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[[Kategorie:Aufgaben]]
===Alter und Händlerverkaufspreis===
===Alter und Händlerverkaufspreis===


Zeile 28: Zeile 29:


===Hypothekenzinssatz===
===Hypothekenzinssatz===
{|class="wikitable"
|
!<math> x_i </math>
!<math> y_i </math>
!<math> x_i - \bar{x} </math>
!<math> (x_i - \bar{x})^2 </math>
!<math> y_i - \bar{y} </math>
!<math> (y_i - \bar{y})^2 </math>
!<math> (x_i - \bar{x}) (y_i - \bar{y}) </math>
|-
|align="right"|1
|align="right"|6
|align="right"|3000
|align="right"| -1
|align="right"|1.0
|align="right"|500
|align="right"|250000.0
|align="right"| -500
|-
|align="right"|2
|align="right"|5
|align="right"|3200
|align="right"| -2
|align="right"|4.0
|align="right"|700
|align="right"|490000.0
|align="right"| -1400.0
|-
|align="right"|3
|align="right"|7
|align="right"|2500
|align="right"|0
|align="right"|0.0
|align="right"|0
|align="right"|0.0
|align="right"|0.0
|-
|align="right"|4
|align="right"|7
|align="right"|2300
|align="right"|0
|align="right"|0.0
|align="right"| -200
|align="right"|40000.0 
|align="right"| -0.0
|-
|align="right"|5
|align="right"|8
|align="right"|2000
|align="right"|1
|align="right"|1.0
|align="right"| -500
|align="right"|250000.0
| align="right"|-500
|-
|align="right"|6
|align="right"|9
|align="right"|2000
|align="right"|2
|align="right"|4.0
| align="right"|-500
|align="right"|250000.0
|align="right"| -1000.0
|-
|Summe
|align="right"|42
|align="right"|15000
|align="right"|0
|align="right"|10.0
|align="right"|0
|align="right"|1280000.0
|align="right"| -3400
|-
|Mittel
|align="right"|7
|align="right"|2500
|align="right"|0
|align="right"|1.7
|align="right"|0
|align="right"|213333.3
|align="right"| -556.7
|}


* <math>\displaystyle r = \frac{-3400}{\sqrt{10\cdot1280000}}= -0.9503</math>
* <math>\displaystyle r = \frac{-3400}{\sqrt{10\cdot1280000}}= -0.9503</math>
Zeile 113: Zeile 197:


===Kunstdünger===
===Kunstdünger===
[[Datei:Kunstduenger.xlsx]]


* ja
* ja
Zeile 224: Zeile 309:


<math>\displaystyle b_1 =  
<math>\displaystyle b_1 =  
\frac{10\cdot\nump[2]{7390}-\nump[2]{700}\cdot\nump[2]{110}}
\frac{10\cdot 7390 - 700 \cdot 110}
{10\cdot\nump[2]{53600}-\nump[2]{700}^2}=\nump{-0.0673913043478261}</math>,<br />
{10\cdot 53600- 700}^2 = -0.0674 </math>,<br />
<math>\displaystyle b_0 =\frac{\nump[2]{110}}{10}-
<math>\displaystyle b_0 =\frac{ 110 }{10}-
\frac{\nump[2]{700}}{10}\cdot\nump{-0.0673913043478261}
\frac{ 700}{10}\cdot -0.0674
=\nump{15.7173913043478}</math>,<br />
= 15.7174</math>,<br />
 
===Querschnittsanalyse von 11 Unternehmen===
===Querschnittsanalyse von 11 Unternehmen===
[[Datei:Querschnittsanalyse.xlsx]]


