SUMMARY OUTPUT Regression Statistics Multiple R 0.836704315 R Square 0.700074111 Adjusted R Square 0.670081522 Standard Error 2.564970628 Observations 12 ANOVA df SS MS F Significance F Regression 1 153.5659234 153.5659234 23.34156994 0.000690421 Residual 10 65.79074322 6.579074322 Total 11 219.3566667 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% "Lower 95,0%" "Upper 95,0%" Intercept -11.88455847 13.28162904 -0.894811806 0.391916237 -41.47787216 17.70875522 -41.47787216 17.70875522 x 3.740826691 0.77428805 4.83131141 0.000690421 2.015605404 5.466047978 2.015605404 5.466047978 RESIDUAL OUTPUT Observation Predicted y Residuals y 1 49.0909166 -4.690916602 44.4 2 50.96132995 -2.561329948 48.4 3 57.32073532 -3.120735323 54.2 4 49.5398158 0.460184195 50 5 55.07623931 -0.176239308 54.9 754.9849132 6 53.20582596 0.694174038 53.9 7 46.84642059 0.153579413 47 8 48.71683393 3.683166067 52.4 9 51.70949529 1.290504714 53 10 50.58724728 2.312752722 52.9 11 53.57990863 -0.479908631 53.1 12 59.56523134 2.434768663 62 9.4739E-15 ##### Sheet/List 2 ##### 1. "In the table, there is an information about the production (y)" and about investments in 10 000Kč (x) in 12 years. in a firm. a) Find a linear regression function modelling dependence of a production in the amount of investment. b) By using of the coefficient of determinarion R2 evaluate an accuracy of the regeression function. c) Calculate residuals of the model d) At a level of significance test a statistical significance of regression coefficients e) Write down an 95% confidence interval for regression coeficient b1? f) What is an expected production in the case of an investment of 2 050 000 Kč? Year x y 1 16.3 44.4 2 16.8 48.4 3 18.5 54.2 4 16.42 50 5 17.9 54.9 6 17.4 53.9 7 15.7 47 8 16.2 52.4 9 17 53 10 16.7 52.9 11 17.5 53.1 12 19.1 62 ##### Sheet/List 3 ##### Year x y 1 16.3 44.4 2 16.8 48.4 3 18.5 54.2 4 16.42 50 5 17.9 54.9 6 17.4 53.9 7 15.7 47 8 16.2 52.4 9 17 53 10 16.7 52.9 11 17.5 53.1 12 19.1 62 13 205 ##### Sheet/List 4 ##### In the table there are results of experiments of a new fertilizer on the production of tomatoes. a) Choose an appropriate type of a regression model describing dependence of production on an amount of fertilizer " is it appropriate to use a linear function, or a quadratic function?" b) Determine an equation of a regression function c) By using of the coefficient of determinarion R2 evaluate an accuracy of the regeression function. d) Find an optimal level of fertilizer Fertilizer (100 kg/ha) 0.7 1.3 3.8 4.2 2.5 5 5.3 6 5.8 6.2 Production (t/ha) 12 14.6 40.3 43.7 28 45 41.7 39 35.4 29.6 4.462939698 ##### Sheet/List 5 ##### x y -2 -5 -1 -3 0 0 1 1 2 4 ##### Sheet/List 8 ##### a) Estimate linear regression model a) Estimate quadratic regression model c) Estimate exponencial regression model d) Estimate powered regression model e) Estimate logaritmic regression model f) which of models