reported information is:  EMBED Equation.3  Using Excel function, TDIST(t,df,#tails), we get a p-value of 0.000068: TDIST(4.236, 70, 2) = 6.8112E-05. There is a linear relationship between frequency of online shopping and the level of perceived risk. 10-81 (From Minitab) The regression equation is Stock Close = (67.6 + 0.407 Oper Income PredictorCoefStdevt-ratiopConstant(67.6212.32(5.490.000Oper Inc0.407250.0357911.380.000 s = 9.633 R-sq = 89.0% R-sq(adj) = 88.3% Analysis of Variance SOURCEDFSSMSFpRegression11201612016129.490.000Error16148593Total1713500Stock close based on an operating income of $305M is  EMBED Equation.3  = $56.24.  4 3 4 6 7 ; < ? @ % & ; < ɿ$j(9 h1CJUVmHnHujh1EHU$j39 h1CJUVmHnHujh1EHU$j9 h1CJUVmHnHujh1U jeh1 h16 h_ACJ h1CJh16 4op   f g > ? ] ^ \n$If_ & F_3ā& \mnvw鷠teTeTeTeTeTe h15CJOJPJQJ\^Jh15CJOJQJ\^J/h156B*CJOJPJQJ\]^Jph h1CJh1CJOJPJQJ^J-h15B*CJOJPJQJ\^JaJph!h15B*OJQJ\^Jphh\<jh1EHU$jN9 h1CJUVmHnHuh1jh1Ujh1EHU nopqrstuv$Ifvwxyz{3----$Ifkd`$$If; @ kMUU ' 'p'''''p'p'p6$$$$4a{|}~$If kdF$$IfJ g @ kMUU ###########6,,,,4aFf $$Ifa$$If&(*,.0246>@JLVXdhҿҘҘҘҘҘ҉xh落ҘҘҘҘҘh15CJH*OJQJ\^J h15CJOJPJQJ\^Jh15CJOJQJ\^Jh1CJOJQJ^J 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"   ,''',-- - -- --' ,- --$111-1-11--oo[[GG22111llYY--"System΁ bčρ -' ,---' ,/---' ,/- -----' ,/--QMO---' ,/--z}vx---' ,/--kgi---' ,/--.*,---' ,/-----' ,/--uqs---' ,/--Y)U%W'---' ,/--i*e&g(---' ,/---' ,/---' ,---' ,---' ,1---' ,1-i-_2-^x---' ,1---' ,---' ,---' ,---' ,KC5 -  Arial-%2 8y = 0.9681x + 16.096---' ,---' , - Arial- 2 -20 2 -10 2 0 2 {10 2 g20 2 S30 2 ?40 2 *50 2 60---',---',-- 2 (-15 2 c-10 2 -5 2 0 2 5 2 R10 2 15---',---',- Arial ????? ?"@ ?- 2 X---',---',u&j- Arial ?k ?@@%@-- 2 sY-  ---',---',- _2- - - -- --- ' ' 'CompObj+.(bObjInfo*Workbook-/SummaryInformation(0h3 !FMicrosoft Excel ChartBiff8Excel.Chart.89q ՜.+,0HP X`hp x   RegressionSolverChart3  WorksheetsCharts      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~ I@Ba=*=xx8X1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1 Arial1 Arial1Symbol1Arial1 Arial1 Arial1Arial1Arial1Arial1 Arial1 Arial1Arial1Arial1Arial1Arial1 Arial1 Arial1QTahoma1Arial1Arial1Arial1 Arial1Arial1Arial1Arial1Arial1 Arial1$Arial1Arial1Arial1Arial1Arial1Arial1 Arial"$"#,##0_);\("$"#,##0\)!"