* <math>\displaystyle\sum_{i=1}^{11} y_i =    \nump[2]{191}</math>, <math>\displaystyle\sum_{i=1}^{11} y_i^2 =  \nump[2]{5183.64909090909}</math>
* <math>\displaystyle\sum_{i=1}^{11} y_i =    191</math>, <math>\displaystyle\sum_{i=1}^{11} y_i^2 =  5183.6491 </math>
* <math>\displaystyle\sum_{i=1}^{11} x_{i1} = \nump[2]{1671.9}</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i1}^2 = \nump[2]{259297.25}</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i1}y_i = \nump[2]{29829.7}</math>,<br />
* <math>\displaystyle\sum_{i=1}^{11} x_{i1} = 1671.9</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i1}^2 = 259297.25</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i1}y_i = 29829.7</math>,<br />
<math>\displaystyle b_1^{(1)} =  
<math>\displaystyle b_1^{(1)} =  
\frac{11\cdot\nump[2]{29829.7}-\nump[2]{1671.9}\cdot\nump[2]{191}}
\frac{11\cdot 29829.7- 1671.9 \cdot 191}
     {11\cdot\nump[2]{259297.25}-\nump[2]{1671.9}^2}=\nump{0.15422270096145}</math>,<br />
     {11\cdot 259297.25-1671.9^2}=0.1542 </math>,<br />
<math>\displaystyle b_0^{(1)} =\frac{\nump[2]{191}}{11}-\frac{\nump[2]{1671.9}}{11\cdot\nump{0.15422270096145}}
<math>\displaystyle b_0^{(1)} =\frac{191}{11}-\frac{1671.9}{11\cdot 0.15422270096145}
=\nump{-6.07681215794991}</math>,<br />
=-6.0768 </math>,<br />
<math>\displaystyle R^2_{y1} =  
<math>\displaystyle R^2_{y1} =  
\frac{(11\cdot\nump[2]{29829.7}-\nump[2]{1671.9}\cdot\nump[2]{191})^2}
\frac{(11\cdot 29829.7- 1671.9\cdot 191)^2}
     {(11\cdot\nump[2]{259297.25}-\nump[2]{1671.9}^2)\cdot(11\cdot\nump[2]{3446.92}-\nump[2]{191}^2)}=\nump{0.945010582888399}</math>,<br />
     {(11\cdot 259297.25- 1671.9^2)\cdot(11\cdot 3446.92-191^2)}= 0.9450</math>,<br />
<math>\displaystyle\hat{y}_1 = \nump{-6.07681215794991} + \nump{0.15422270096145} x_1</math>
<math>\displaystyle\hat{y}_1 = -6.0768 + 0.1542 x_1</math>
* <math>\displaystyle\sum_{i=1}^{11} x_{i2} = \nump[2]{1197.4}</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i2}^2 = \nump[2]{132804.82}</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i2}y_i = \nump[2]{21344.04}</math>,<br />
* <math>\displaystyle\sum_{i=1}^{11} x_{i2} = 1197.4</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i2}^2 = 132804.82</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i2}y_i = 21344.04</math>,<br />
<math>\displaystyle b_1^{(2)} =  
<math>\displaystyle b_1^{(2)} = \frac{11\cdot 21344.04- 1197.4\cdot 191}{11\cdot 132804.82}-1197.4^2= 0.2245</math>,<br />
\frac{11\cdot\nump[2]{21344.04}-\nump[2]{1197.4}\cdot\nump[2]{191}}
<math>\displaystyle b_0^{(2)} =\frac{ 191}{11}-\frac{1197.4}{11\cdot 0.2245}
{11\cdot\nump[2]{132804.82}-\nump[2]{1197.4}^2}=\nump{0.224506447180232}</math>,<br />
= -7.0749</math>,<br />
<math>\displaystyle b_0^{(2)} =\frac{\nump[2]{191}}{11}-\frac{\nump[2]{1197.4}}{11\cdot\nump{0.224506447180232}}
=\nump{-7.0749108957827}</math>,<br />
<math>\displaystyle R^2_{y2} =  
<math>\displaystyle R^2_{y2} =  
\frac{(11\cdot\nump[2]{21344.04}-\nump[2]{1197.4}\cdot\nump[2]{191})^2}
\frac{(11\cdot 21344.04- 1197.4\cdot 191)^2}
{(11\cdot\nump[2]{132804.82}-\nump[2]{1197.4}^2)\cdot(11\cdot\nump[2]{3446.92}-\nump[2]{191}^2)}=\nump{0.951302111015713}</math>,<br />
{(11\cdot 132804.82- 1197.4^2)\cdot(11\cdot 3446.92- 191^2)}= 0.9513</math>,<br />
<math>\displaystyle\hat{y}21 = \nump{-7.0749108957827} + \nump{0.224506447180232} x_2</math>
<math>\displaystyle\hat{y}21 = -7.0749 + 0.2245 x_2</math>
* <math>\displaystyle\sum_{i=1}^{11} x_{i3} = \nump[2]{29.2}</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i3}^2 = \nump[2]{88.44}</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i3}y_i = \nump[2]{519.52}</math>,<br />
* <math>\displaystyle\sum_{i=1}^{11} x_{i3} = 29.2</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i3}^2 = 88.44 </math>, <math>\displaystyle\sum_{i=1}^{11} x_{i3}y_i = 519.52</math>,<br />
<math>\displaystyle b_1^{(3)} =  
<math>\displaystyle b_1^{(3)} =  
\frac{11\cdot\nump[2]{519.52}-\nump[2]{29.2}\cdot\nump[2]{191}}
\frac{11\cdot 519.52 - 29.2 \cdot 191}
{11\cdot\nump[2]{88.44}-\nump[2]{29.2}^2}=\nump{1.1440931780366}</math>,<br />
{11\cdot 88.44} - 29.2 ^2 = 1.1441 </math>,<br />
<math>\displaystyle b_0^{(3)} =\frac{\nump[2]{191}}{11}-\frac{\nump[2]{29.2}}{11\cdot\nump{1.1440931780366}}
<math>\displaystyle b_0^{(3)} =\frac{ 191}{11}-\frac{29.2}{11\cdot1.1441}
=\nump{14.3265890183028}</math>,<br />
= 14.3266 </math>,<br />
<math>\displaystyle R^2_{y3} =  
<math>\displaystyle R^2_{y3} =  