a)-e) discrabes the situation most precisely and why? Income (in 1000 Kč) Savings (in 1000 Kč) 104 6 125 5.6 146 9.2 167 14 111 8 135 9.1 189 20.5 196 29 205 23.2 210 38.5 170 25 230 40 ##### Sheet/List 9 ##### Tabulka zachycuje čtvrtletnou míru nezaměstnanosti v německu v letech 1969-2014. Zdroj: https://research.stlouisfed.org a) Načrtněte graf této časové řady. b) Tuto časovou řadu vyrovnejte pomocí klouzavých průměrů. "c) Vyrovnanou časovou řadu načrtněte, porovnejte graf s výsledkem úlohy a)." DATE Pořadí VALUE 1969-01-01 1 1.23 1969-04-01 2 0.50 1969-07-01 3 0.40 0.666666667 1969-10-01 4 0.53 0.6 1970-01-01 5 0.97 0.583333333 1970-04-01 6 0.43 0.583333333 1970-07-01 7 0.40 0.583333333 1970-10-01 8 0.53 0.583333333 1971-01-01 9 0.97 0.608333333 1971-04-01 10 0.53 0.65 1971-07-01 11 0.57 0.716666667 1971-10-01 12 0.80 0.791666667 1972-01-01 13 1.27 0.858333333 1972-04-01 14 0.80 0.9 1972-07-01 15 0.73 0.933333333 1972-10-01 16 0.93 0.925 1973-01-01 17 1.23 0.933333333 1973-04-01 18 0.83 0.95 1973-07-01 19 0.80 1.05 1973-10-01 20 1.33 1.3 1974-01-01 21 2.23 1.533333333 1974-04-01 22 1.77 1.825 1974-07-01 23 1.97 2.241666667 1974-10-01 24 3.00 2.758333333 1975-01-01 25 4.30 3.283333333 1975-04-01 26 3.87 3.741666667 1975-07-01 27 3.80 4.058333333 1975-10-01 28 4.27 4.208333333 1976-01-01 29 4.90 4.175 1976-04-01 30 3.73 4.1 1976-07-01 31 3.50 3.983333333 1976-10-01 32 3.80 3.875 1977-01-01 33 4.47 3.866666667 1977-04-01 34 3.70 3.9 1977-07-01 35 3.63 3.916666667 1977-10-01 36 3.87 3.925 1978-01-01 37 4.50 3.891666667 1978-04-01 38 3.57 3.841666667 1978-07-01 39 3.43 3.766666667 1978-10-01 40 3.57 3.675 1979-01-01 41 4.13 3.541666667 1979-04-01 42 3.03 3.416666667 1979-07-01 43 2.93 3.291666667 1979-10-01 44 3.07 3.175 1980-01-01 45 3.67 3.158333333 1980-04-01 46 2.97 3.225 1980-07-01 47 3.20 3.383333333 1980-10-01 48 3.70 3.666666667 1981-01-01 49 4.80 3.983333333 1981-04-01 50 4.23 4.366666667 1981-07-01 51 4.73 4.866666667 1981-10-01 52 5.70 5.416666667 1982-01-01 53 7.00 5.891666667 1982-04-01 54 6.13 6.333333333 1982-07-01 55 6.50 6.783333333 1982-10-01 56 7.50 7.275 1983-01-01 57 8.97 7.716666667 1983-04-01 58 7.90 8.041666667 1983-07-01 59 7.80 8.158333333 1983-10-01 60 7.97 8.15 1984-01-01 61 8.93 8.116666667 1984-04-01 62 7.77 8.125 1984-07-01 63 7.83 8.116666667 1984-10-01 64 7.93 8.166666667 1985-01-01 65 9.13 8.2 1985-04-01 66 7.90 8.191666667 1985-07-01 67 7.80 8.183333333 1985-10-01 68 7.90 8.158333333 1986-01-01 69 9.03 8.083333333 1986-04-01 70 7.60 8 1986-07-01 71 7.47 7.891666667 1986-10-01 72 7.47 7.816666667 1987-01-01 73 8.73 7.8 1987-04-01 74 7.53 7.841666667 1987-07-01 75 7.63 7.9 1987-10-01 76 7.70 7.891666667 1988-01-01 77 8.70 7.908333333 1988-04-01 78 7.60 7.883333333 1988-07-01 79 7.53 7.791666667 1988-10-01 80 7.33 7.583333333 1989-01-01 81 7.87 7.4 1989-04-01 82 6.87 7.208333333 1989-07-01 83 6.77 7.091666667 1989-10-01 84 6.87 