$"#,##0_);[Red]\("$"#,##0\)""$"#,##0.00_);\("$"#,##0.00\)'""$"#,##0.00_);[Red]\("$"#,##0.00\)7*2_("$"* #,##0_);_("$"* \(#,##0\);_("$"* "-"_);_(@_).))_(* #,##0_);_(* \(#,##0\);_(* "-"_);_(@_)?,:_("$"* #,##0.00_);_("$"* \(#,##0.00\);_("$"* "-"??_);_(@_)6+1_(* #,##0.00_);_(* \(#,##0.00\);_(* "-"??_);_(@_) 0.0000000 0.000000 0.00000 0.0000 0.00000000 0.000 0.000E+00 0.0E+00 0E+00"Yes";"Yes";"No""True";"True";"False""On";"On";"Off"                + ) , * ' &          "8@ @       "8@ @ #8@ @ "8@ @ "<@ @ " solver_rel1 solver_rhs1 solver_scl solver_sho solver_timd" solver_tol? solver_typ solver_typ solver_val solver_valSSE:7'X:;B"N7'Y:;B"N7'Z:;B"N`iP  3  @@  UDXYErrorSSE LINEST Output LINEST Legendb1b0s(b1) s(b0) r2sFdf(SSE)SSR ANOVA TableSourceSSdfMSRegn.Total+ or -rQuantile(1-a) C.I. for b1 Confidence Interval for Slope(1-a) C.I. for b0 !Confidence Interval for InterceptPrediction Interval for YSimple RegressionZr25Scatter Plot, Regression Line and Regression EquationCoefficient of DeterminationCoefficient of CorrelationDurbin-Watson statisticStandard Error of predictionStandard Error of Slopes(b0)s(b1)Standard Error of Interceptd Fcriticalp-value Prediction Interval for E[Y|X]1-aResidual AnalysisRegression Using the SolverTo use the Solver: InterceptSlope PredictionUnprotect the sheet.+Choose the Solver command under Tools menu.+Enter the constraints using the Add button.Press Solve button*Adjust the scale of the axes if necessary.b0b1VolumeWeight(1-a) P.I. for Y given X  (1-a) P.I. for E[Y | X]   Inflation & return on stocksYearValueAverage value of Aston MartinJ Xtx\&  I@" ??)3` 0x*` 0x+` 0x,` -п_3d23 M 4 3Q: YQ9%Q9$Q3_ M NM   <4E4 3QQQQ3_  NM  MM<4JK4D$% MP+3O&*Q4$% MP+3O&,Q4FA  3O$d 3*#M43*#M4%  rsM3O &+Q X'4% X-MZ3O &+Q Y'4523   43d" 3_ M NM  MM<444% M3OQ'4%  #@ *?3O{Dy&-Q'44e@Ȟ@@@@@eA@L@AjAe>  I@  dMbP?_*+%M hp LaserJet 1012 Series Driver<4XSDDMhp LaserJet 1012-dd"A,,??U} } I } I} m} } $}  I}  } $ } m } $ } $} } } } $ } } $ ;J@@ ;;,      2Simple Regression&/Average value of Aston Martin"001] A D ~ @2]  D~  @Year@Value  7r2 4̾? D%Coefficient of Determination X YErrorQuantile Z&Confidence Interval for Slope   7r' 4: 2?DADA#Coefficient of Correlation  LINEST Output LINEST Legend4?DA B^@_AW>@ ADDB$DDDD B*?!dhdc  "dc  "c B:*Ъ?$D DA( B .1-a,+(1-a) C.I. for b1  ,- f@! #%#$B1!1Gb1b0 :@$DA D B^Ȟ@_@W>@ ADDB$DDDD B*UUUUUU?!dhdc  "dc  "c B:*Ъ $D DA( B~ 6W@Nf@ D =+ or -- Mgz @ DDALD  7s(b1) 9?