Multiple Regression
praisons
June 20, 2016
R Markdown
This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see http://rmarkdown.rstudio.com.
When you click the Knit button a document will be generated that includes both content as well as the output of any embedded R code chunks within the document. You can embed an R code chunk like this:
setwd('C:/Users/praisons/Documents/CBA/Term3/SA2')
cigdata <- read.csv('CigaretteConsumption.csv', header = TRUE, sep=',')
fit <- lm(formula = Sales~State+Age+HS+Income+Black+Female+Price, data = cigdata)
names(cigdata)## [1] "State" "Age" "HS" "Income" "Black" "Female" "Price" "Sales"summary(fit)##
## Call:
## lm(formula = Sales ~ State + Age + HS + Income + Black + Female +
## Price, data = cigdata)
##
## Residuals:
## ALL 51 residuals are 0: no residual degrees of freedom!
##
## Coefficients: (6 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.213e+02 NA NA NA
## StateAL -3.150e+01 NA NA NA
## StateAR -2.100e+01 NA NA NA
## StateAZ -6.100e+00 NA NA NA
## StateCA 1.700e+00 NA NA NA
## StateCO 3.500e+00 NA NA NA
## StateCT -1.300e+00 NA NA NA
## StateDC 7.910e+01 NA NA NA
## StateDE 3.370e+01 NA NA NA
## StateFL 2.300e+00 NA NA NA
## StateGA -1.140e+01 NA NA NA
## StateHI -3.920e+01 NA NA NA
## StateID -1.890e+01 NA NA NA
## StateIL 3.500e+00 NA NA NA
## StateIN 1.330e+01 NA NA NA
## StateIO -1.280e+01 NA NA NA
## StateKA -7.300e+00 NA NA NA
## StateKY 3.450e+01 NA NA NA
## StateLA -5.400e+00 NA NA NA
## StateMA 3.000e+00 NA NA NA
## StateMD 2.200e+00 NA NA NA
## StateME 7.200e+00 NA NA NA
## StateMI 7.300e+00 NA NA NA
## StateMN -1.700e+01 NA NA NA
## StateMO 9.723e-14 NA NA NA
## StateMS -2.790e+01 NA NA NA
## StateMT -1.010e+01 NA NA NA
## StateNB -1.320e+01 NA NA NA
## StateNC 5.110e+01 NA NA NA
## StateND -2.750e+01 NA NA NA
## StateNH 1.444e+02 NA NA NA
## StateNJ -6.000e-01 NA NA NA
## StateNM -3.130e+01 NA NA NA
## StateNV 6.820e+01 NA NA NA
## StateNY -2.300e+00 NA NA NA
## StateOH 3.000e-01 NA NA NA
## StateOK -1.290e+01 NA NA NA
## StateOR 3.570e+01 NA NA NA
## StatePA -1.400e+01 NA NA NA
## StateRI 2.600e+00 NA NA NA
## StateSC -1.770e+01 NA NA NA
## StateSD -2.860e+01 NA NA NA
## StateTN -2.150e+01 NA NA NA
## StateTX -1.490e+01 NA NA NA
## StateUT -5.580e+01 NA NA NA
## StateVA 3.000e+00 NA NA NA
## StateVT 1.300e+00 NA NA NA
## StateWA -2.460e+01 NA NA NA
## StateWI -1.490e+01 NA NA NA
## StateWV -6.800e+00 NA NA NA
## StateWY 1.090e+01 NA NA NA
## Age NA NA NA NA
## HS NA NA NA NA
## Income NA NA NA NA
## Black NA NA NA NA
## Female NA NA NA NA
## Price NA NA NA NA
##
## Residual standard error: NaN on 0 degrees of freedom
## Multiple R-squared: 1, Adjusted R-squared: NaN
## F-statistic: NaN on 50 and 0 DF, p-value: NAcoefficients(fit)## (Intercept) StateAL StateAR StateAZ StateCA
## 1.213000e+02 -3.150000e+01 -2.100000e+01 -6.100000e+00 1.700000e+00
## StateCO StateCT StateDC StateDE StateFL
## 3.500000e+00 -1.300000e+00 7.910000e+01 3.370000e+01 2.300000e+00
## StateGA StateHI StateID StateIL StateIN
## -1.140000e+01 -3.920000e+01 -1.890000e+01 3.500000e+00 1.330000e+01
## StateIO StateKA StateKY StateLA StateMA
## -1.280000e+01 -7.300000e+00 3.450000e+01 -5.400000e+00 3.000000e+00
## StateMD StateME StateMI StateMN StateMO
## 2.200000e+00 7.200000e+00 7.300000e+00 -1.700000e+01 9.723124e-14
## StateMS StateMT StateNB StateNC StateND
## -2.790000e+01 -1.010000e+01 -1.320000e+01 5.110000e+01 -2.750000e+01
## StateNH StateNJ StateNM StateNV StateNY
## 1.444000e+02 -6.000000e-01 -3.130000e+01 6.820000e+01 -2.300000e+00
## StateOH StateOK StateOR StatePA StateRI
## 3.000000e-01 -1.290000e+01 3.570000e+01 -1.400000e+01 2.600000e+00
## StateSC StateSD StateTN StateTX StateUT
## -1.770000e+01 -2.860000e+01 -2.150000e+01 -1.490000e+01 -5.580000e+01
## StateVA StateVT StateWA StateWI StateWV
## 3.000000e+00 1.300000e+00 -2.460000e+01 -1.490000e+01 -6.800000e+00
## StateWY Age HS Income Black
## 1.090000e+01 NA NA NA NA
## Female Price
## NA NA# Run regression for cars data
carsdata <- read.csv('Cars.csv', header = TRUE, sep=',')
