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multiple_regression_examples [2018/11/09 11:58] – [Regression] hkimscilmultiple_regression_examples [2019/11/01 12:30] – [e.g.,] hkimscil
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 x3  work ethic x3  work ethic
 </code> </code>
 +from the above output:
 | x  | zero-order cor  | part cor  | squared zero-order cor  | squared part cor  | shared square cor | | x  | zero-order cor  | part cor  | squared zero-order cor  | squared part cor  | shared square cor |
 | x1 | .764  | .588  | 0.583696  | 0.345744  | 0.237952  | | x1 | .764  | .588  | 0.583696  | 0.345744  | 0.237952  |
 | x2 | .769  | .594  | 0.591361  | 0.352836  | 0.238525  | | x2 | .769  | .594  | 0.591361  | 0.352836  | 0.238525  |
-note that the values of two raws at the last column are similar. +note that the values of two raws at the last column are similar. The portion is the shared effects from both x1 and x2.  
  
 $$ \hat{Y_{i}} = 101.222 + 1.000X1_{i} + 1.071X2_{i} $$ $$ \hat{Y_{i}} = 101.222 + 1.000X1_{i} + 1.071X2_{i} $$
Line 608: Line 609:
          
 </code> </code>
 +
 +====== e.g., ======
 +<code>
 +> stepAIC(lm.full)
 +Start:  AIC=26.82
 +Sales ~ CompPrice + Income + Advertising + Population + Price + 
 +    ShelveLoc + Age + Education + Urban + US
 +
 +              Df Sum of Sq     RSS    AIC
 +- Population   1      0.33  403.16  25.15
 +- Education    1      1.19  404.02  26.00
 +- Urban        1      1.23  404.06  26.04
 +- US           1      1.57  404.40  26.38
 +<none>                      402.83  26.82
 +- Income       1     76.16  478.99  94.09
 +- Advertising  1    127.14  529.97 134.54
 +- Age          1    217.44  620.27 197.48
 +- CompPrice    1    519.91  922.74 356.35
 +- ShelveLoc    2   1053.20 1456.03 536.80
 +- Price        1   1323.23 1726.06 606.85
 +
 +Step:  AIC=25.15
 +Sales ~ CompPrice + Income + Advertising + Price + ShelveLoc + 
 +    Age + Education + Urban + US
 +
 +              Df Sum of Sq     RSS    AIC
 +- Urban        1      1.15  404.31  24.29
 +- Education    1      1.36  404.52  24.49
 +- US           1      1.89  405.05  25.02
 +<none>                      403.16  25.15
 +- Income       1     75.94  479.10  92.18
 +- Advertising  1    145.38  548.54 146.32
 +- Age          1    218.52  621.68 196.38
 +- CompPrice    1    521.69  924.85 355.27
 +- ShelveLoc    2   1053.18 1456.34 534.89
 +- Price        1   1323.51 1726.67 605.00
 +
 +Step:  AIC=24.29
 +Sales ~ CompPrice + Income + Advertising + Price + ShelveLoc + 
 +    Age + Education + US
 +
 +              Df Sum of Sq     RSS    AIC
 +- Education    1      1.44  405.76  23.72
 +- US           1      1.85  406.16  24.12
 +<none>                      404.31  24.29
 +- Income       1     76.64  480.96  91.73
 +- Advertising  1    146.03  550.34 145.63
 +- Age          1    217.59  621.91 194.53
 +- CompPrice    1    526.17  930.48 355.69
 +- ShelveLoc    2   1053.93 1458.25 533.41
 +- Price        1   1322.80 1727.11 603.10
 +
 +Step:  AIC=23.72
 +Sales ~ CompPrice + Income + Advertising + Price + ShelveLoc + 
 +    Age + US
 +
 +              Df Sum of Sq     RSS    AIC
 +- US           1      1.63  407.39  23.32
 +<none>                      405.76  23.72
 +- Income       1     77.87  483.62  91.94
 +- Advertising  1    145.30  551.06 144.15
 +- Age          1    217.97  623.73 193.70
 +- CompPrice    1    525.25  931.00 353.92
 +- ShelveLoc    2   1056.88 1462.64 532.61
 +- Price        1   1322.83 1728.58 601.44
 +
 +Step:  AIC=23.32
 +Sales ~ CompPrice + Income + Advertising + Price + ShelveLoc + 
 +    Age
 +
 +              Df Sum of Sq     RSS    AIC
 +<none>                      407.39  23.32
 +- Income       1     76.68  484.07  90.30
 +- Age          1    219.12  626.51 193.48
 +- Advertising  1    234.03  641.42 202.89
 +- CompPrice    1    523.83  931.22 352.01
 +- ShelveLoc    2   1055.51 1462.90 530.68
 +- Price        1   1324.42 1731.81 600.18
 +
 +Call:
 +lm(formula = Sales ~ CompPrice + Income + Advertising + Price + 
 +    ShelveLoc + Age, data = Carseats)
 +
 +Coefficients:
 +    (Intercept)        CompPrice           Income      Advertising  