@D Standard Error of Slope "?@#$=RAs(b1) s(b0) :@$DA D B^@_L@W> ADDB$DDDD B*UUUUUU?!dhdc  "dc  "c B:*`z ۿ $D DA( B"̾?#+I@r2 s :@$DA D B^@_AW>1@@ ADDB$DDDD B*?!dhdc  "dc  "c B:* $D DA( B*!Confidence Interval for Intercept$rAA?%@ Fdf(SSE) :@ $DA D B^@@_jAW>@ ADDB$DDDD B*UUUUUU?!dhdc  "dc  "c B:*`z ? $D DA( B .1-a,+(1-a) C.I. for b0  ,-&8A'2oB SSR SSE : .H $D A D B ^_W >1.H AD D B$D DD D B *$X0H  !  d hd c  "d c  "c B: *\0H $D  D A( B ~ 6W@ N1G D =+ or -- M*nA D DALD  7s(b0) 9$=RA D$ Standard Error of Intercept : .H $D A D  B ^_W >D/H AD D B$D DD D B */H  !  d hd c  "d c  "c B: */H $D  D A( B* : .H $D A D  B ^_W >H/H AD D B$D DD D B *ה/H  !  d hd c  "d c  "c B: */H $D  D A( B " Prediction Interval for Y& : .H $D A D  B ^_W >\L/H AD D B$D DD D B */H  !  d hd c  "d c  "c B: */H $D  D A( B  .1-a AX7 +(1-a) P.I. for Y given X  " ,-: .H$D A D  B ^_W >P/HAD D B$D DD D B */H  !  d hd c  "d c  "c B: */H$D  D A( B 6)P NHH :D D B$DD D B 3+ or -} MLH gD OD DALD#$BD #$B#$B>A B 7s 9+I@D A% Standard Error of prediction :.H$DA D  B ^_W>hT/HADDB$DDDD B*/H!dhdc  "dc  "c B:*/H$D DA( B*:.H$DA D B ^_W>X/HADDB$DDDD B*/H!dhdc  "dc  "c B:*/H$D DA( B'Prediction Interval for E[Y|X]&:.H$DA D B ^_W>G\/HADDB$DDDD B*Q/H!dhdc  "dc  "c B:*/H$D DA( B .1-a X: +(1-a) P.I. for E[Y | X]    ,-:D.H$DA D B ^_W>`/HADDB$DDDD B*/H!dhdc  "dc  "c B:*/H$D DA( B 6)P NlPH :DDB$DDD B 3+ or -y MTH cD KDDALD#$BD#$B#$B>A B :H.H$DA D B ^_W>d/HADDB$DDDD B*/H!dhdc  "dc  "c B:* 0H$D DA( B:L.H$DA D B ^_W>h/HADDB$DDDD B*0H!dhdc  "dc  "c B:*0H$D DA( B ANOVA Table:P.H$DA D B ^_W>l/HADDB$DDDD B*0H!dhdc  "dc  "c B:*0H$D DA( BSource SS  df  MS  AF A Fcritical p-value ?:T.H$DA D B ^_W>p/HADDB$DDDD B*z 0H!dhdc  "dc  "c B:*$0H$D DA( BRegn.58AD~  5?! 58A DD ! 5rAA? 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D%Coefficient of Determination X YErrorQuantile Z&Confidence Interval for Slope   4r' 17'?DADA#Coefficient of Correlation  LINEST Output LINEST Legend4?DA B(?(@W;? ADDB$DDDD B*UUUUUU?!dhdc  "dc  "c B:*`z ?$D DA( B .1-a,+(1-a) C.I. for b1  ,- = ףp=$@! #%#$B1!Q@b1b0 :@$DA D B(@(p@W;(\( ADDB$DDDD B*UUUUUU?!dhdc  "dc  "c B:*Ъ $D DA( B~ 3W@K= ףp=$@ D :+ or -- J_<@ DDALD  4s(b1) 6\c?D Standard Error of Slope "\c?#[,@s(b1) s(b0) :@$DA D B(@(h@W;Gz @ ADDB$DDDD B*?!dhdc  "dc  "c B:*Ъ? $D DA( B"%L?