head(carsdata)## HP MPG VOL SP WT
## 1 49 53.70068 89 104.1854 28.76206
## 2 55 50.01340 92 105.4613 30.46683
## 3 55 50.01340 92 105.4613 30.19360
## 4 70 45.69632 92 113.4613 30.63211
## 5 53 50.50423 92 104.4613 29.88915
## 6 70 45.69632 89 113.1854 29.59177names(carsdata)## [1] "HP" "MPG" "VOL" "SP" "WT"fit <- lm(formula = MPG~HP+VOL+SP+WT, data = carsdata)
fit##
## Call:
## lm(formula = MPG ~ HP + VOL + SP + WT, data = carsdata)
##
## Coefficients:
## (Intercept) HP VOL SP WT
## 30.6773 -0.2054 -0.3361 0.3956 0.4006summary(fit)##
## Call:
## lm(formula = MPG ~ HP + VOL + SP + WT, data = carsdata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.6320 -2.9944 -0.3705 2.2149 15.6179
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 30.67734 14.90030 2.059 0.0429 *
## HP -0.20544 0.03922 -5.239 1.4e-06 ***
## VOL -0.33605 0.56864 -0.591 0.5563
## SP 0.39563 0.15826 2.500 0.0146 *
## WT 0.40057 1.69346 0.237 0.8136
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.488 on 76 degrees of freedom
## Multiple R-squared: 0.7705, Adjusted R-squared: 0.7585
## F-statistic: 63.8 on 4 and 76 DF, p-value: < 2.2e-16coefficients(fit)## (Intercept) HP VOL SP WT
## 30.6773359 -0.2054437 -0.3360508 0.3956269 0.4005741anova(fit)## Analysis of Variance Table
##
## Response: MPG
## Df Sum Sq Mean Sq F value Pr(>F)
## HP 1 3506.6 3506.6 174.1099 < 2.2e-16 ***
## VOL 1 1500.8 1500.8 74.5153 6.763e-13 ***
## SP 1 131.5 131.5 6.5274 0.01262 *
## WT 1 1.1 1.1 0.0560 0.81365
## Residuals 76 1530.7 20.1
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1plot(fit)
fitted(fit)## 1 2 3 4 5 6 7 8
## 43.44193 42.38879 42.27934 42.53836 42.17265 43.02062 42.32536 48.07622
## 9 10 11 12 13 14 15 16
## 48.28120 40.79123 41.52153 47.80957 39.95980 41.52758 41.76632 41.61814
## 17 18 19 20 21 22 23 24
## 41.15094 47.98606 41.30861 37.87128 38.57706 37.35200 37.89770 39.56251
## 25 26 27 28 29 30 31 32
## 39.93381 46.73871 35.48166 38.78153 38.24861 36.00285 34.84604 37.21630
## 33 34 35 36 37 38 39 40
## 37.13920 34.82541 37.22361 37.53950 39.27145 38.24220 38.54286 35.93917
## 41 42 43 44 45 46 47 48
## 34.21298 35.36313 37.50473 38.07998 35.79652 36.26134 34.21826 35.59393
## 49 50 51 52 53 54 55 56
## 36.91805 33.31108 33.21313 33.30236 29.19865 27.52359 28.32071 28.56723
## 57 58 59 60 61 62 63 64
## 35.81584 33.02108 35.37335 32.29910 29.87686 28.76094 25.14188 26.47041
## 65 66 67 68 69 70 71 72
## 25.97652 36.35652 26.09759 23.64162 24.39887 20.21195 27.80846 22.44207
## 73 74 75 76 77 78 79 80
## 23.07668 18.71731 23.84935 21.07461 21.28210 17.89905 26.13645 12.31661
## 81
## 15.55948coef(fit)## (Intercept) HP VOL SP WT
## 30.6773359 -0.2054437 -0.3360508 0.3956269 0.4005741residuals(fit)## 1 2 3 4 5 6
## 10.2587466 7.6246083 7.7340597 3.1579626 8.3315838 2.6757032
## 7 8 9 10 11 12
## 7.6880405 -1.3596642 -1.5646482 1.5078500 3.1313020 -8.4554734
## 13 14 15 16 17 18
## -0.6057086 3.1252554 3.9685696 3.0346894 1.6389684 -8.6319611
## 19 20 21 22 23 24
## 1.4812984 1.0305547 -0.1660608 5.4764823 0.4129031 0.9122089
## 25 26 27 28 29 30
## -1.6232007 -8.3277058 2.9293443 -0.3705217 5.2208220 -0.5986605
## 31 32 33 34 35 36
## 4.5851953 2.2149327 -0.8537415 1.4600425 2.3080186 0.4192422
## 37 38 39 40 41 42
## -1.3127053 -4.1715306 -4.4721963 -4.9250413 0.9397515 -0.2104056
## 43 44 45 46 47 48
## -3.4340655 -2.9272579 -0.1529590 -1.6998387 0.3432343 -0.5416044
## 49 50 51 52 53 54
## -5.9039220 -3.6811456 -3.5831982 -3.6724290 0.4312871 -3.0362191
## 55 56 57 58 59 60
## -1.4684346 -0.7109743 -4.7022521 -3.3911486 -5.2414271 -3.4388698
## 61 62 63 64 65 66
## -2.5225932 -4.1518066 -1.6259672 -2.9544920 -2.3713610 3.6934752
## 67 68 69 70 71 72
## -2.9944195 -0.5384461 -1.2957003 1.0617543 -8.1299580 0.7615007
## 73 74 75 76 77 78
## 0.1268910 0.3690266 -4.7630064 -2.3117761 15.6179040 1.2988377
## 79 80 81
## 7.8635469 7.5171216 -3.4582177Including Plots
You can also embed plots, for example:
Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.