ISLR Chapter 3, Saturday April 15, 2017 Linear Regression
Advertising=read.csv('/Users/russconte/advertising.csv', header=TRUE, sep=',')
head(Advertising)## X TV Radio Newspaper Sales
## 1 1 230.1 37.8 69.2 22.1
## 2 2 44.5 39.3 45.1 10.4
## 3 3 17.2 45.9 69.3 9.3
## 4 4 151.5 41.3 58.5 18.5
## 5 5 180.8 10.8 58.4 12.9
## 6 6 8.7 48.9 75.0 7.2Advertising=Advertising[,c(2:5)]
head(Advertising)## TV Radio Newspaper Sales
## 1 230.1 37.8 69.2 22.1
## 2 44.5 39.3 45.1 10.4
## 3 17.2 45.9 69.3 9.3
## 4 151.5 41.3 58.5 18.5
## 5 180.8 10.8 58.4 12.9
## 6 8.7 48.9 75.0 7.2attach(Advertising)sales.lm=lm(Sales~TV, data=Advertising)
summary(sales.lm)##
## Call:
## lm(formula = Sales ~ TV, data = Advertising)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.3860 -1.9545 -0.1913 2.0671 7.2124
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.032594 0.457843 15.36 <2e-16 ***
## TV 0.047537 0.002691 17.67 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.259 on 198 degrees of freedom
## Multiple R-squared: 0.6119, Adjusted R-squared: 0.6099
## F-statistic: 312.1 on 1 and 198 DF, p-value: < 2.2e-16plot(x=TV, y=Sales)
7.032594 -2*0.457843## [1] 6.116908sales.radio.lm=lm(Sales~Radio, data=Advertising)
summary(sales.radio.lm)##
## Call:
## lm(formula = Sales ~ Radio, data = Advertising)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.7305 -2.1324 0.7707 2.7775 8.1810
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.31164 0.56290 16.542 <2e-16 ***
## Radio 0.20250 0.02041 9.921 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.275 on 198 degrees of freedom
## Multiple R-squared: 0.332, Adjusted R-squared: 0.3287
## F-statistic: 98.42 on 1 and 198 DF, p-value: < 2.2e-16sales.newspaper.lm=lm(Sales~Newspaper, data=Advertising)
summary(sales.newspaper.lm)##
## Call:
## lm(formula = Sales ~ Newspaper, data = Advertising)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.2272 -3.3873 -0.8392 3.5059 12.7751
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.35141 0.62142 19.88 < 2e-16 ***
## Newspaper 0.05469 0.01658 3.30 0.00115 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.092 on 198 degrees of freedom
## Multiple R-squared: 0.05212, Adjusted R-squared: 0.04733
## F-statistic: 10.89 on 1 and 198 DF, p-value: 0.001148sales.total.lm=lm(Sales~TV+Radio+Newspaper, data=Advertising)
summary(sales.total.lm)##
## Call:
## lm(formula = Sales ~ TV + Radio + Newspaper, data = Advertising)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.8277 -0.8908 0.2418 1.1893 2.8292
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.938889 0.311908 9.422 <2e-16 ***
## TV 0.045765 0.001395 32.809 <2e-16 ***
## Radio 0.188530 0.008611 21.893 <2e-16 ***
## Newspaper -0.001037 0.005871 -0.177 0.86
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.686 on 196 degrees of freedom
## Multiple R-squared: 0.8972, Adjusted R-squared: 0.8956
## F-statistic: 570.3 on 3 and 196 DF, p-value: < 2.2e-16cor(Advertising)## TV Radio Newspaper Sales
## TV 1.00000000 0.05480866 0.05664787 0.7822244
## Radio 0.05480866 1.00000000 0.35410375 0.5762226
## Newspaper 0.05664787 0.35410375 1.00000000 0.2282990
## Sales 0.78222442 0.57622257 0.22829903 1.0000000credit=read.csv('/Users/russconte/Credit.csv', header=TRUE, sep=',')
head(credit)## X Income Limit Rating Cards Age Education Gender Student Married