#:@r2 s :@$DA D B(@(@W;)\ ADDB$DDDD B*UUUUUU?!dhdc  "dc  "c B:*`z ۿ $D DA( B*!Confidence Interval for Intercept$ D`@%@ Fdf(SSE) :@ $DA D B(@(0@W;ףp= ǿ ADDB$DDDD B*?!dhdc  "dc  "c B:* $D DA( B .1-a,+(1-a) C.I. for b0  ,-&~jt@'S6@ SSR SSE : .} $D A D B ((W ;.} AD D B$D DD D B *;`/}  !  d hd c  "d c  "c B: *d/} $D  D A( B ~ 3W@ KQ@ D :+ or -- JPp"@ D DALD  4s(b0) 6[,@ D$ Standard Error of Intercept : .} $D A D  B ((W ;.} AD D B$D DD D B *h/}  !  d hd c  "d c  "c B: *l/} $D  D A( B* : .} $D A D  B ((W ;.} AD D B$D DD D B *p/}  !  d hd c  "d c  "c B: *t/} $D  D A( B " Prediction Interval for Y& : .} $D A D  B ((W ;.} AD D B$D DD D B *;x/}  !  d hd c  "d c  "c B: *|/} $D  D A( B  .1-a >X7 +(1-a) P.I. for Y given X  " ,-: .}$D A D  B ((W ;4/}AD D B$D DD D B */}  !  d hd c  "d c  "c B: */}$D  D A( B 3)P K#} :D D B$DD D B 0+ or -} J#} gD OD DALD#$BD #$B#$B>A B 4s 6:@D A% Standard Error of prediction :.}$DA D  B ((W;/}ADDB$DDDD B*؈/}!dhdc  "dc  "c B:*/}$D DA( B*:.}$DA D B ((W;O/}ADDB$DDDD B*v/}!dhdc  "dc  "c B:*/}$D DA( B'Prediction Interval for E[Y|X]&:.}$DA D B ((W;T /}ADDB$DDDD B*;/}!dhdc  "dc  "c B:*/}$D DA( B .1-a X: +(1-a) P.I. for E[Y | X]    ,-:.}$DA D B ((W;/}ADDB$DDDD B*/}!dhdc  "dc  "c B:*/}$D DA( B 3)P Kl#} :DDB$DDD B 0+ or -y J#} cD KDDALD#$BD#$B#$B>A B :.}$DA D B ((W;/}ADDB$DDDD B*ب/}!dhdc  "dc  "c B:*/}$D DA( B+(9?p= ף?!AAL:.}$DA D B ((W;u/}ADDB$DDDD B*ذ/}!dhdc  "dc  "c B:*/}$D DA( B ANOVA Table.p ?)\(?!AA-:.}$DA D B ((W;/}ADDB$DDDD B*/}!dhdc  "dc  "c B:*/}$D DA( BSource SS  df  MS  >F > Fcritical p-value <:.}$DA D B ((W; /}ADDB$DDDD B*b/}!dhdc  "dc  "c B:*/}$D DA( BRegn.2~jt@D~  2?! 2~jt@ DD ! 2 D`@ D D ' 6@KA$@- D D A( 1ߢV? 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NM  !!d4E4D$% M 3O&"Q4$% M 3O&%Q4FA1 3OB3*#M43*#M4% ThM3O &#Q X'4% PMZ3O&$Q Y'4523   43d" 3_ M NM  MM<4444eee xx  6uXPP? rZ]4@uD UUiĵEPC?X $<%Use this row for naming the columns.<$tt"Jayavel Sounderpandianm>@ 7 Oh+'0@. PXx Jayavel Sounderpandian L PatilleunMicrosoft Excel@,i@:%׼@;Gh-R  &"WMFClR EMF@@     !" !" !  " !  '% %    , &% '% (  , % % " !% %   '% ( % (    V088888888&% 88  68668688&% ( 8868RpArial `[wLLJ L4Q0I| $X Arialj @wwJ \|I`r$0dv% 56;56;5r6;r5U6;U586;88r6r% % % " !% % %   % % % " !% % %   66% % % " !% % %   66% ( {f'% &% (     *yd|g% % % " !% % %   66  *% % % " !% % %   66@  *>A% % % " !