\frac{(11\cdot\nump[2]{519.52}-\nump[2]{29.2}\cdot\nump[2]{191})^2}
\frac{(11\cdot 519.52- 29.2 \cdot 191)^2}
{(11\cdot\nump[2]{88.44}-\nump[2]{29.2}^2)\cdot(11\cdot\nump[2]{3446.92}-\nump[2]{191}^2)}=\nump{0.109632430628514}</math>,<br />
{(11\cdot 88.44- 29.2^2)\cdot(11\cdot 3446.92- 191^2)}= 0.1096</math>,<br />
<math>\displaystyle\hat{y}_3 = \nump{14.3265890183028} + \nump{1.1440931780366} x_3</math>
<math>\displaystyle\hat{y}_3 = 14.3266 + 1.1441 x_3</math>
* <math>r_{y1} = \sqrt{R^2_{y1}} = \nump{0.97211654799638}</math>; <math>r_{y2} = \sqrt{R^2_{y2}} = \nump{0.975347174607951}</math>; <math>r_{y3} = \sqrt{R^2_{y3}} = \nump{0.331107883670132}</math>;
* <math>r_{y1} = \sqrt{R^2_{y1}} = 0.9721</math>; <math>r_{y2} = \sqrt{R^2_{y2}} = 0.9753 </math>; <math>r_{y3} = \sqrt{R^2_{y3}} = 0.3311</math>;
* <math>\displaystyle\sum_{i=1}^{11} x_{i1} = \nump[2]{1671.9}</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i1}^2 = \nump[2]{259297.25}</math>,<br />
* <math>\displaystyle\sum_{i=1}^{11} x_{i1} = 1671.9</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i1}^2 = 259297.25</math>,<br />
<math>\displaystyle\sum_{i=1}^{11} x_{i2} = \nump[2]{1197.4}</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i2}^2 = \nump[2]{132804.82}</math>,<br />
<math>\displaystyle\sum_{i=1}^{11} x_{i2} = 1197.4</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i2}^2 = 132804.82</math>,<br />
<math>\displaystyle\sum_{i=1}^{11} x_{i1}x_{i2} = \nump[2]{185557.02}</math>,<br />
<math>\displaystyle\sum_{i=1}^{11} x_{i1}x_{i2} = 185557.02</math>,<br />
<math>\displaystyle r_{12} = \frac{11\cdot\nump[2]{185557.02}-\nump[2]{1671.9}\cdot\nump[2]{1197.4}}{\sqrt{(11\cdot \nump[2]{259297.25}-\nump[2]{1671.9}^2)\cdot(11\cdot \nump[2]{132804.82}-\nump[2]{1197.4}^2)}}</math><br />
<math>\displaystyle r_{12} = \frac{11\cdot 185557.02-1671.9 \cdot 1197.4}{\sqrt{(11\cdot 259297.25-1671.9^2)\cdot(11\cdot 132804.82-1197.4^2)}}</math><br />
<math>\displaystyle r_{12} = \nump{0.997315801525063}</math><br />
<math>\displaystyle r_{12} = 0.9973</math><br />
<math>\displaystyle\sum_{i=1}^{11} x_{i1} = \nump[2]{1671.9}</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i1}^2 = \nump[2]{259297.25}</math>,<br />
<math>\displaystyle\sum_{i=1}^{11} x_{i1} = 1671.9</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i1}^2 = 259297.25</math>,<br />
<math>\displaystyle\sum_{i=1}^{11} x_{i3} = \nump[2]{29.2}</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i3}^2 = \nump[2]{88.44}</math>,<br />
<math>\displaystyle\sum_{i=1}^{11} x_{i3} = 29.2</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i3}^2 = 88.44</math>,<br />
<math>\displaystyle\sum_{i=1}^{11} x_{i1}x_{i3} = \nump[2]{4478.28}</math>,<br />
<math>\displaystyle\sum_{i=1}^{11} x_{i1}x_{i3} = 4478.28</math>,<br />
<math>\displaystyle r_{12} = \frac{11\cdot\nump[2]{4478.28}-\nump[2]{1671.9}\cdot\nump[2]{29.2}}{\sqrt{(11\cdot \nump[2]{259297.25}-\nump[2]{1671.9}^2)\cdot(11\cdot \nump[2]{88.44}-\nump[2]{29.2}^2)}}</math><br />
<math>\displaystyle r_{12} = \frac{11\cdot 4478.28-1671.9\cdot 29.2}{\sqrt{(11\cdot 259297.25-1671.9^2)\cdot(11\cdot 88.44-29.2^2)}}</math><br />
<math>\displaystyle r_{12} = \nump{0.168679650013795}</math><br />
<math>\displaystyle r_{12} = 0.16868 </math><br />
<math>\displaystyle\sum_{i=1}^{11} x_{i2} = \nump[2]{1197.4}</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i2}^2 = \nump[2]{132804.82}</math>,<br />
<math>\displaystyle\sum_{i=1}^{11} x_{i2} = 1197.4</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i2}^2 = 132804.82</math>,<br />
<math>\displaystyle\sum_{i=1}^{11} x_{i3} = \nump[2]{29.2}</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i3}^2 = \nump[2]{88.44}</math>,<br />
<math>\displaystyle\sum_{i=1}^{11} x_{i3} = 29.2</math>, <math>\displaystyle\sum_{i=1}^{11} x_{i3}^2 = 88.44 </math>,<br />
<math>\displaystyle\sum_{i=1}^{11} x_{i2}x_{i3} = \nump[2]{3203.89}</math>,<br />
<math>\displaystyle\sum_{i=1}^{11} x_{i2}x_{i3} = 3203.89</math>,<br />
<math>\displaystyle r_{12} = \frac{11\cdot\nump[2]{3203.89}-\nump[2]{1197.4}\cdot\nump[2]{29.2}}{\sqrt{(11\cdot \nump[2]{132804.82}-\nump[2]{1197.4}^2)\cdot(11\cdot \nump[2]{88.44}-\nump[2]{29.2}^2)}}</math><br />
<math>\displaystyle r_{12} = \frac{11\cdot 3203.89- 1197.4 \cdot 29.2}{\sqrt{(11\cdot 132804.82-1197.4^2)\cdot(11\cdot 88.44-29.2^2)}}</math><br />
<math>\displaystyle r_{12} = \nump{0.15446347321087}</math><br />
<math>\displaystyle r_{12} = 0.1545</math><br />
 