 +        5.47523          0.09257          0.01578          0.11590  
 +          Price    ShelveLocGood  ShelveLocMedium              Age  
 +       -0.09532          4.83567          1.95199         -0.04613  
 +
 +> 
 +</code>
 +
 +
 +<WRAP col2>
 +The Carseats data set tracks sales information for car seats. It has 400 observations (each at a different store) and 11 variables:
 +
 +Sales: unit sales in thousands
 +
 +CompPrice: price charged by competitor at each location
 +
 +Income: community income level in 1000s of dollars
 +
 +Advertising: local ad budget at each location in 1000s of dollars
 +
 +Population: regional pop in thousands
 +
 +Price: price for car seats at each site
 +
 +ShelveLoc: Bad, Good or Medium indicates quality of shelving location
 +
 +Age: age level of the population
 +
 +Education: ed level at location
 +
 +Urban: Yes/No
 +
 +US: Yes/NoThe Carseats data set tracks sales information for car seats. It has 400 observations (each at a different store) and 11 variables:
 +
 +Sales: unit sales in thousands
 +
 +CompPrice: price charged by competitor at each location
 +
 +Income: community income level in 1000s of dollars
 +
 +Advertising: local ad budget at each location in 1000s of dollars
 +
 +Population: regional pop in thousands
 +
 +Price: price for car seats at each site
 +
 +ShelveLoc: Bad, Good or Medium indicates quality of shelving location
 +
 +Age: age level of the population
 +
 +Education: ed level at location
 +
 +Urban: Yes/No
 +
 +US: Yes/No
 +The Carseats data set tracks sales information for car seats. It has 400 observations (each at a different store) and 11 variables:
 +
 +Sales: unit sales in thousands
 +
 +CompPrice: price charged by competitor at each location
 +
 +Income: community income level in 1000s of dollars
 +
 +Advertising: local ad budget at each location in 1000s of dollars
 +
 +Population: regional pop in thousands
 +
 +Price: price for car seats at each site
 +
 +ShelveLoc: Bad, Good or Medium indicates quality of shelving location
 +
 +Age: age level of the population
 +
 +Education: ed level at location
 +
 +Urban: Yes/No
 +
 +US: Yes/No
 +The Carseats data set tracks sales information for car seats. It has 400 observations (each at a different store) and 11 variables:
 +
 +Sales: unit sales in thousands
 +
 +CompPrice: price charged by competitor at each location
 +
 +Income: community income level in 1000s of dollars
 +
 +Advertising: local ad budget at each location in 1000s of dollars
 +
 +Population: regional pop in thousands
 +
 +Price: price for car seats at each site
 +
 +ShelveLoc: Bad, Good or Medium indicates quality of shelving location
 +
 +Age: age level of the population
 +
 +Education: ed level at location
 +
 +Urban: Yes/No
 +
 +US: Yes/No
 +The Carseats data set tracks sales information for car seats. It has 400 observations (each at a different store) and 11 variables:
 +
 +Sales: unit sales in thousands
 +
 +CompPrice: price charged by competitor at each location
 +
 +Income: community income level in 1000s of dollars
 +
 +Advertising: local ad budget at each location in 1000s of dollars
 +
 +Population: regional pop in thousands
 +
 +Price: price for car seats at each site
 +
 +ShelveLoc: Bad, Good or Medium indicates quality of shelving location
 +
 +Age: age level of the population
 +
 +Education: ed level at location
 +
 +Urban: Yes/No
 +
 +US: Yes/No
 +The Carseats data set tracks sales information for car seats. It has 400 observations (each at a different store) and 11 variables:
 +
 +Sales: unit sales in thousands
 +
 +CompPrice: price charged by competitor at each location
 +
 +Income: community income level in 1000s of dollars
 +
 +Advertising: local ad budget at each location in 1000s of dollars
 +
 +Population: regional pop in thousands
 +
 +Price: price for car seats at each site
 +
 +ShelveLoc: Bad, Good or Medium indicates quality of shelving location
 +
 +Age: age level of the population
 +
 +Education: ed level at location
 +
 +Urban: Yes/No
 +
 +US: Yes/No
 +</WRAP>
multiple_regression_examples.txt · Last modified: 2023/10/21 13:26 by hkimscil
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