% % %   66B  *@C% % % " !% % %   66t  *ru% % % " !% % %   66% % % " !% % %   66% % % " !% % %   Rp Arial "`[wL # L4Q0"| TX ArialPwwJ \|"`r$0dv% % % % % % " !% % %       TaAaA LhResidual Plot  % % % % " !% % %   % % % " !% % %   % % % % " !% % %      TX&/aAaA&LP-4TX&/aAaA&LP-2TT*k/xaAaA*kLP0TT*N/[aAaA*NLP2TT*1/>aAaA*1LP4% % % " !% % %   RpArial `[wLD! 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"   ,  '' ' ,--  --  --'-- ,--  $888888-888888-8Arial-5;5;r5r;U5U;858;r8r--"System-'--- ,---'--- ,66---'--- ,66-f{--  h}dy---'--- ,66 ---'--- ,66@ B>---'--- ,66B D@---'--- ,66t vr---'--- ,66---'--- ,66---'--- , Arial------'--- ,  2  Residual Plot  ----'--- ,---'--- ,----'--- ,   2 &-4 2 &-2 2 k*0 2 N*2 2 1*4---'--- ,Arial- - - ---'- -- ,  2 X- ---'- -- ,- - ---'- -- ,a Arial- 2 Error-  - ---'- -- ,---'- -- ,- -   -- ' ' 'DocumentSummaryInformation8(_1247297534 !FT<Y<Ole -CompObj  .b՜.+,0HP X`hp x   RegressionSolverChart1  WorksheetsCharts !FMicrosoft Excel ChartBiff8Excel.Chart.89qObjInfo0Workbook vMSummaryInformation(R7DocumentSummaryInformation81՜.+,0HP X`hp x   RegressionSolverChart2  WorksheetsCharts FMicrosoft Equation 3.0 DS Eq      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQSTUVWXYZ[\]^_`abcdefghijklmprqsutvwx{|}~ @Ba=H<K=xx8X1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1 Arial1 Arial1Symbol1Arial1 Arial1 Arial1Arial1Arial1Arial1 Arial1 Arial1Arial1Arial1Arial1Arial1 Arial1 Arial1QTahoma1Arial1Arial1Arial1 Arial1Arial1Arial1Arial1Arial1 Arial1$Arial1Arial1Arial1 Arial1Arial1Arial1Arial1Arial"$"#,##0_);\("$"#,##0\)!"$"#,##0_);[Red]\("$"#,##0\)""$"#,##0.00_);\("$"#,##0.00\)'""$"#,##0.00_);[Red]\("$"#,##0.00\)7*2_("$"* #,##0_);_("$"* \(#,##0\);_("$"* "-"_);_(@_).))_(* #,##0_);_(* \(#,##0\);_(* "-"_);_(@_)?,:_("$"* #,##0.00_);_("$"* \(#,##0.00\);_("$"* "-"??_);_(@_)6+1_(* #,##0.00_);_(* \(#,##0.00\);_(* "-"??_);_(@_) 0.0000000 0.000000 0.00000 0.0000 0.00000000 0.000 0.000E+00 0.0E+00 0E+00                + ) , * ' &          "8@ @       "8@ @ #8@ @ "8@ @ "<@ @ " solver_rel1 solver_rhs1 solver_scl solver_sho solver_timd" solver_tol? solver_typ solver_typ solver_val solver_valSSE:7'X:;B"N7'Y:;B"N7'Z:;B"N`iP$  3  @@  SBXYErrorSSE LINEST Output LINEST Legendb1b0s(b1) s(b0) r2sFdf(SSE)SSR ANOVA TableSourceSSdfMSRegn.Total+ or -rQuantile(1-a) C.I. for b1 