6.941666667 1990-01-01 85 7.27 6.808333333 1990-04-01 86 6.33 6.658333333 1990-07-01 87 6.17 6.416666667 1990-10-01 88 5.90 6.133333333 1991-01-01 89 6.13 5.9 1991-04-01 90 5.40 5.75 1991-07-01 91 5.57 5.866666667 1991-10-01 92 6.37 6.35 1992-01-01 93 8.07 6.858333333 1992-04-01 94 7.43 7.383333333 1992-07-01 95 7.67 7.741666667 1992-10-01 96 7.80 7.95 1993-01-01 97 8.90 8.216666667 1993-04-01 98 8.50 8.558333333 1993-07-01 99 9.03 8.933333333 1993-10-01 100 9.30 9.3 1994-01-01 101 10.37 9.566666667 1994-04-01 102 9.57 9.65 1994-07-01 103 9.37 9.575 1994-10-01 104 9.00 9.45 1995-01-01 105 9.87 9.341666667 1995-04-01 106 9.13 9.325 1995-07-01 107 9.30 9.441666667 1995-10-01 108 9.47 9.7 1996-01-01 109 10.90 9.941666667 1996-04-01 110 10.10 10.15833333 1996-07-01 111 10.17 10.39166667 1996-10-01 112 10.40 10.675 1997-01-01 113 12.03 10.93333333 1997-04-01 114 11.13 11.225 1997-07-01 115 11.33 11.48333333 1997-10-01 116 11.43 11.58333333 1998-01-01 117 12.43 11.53333333 1998-04-01 118 10.93 11.33333333 1998-07-01 119 10.53 11.075 1998-10-01 120 10.40 10.81666667 1999-01-01 121 11.40 10.66666667 1999-04-01 122 10.33 10.59166667 1999-07-01 123 10.23 10.50833333 1999-10-01 124 10.07 10.36666667 2000-01-01 125 10.83 10.13333333 2000-04-01 126 9.40 9.875 2000-07-01 127 9.20 9.616666667 2000-10-01 128 9.03 9.4 2001-01-01 129 9.97 9.333333333 2001-04-01 130 9.13 9.316666667 2001-07-01 131 9.13 9.375 2001-10-01 132 9.27 9.45 2002-01-01 133 10.27 9.558333333 2002-04-01 134 9.57 9.675 2002-07-01 135 9.60 9.791666667 2002-10-01 136 9.73 10.01666667 2003-01-01 137 11.17 10.24166667 2003-04-01 138 10.47 10.41666667 2003-07-01 139 10.30 10.51666667 2003-10-01 140 10.13 10.475 2004-01-01 141 11.00 10.45833333 2004-04-01 142 10.40 10.49166667 2004-07-01 143 10.43 10.55833333 2004-10-01 144 10.40 10.95 2005-01-01 145 12.57 11.30833333 2005-04-01 146 11.83 11.575 2005-07-01 147 11.50 11.725 2005-10-01 148 11.00 11.60833333 2006-01-01 149 12.10 11.39166667 2006-04-01 150 10.97 11.10833333 2006-07-01 151 10.37 10.775 2006-10-01 152 9.67 10.25833333 2007-01-01 153 10.03 9.8 2007-04-01 154 9.13 9.375 2007-07-01 155 8.67 8.983333333 2007-10-01 156 8.10 8.608333333 2008-01-01 157 8.53 8.275 2008-04-01 158 7.80 7.983333333 2008-07-01 159 7.50 7.758333333 2008-10-01 160 7.20 7.733333333 2009-01-01 161 8.43 7.85 2009-04-01 162 8.27 8 2009-07-01 163 8.10 8.125 2009-10-01 164 7.70 8.158333333 2010-01-01 165 8.57 8.033333333 2010-04-01 166 7.77 7.875 2010-07-01 167 7.47 7.7 2010-10-01 168 7.00 7.508333333 2011-01-01 169 7.80 7.333333333 2011-04-01 170 7.07 7.183333333 2011-07-01 171 6.87 7.058333333 2011-10-01 172 6.50 6.933333333 2012-01-01 173 7.30 6.858333333 2012-04-01 174 6.77 6.816666667 2012-07-01 175 6.70 6.833333333 2012-10-01 176 6.57 6.85 2013-01-01 177 7.37 6.866666667 2013-04-01 178 6.83 6.875 2013-07-01 179 6.73 6.875 2013-10-01 180 6.57 6.841666667 2014-01-01 181 7.23 2014-04-01 182 6.63