===Umsatz und Werbeetat===
===Umsatz und Werbeetat===

Version vom 25. Juni 2019, 07:48 Uhr

Alter und Händlerverkaufspreis

Gegeben:
Es ist . Daraus folgt:
Ferner ist: ( und die Kovarianz haben das gleiche Vorzeichen);

Arbeitslosenquoten

Gesamtkosten und Produktionsmenge

Gewinn eines Unternehmens

Hypothekenzinssatz

1 6 3000 -1 1.0 500 250000.0 -500
2 5 3200 -2 4.0 700 490000.0 -1400.0
3 7 2500 0 0.0 0 0.0 0.0
4 7 2300 0 0.0 -200 40000.0 -0.0
5 8 2000 1 1.0 -500 250000.0 -500
6 9 2000 2 4.0 -500 250000.0 -1000.0
Summe 42 15000 0 10.0 0 1280000.0 -3400
Mittel 7 2500 0 1.7 0 213333.3 -556.7
  • ,

  • Mio EUR, Mio EUR

Immobiliensachverständiger

Objekt Alter Preis
1 15 190 2850 225
2 12 210 2520 144
3 3 400 1200 9
4 17 125 2125 289
5 5 300 1500 25
6 8 197 1576 64
60 1422 11771 756

Konsumausgaben

  • = 211,82 + 0,813
  • 2488,22 EUR Konsumausgaben

Konsumausgaben und verfügbares Einkommen

Kosten und Output


Gegeben:
Gesucht:

Kunstdünger

Datei:Kunstduenger.xlsx

  • ja
  • = 19,93 + 5,0526
  • 75,5086 dt
  • = 0,9753

Ökonomische Variablen

Quadratmetermiete

1 40 12 1 600 144,0 480
2 40 12 1 600 144,0 480
3 40 15 1 600 225,0 600
4 60 12 3 600 144,0 720
5 80 10 6 400 100,0 800
6 80 10 6 400 100,0 800
7 90 9 8 100 81,0 810
8 90 10 8 100 100,0 900
9 90 10 8 100 100,0 900
10 90 10 8 100 100,0 900
Summe 700 110 53 600 1 238,0 7 390
Mittel 70 11 5 360 123,8 739

,
,

Querschnittsanalyse von 11 Unternehmen

Datei:Querschnittsanalyse.xlsx

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  • , , ,

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Umsatz und Werbeetat

Schätzung des Parameters in der linearen Regressionsfunktion .

Filiale 1 2 3 4 5 6
20 16 18 17 12 13 96
29 25 28 26 20 22 150
841 625 784 676 400 484 3810
580 400 504 442 240 286 2452

Zusätzliche statistische Einheit

Lösung g)