Confidence Interval for Slope(1-a) C.I. for b0 !Confidence Interval for InterceptPrediction Interval for YSimple RegressionZr25Scatter Plot, Regression Line and Regression EquationCoefficient of DeterminationCoefficient of CorrelationDurbin-Watson statisticStandard Error of predictionStandard Error of Slopes(b0)s(b1)Standard Error of Interceptd Fcriticalp-value Prediction Interval for E[Y|X]1-aResidual AnalysisRegression Using the SolverTo use the Solver: InterceptSlope PredictionUnprotect the sheet.+Choose the Solver command under Tools menu.+Enter the constraints using the Add button.Press Solve button*Adjust the scale of the axes if necessary.b0b1VolumeWeightMilesDollars(1-a) P.I. for Y given X  (1-a) P.I. for E[Y | X]   JB X\&#i  @" ??)3` 0x*` +` 0x,` 0x-` .@a3d23 M 4 3QQ9&Q9Q3_ M NM   <4E4 3QQ ;Q ;Q3_ ! NM  !!d43_ ! NM  !!d4E4D$% M 3O&-Q4$% M 3O&,Q4FAn{  3O' 3*#M&.43*@N#M&.4% &o M3O<&+Q  Residuals'4% WJ MZ3O&+Q 0Corresponding Normal Z'4523   43d" 3_ M NM  MM<444%  3O &*Q L$Normal Probability Plot of Residuals'44e?먟 @(\(먟 Gz @)\ףp= ǿe`z ?@ЪЪ?`z ۿe>  @  dMbP?_*+%MHP LaserJet 6L PCL@g,, @MSUDHP LaserJet 6L PCL&d "A,,??U} } I } I} m} } $}  I}  } $ } m } $ } $} } } } $ } } $ ;J@@ ;;,      /Simple Regression0[[[[먟 @ D ~ @2먟  D~ =Miles=Dollars  4r2 1%L? D%Coefficient of Determination X YErrorQuantile Z&Confidence Interval for Slope   4r' 17'?DADA#Coefficient of Correlation  LINEST Output LINEST Legend4?DA B(?(@W;? ADDB$DDDD B*UUUUUU?!dhdc  "dc  "c B:*`z ?$D DA( B .1-a,+(1-a) C.I. for b1  ,- = ףp=$@! #%#$B1!Q@b1b0 :@$DA D B(@(p@W;(\( ADDB$DDDD B*UUUUUU?!dhdc  "dc  "c B:*Ъ $D DA( B~ 3W@K= ףp=$@ D :+ or -- J_<@ DDALD  4s(b1) 6\c?D Standard Error of Slope "\c?#[,@s(b1) s(b0) :@$DA D B(@(h@W;Gz @ ADDB$DDDD B*?!dhdc  "dc  "c B:*Ъ? $D DA( B"%L?#:@r2 s :@$DA D B(@(@W;)\ ADDB$DDDD B*UUUUUU?!dhdc  "dc  "c B:*`z ۿ $D DA( B*!Confidence Interval for Intercept$ D`@%@ Fdf(SSE) :@ $DA D B(@(0@W;ףp= ǿ ADDB$DDDD B*?!dhdc  "dc  "c B:* $D DA( B .1-a,+(1-a) C.I. for b0  ,-&~jt@'S6@ SSR SSE : .} $D A D B ((W ;.} AD D B$D DD D B *;`/}  !  d hd c  "d c  "c B: *d/} $D  D A( B ~ 3W@ KQ@ D :+ or -- JPp"@ D DALD  4s(b0) 6[,@ D$ Standard Error of Intercept : .} $D A D  B ((W ;.} AD D B$D DD D B *h/}  !  d hd c  "d c  "c B: *l/} $D  D A( B* : .} $D A D  B ((W ;.} AD D B$D DD D B *p/}  !  d hd c  "d c  "c B: *t/} $D  D A( B " Prediction Interval for Y& : .} $D A D  B ((W ;.} AD D B$D DD D B *;x/}  !  d hd c  "d c  "c B: *|/} $D  D A( B  .1-a >X7 +(1-a) P.I. for Y given X  " ,-: .}$D A D  B ((W ;4/}AD D B$D DD D B */}  !  d hd c  "d c  "c B: */}$D  D A( B 3)P K#} :D D B$DD D B 0+ or -} J#} gD OD DALD#$BD #$B#$B>A B 4s 6:@D A% Standard Error of prediction :.}$DA D  B ((W;/}ADDB$DDDD B*؈/}!dhdc  "dc  "c B:*/}$D DA( B*:.}$DA D B ((W;O/}ADDB$DDDD B*v/}!dhdc  "dc  "c B:*/}$D DA( B'Prediction Interval for E[Y|X]&:.}$DA D B ((W;T /}ADDB$DDDD B*;/}!dhdc  "dc  "c B:*/}$D DA( B .1-a X: +(1-a) P.I. for E[Y | X]    ,-:.}$DA D B ((W;/}ADDB$DDDD B*/}!dhdc  "dc  "c B:*/}$D DA( B 3)P Kl#} :DDB$DDD B 0+ or -y J#} cD KDDALD#$BD#$B#$B>A B :.}$DA D B ((W;/}ADDB$DDDD B*ب/}!dhdc  "dc  "c B:*/}$D DA( B+(9?p= ף?!AAL:.}$DA D B ((W;u/}ADDB$DDDD B*ذ/}!dhdc  "dc  "c B:*/}$D DA( B ANOVA Table.p ?)\(?!AA-:.}$DA D B ((W;/}ADDB$DDDD B*/}!dhdc  "dc  "c B:*/}$D DA( BSource SS  df  MS  >F > Fcritical p-value <:.}$DA D B ((W; /}ADDB$DDDD B*b/}!dhdc  "dc  "c B:*/}$D DA( BRegn.2~jt@D~  2?! 2~jt@ DD ! 2 D`@ D D ' 6@KA$@- D D A( 1ߢV? 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NM  !!d43_ ! NM  !!d4E4D$% MP+3O&-Q4$% MP+3O&,Q4FA 3Oe 3*#M&.43*@N#M&.4% W GM3O:&+Q  Residuals'4% ejMZ3O$X&+Q 0Corresponding Normal Z'4523   43d" 3_ M NM  MM<444%  3O &*Q L$Normal Probability Plot of Residuals'44ex?9 @ϫ@b2@ϫ0h?`_ˮ fP ԑ? @? uV hJ! s5bJ Op i٢?eg?@$Ë?xd?H߿9"Ŀll?Nc? $Ë xdԿ g Nc 9"?H?e>  I@  dMbP?_*+%MHP LaserJet 4 Plus@w ,,@MSUDHP LaserJet 4 Plus<d "A,,??U} } I } I} m} } $}  I}  } $ } m } $ } $} } } } $ } } $ !!;!J@!@! !;!J !!!,  ! ! !  ! ! !!!! ! !!! !!!!!!!!!!2Simple Regression0/001ϫ@ D ~ @ 2ϫ D~   @D/C @ROC  7r2 4=? D%Coefficient of Determination*  X YErrorQuantile Z&Confidence Interval for Slope   7r' 4[%gZ7?DADA#Coefficient of Correlation  LINEST Output LINEST Legend  4?DA B(@(r@W>x?9 @ ADDB$DDDD B*?!dhdc  "dc  "c B:*g?$D DA( B .1-a,+(1-a) C.I. for b1  ,- Y҇ܫ?! #%#$B1!zsb1b0 E@ D SUMMARY OUTPUT (Б@(`@  :@$DA D B(@(@1@W>b2@ ADDB$DDDD B*?!dhdc  "dc  "c B:*$Ë? $D DA( B~ 6W@NY҇ܫ? D =+ or -- ML/w? DDALD  7s(b1) 9{`')?D Standard Error of Slope "{`')?#H'@s(b1) s(b0) @A@ D(8@(9@  :@$DA D B(@(x@W>0h? ADDB$DDDD B*?!dhdc  "dc  "c B:*xd? $D DA( B"=?#ranr@r2 s333333:@ D aRegression Statistics a(4@(1@  :@$DA D B(@(|@W>`_ ADDB$DDDD B*?!dhdc  "dc  "c B:*H߿ $D DA( B*!Confidence Interval for Intercept$ Xg~F@%*@ Fdf(SSE){G:B@ D ^ Multiple R^? (@($@  :@ $DA D B(D@(Р@W>ˮ ADDB$DDDD B*?!dhdc  "dc  "c B:*9"Ŀ $D DA( B .1-a,+(1-a) C.I. for b0  ,-&wt\1n@']LGQ@ SSR SSEQE@ D ^R Square^a/a? (@(/@  : @ $D A D B (,@(@W > f AD D B$D DD D B *?  !  d hd c  "d c  "c B: *l $D  D A( B ~ 6W@ Nzs D =+ or -- M&U@ D DALD  7s(b0) 9H'@ D$ Standard Error of Intercept  Q:@ D   ^Adjusted R Square ^ 8?  (@(@  : @ $D A D  B (@(@W >P ԑ? AD D B$D DD D B *?  !  d hd c  "d c  "c B: *l? $D  D A( B$  Gz?@  D   ^Standard Error ^Vc"@  (h@(@  :  @ $D A D  B (̛@(T@W > @ AD D B$D DD D B *?  !  d hd c  "d c  "c B: *Nc? $D  D A( B " Prediction Interval for Y  Gz.F@  D   _ Observations~ _8@  (@(0@  : "@ $D A D  B ((@(h@W >? AD D B$D DD D B *?  !  d hd c  "d c  "c B: * $D  D A( B  .1-a AX7 +(1-a) P.I. for Y given X   ,- (\B@@  D   (Б@(`@  : $@$D A D  B (H@(@W >uVAD D B$D DD D B *?  !  d hd c  "d c  "c B: *$Ë $D  D A( B  6W@)$@P Nj](%@ :D D B$DD D B 3+ or -} MXS{m@ gD OD DALD#$BD #$B#$B>A B 7s 9qanr@D A% Standard Error of prediction  (\&@  D   ANOVA  (X@(/@  :&@$DA D  B(&@(|@W>hJ!ADDB$DDDD B*?!dhdc  "dc  "c B:*xdԿ $D DA( B$5@  D ` `df `SS `MS(>@(x@  :(@$DA D B(@(@W>s5bJADDB$DDDD B*?!dhdc  "dc  "c B:*g $D DA( B'Prediction Interval for E[Y|X] \(A@ D ^ Regression~ ^?^Z/z@^Z/z@(@(@  :*@$DA D B(@()@W>OpADDB$DDDD B*?!dhdc  "dc  "c B:*Nc $D DA( B .1-a X: +(1-a) P.I. for E[Y | X]    ,-9@ D ^Residual~ ^6@^\\@^kξU@((`@  :,@$DA D B(x@(@W>i٢ADDB$DDDD B*?!dhdc  "dc  "c B:*9"? $D DA( B 6)P Nl44 :DDB$DDD B 3+ or -y M84 cD KDDALD#$BD#$B#$B>A B (\B2@ D _Total~ _7@_%(9@_(9@(0@  :.@$DA D B( @(@W>?ADDB$DDDD B*?!dhdc  "dc  "c B:*H? $D DA( B$= ףp;@ D((@  :0U$DA D B ((W>LUADDB$DDDD B*YhU!dhdc  "dc  "c B:*lU$D DA( B ANOVA Table  D `` Coefficients`Standard Error`t Stat(@(7@` Upper 95%` Lower 95.0% ` Upper 95.0%:4U$DA D B ((W>PUADDB$DDDD B*MpU!dhdc  "dc  "c B:*tU$D DA( BSource SS  df  MS  AF A Fcritical p-value .?fk(@dm"J@Ș@ D ^ Intercept^0E[=@^70Y@^w_kJ#@($@(@^A@^`EŲ 7@ ^A@:8U$DA D B ((W>TUADDB$DDDD B*MxU!dhdc  "dc  "c B:*|U$D DA( BRegn.5wt\1n@D~  5?! 5wt\1n@ DD ! 5 Xg~F@ D D ' 92@- D D A( 4'> D D D A D _ X Variable 1_4ɯп_ݕꀾ?_˥(@(l@_М5C9_<F _М5C9:#XUADDB$DDDD B*ӀU!dhdc  "dc  "c B:*U$D DA( BError5]LGQ@ D 5*@ D! 5qD@ DD  ::;)sŎ#~jпQI? 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