## 1 1 14.891 3606 283 2 34 11 Male No Yes
## 2 2 106.025 6645 483 3 82 15 Female Yes Yes
## 3 3 104.593 7075 514 4 71 11 Male No No
## 4 4 148.924 9504 681 3 36 11 Female No No
## 5 5 55.882 4897 357 2 68 16 Male No Yes
## 6 6 80.180 8047 569 4 77 10 Male No No
## Ethnicity Balance
## 1 Caucasian 333
## 2 Asian 903
## 3 Asian 580
## 4 Asian 964
## 5 Caucasian 331
## 6 Caucasian 1151dim(credit)## [1] 400 12credit=credit[,c(2:12)]
head(credit)## Income Limit Rating Cards Age Education Gender Student Married
## 1 14.891 3606 283 2 34 11 Male No Yes
## 2 106.025 6645 483 3 82 15 Female Yes Yes
## 3 104.593 7075 514 4 71 11 Male No No
## 4 148.924 9504 681 3 36 11 Female No No
## 5 55.882 4897 357 2 68 16 Male No Yes
## 6 80.180 8047 569 4 77 10 Male No No
## Ethnicity Balance
## 1 Caucasian 333
## 2 Asian 903
## 3 Asian 580
## 4 Asian 964
## 5 Caucasian 331
## 6 Caucasian 1151pairs(credit)
balance1.lm=lm(Balance~Gender, data=credit)
summary(balance1.lm)##
## Call:
## lm(formula = Balance ~ Gender, data = credit)
##
## Residuals:
## Min 1Q Median 3Q Max
## -529.54 -455.35 -60.17 334.71 1489.20
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 509.80 33.13 15.389 <2e-16 ***
## GenderFemale 19.73 46.05 0.429 0.669
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 460.2 on 398 degrees of freedom
## Multiple R-squared: 0.0004611, Adjusted R-squared: -0.00205
## F-statistic: 0.1836 on 1 and 398 DF, p-value: 0.6685balance2.lm=lm(Balance~Ethnicity, data=credit)
summary(balance2.lm)##
## Call:
## lm(formula = Balance ~ Ethnicity, data = credit)
##
## Residuals:
## Min 1Q Median 3Q Max
## -531.00 -457.08 -63.25 339.25 1480.50
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 531.00 46.32 11.464 <2e-16 ***
## EthnicityAsian -18.69 65.02 -0.287 0.774
## EthnicityCaucasian -12.50 56.68 -0.221 0.826
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 460.9 on 397 degrees of freedom
## Multiple R-squared: 0.0002188, Adjusted R-squared: -0.004818
## F-statistic: 0.04344 on 2 and 397 DF, p-value: 0.9575sales.lm2=lm(Sales~Radio+TV+Radio*TV, data=Advertising)
summary(sales.lm2)##
## Call:
## lm(formula = Sales ~ Radio + TV + Radio * TV, data = Advertising)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.3366 -0.4028 0.1831 0.5948 1.5246
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.750e+00 2.479e-01 27.233 <2e-16 ***
## Radio 2.886e-02 8.905e-03 3.241 0.0014 **
## TV 1.910e-02 1.504e-03 12.699 <2e-16 ***
## Radio:TV 1.086e-03 5.242e-05 20.727 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9435 on 196 degrees of freedom
## Multiple R-squared: 0.9678, Adjusted R-squared: 0.9673
## F-statistic: 1963 on 3 and 196 DF, p-value: < 2.2e-16balance3.lm=lm(Balance~Income+Student, data=credit)
summary(balance3.lm)##
## Call:
## lm(formula = Balance ~ Income + Student, data = credit)
##
## Residuals:
## Min 1Q Median 3Q Max
## -762.37 -331.38 -45.04 323.60 818.28
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 211.1430 32.4572 6.505 2.34e-10 ***
## Income 5.9843 0.5566 10.751 < 2e-16 ***
## StudentYes 382.6705 65.3108 5.859 9.78e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 391.8 on 397 degrees of freedom
## Multiple R-squared: 0.2775, Adjusted R-squared: 0.2738
## F-statistic: 76.22 on 2 and 397 DF, p-value: < 2.2e-16balance4.lm=lm(Balance~Age+Limit, data=credit)
summary(balance4.lm)##
## Call:
## lm(formula = Balance ~ Age + Limit, data = credit)
##
## Residuals:
## Min 1Q Median 3Q Max
## -696.84 -150.78 -13.01 126.68 755.56
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.734e+02 4.383e+01 -3.957 9.01e-05 ***
## Age -2.291e+00 6.725e-01 -3.407 0.000723 ***
## Limit 1.734e-01 5.026e-03 34.496 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 230.5 on 397 degrees of freedom
## Multiple R-squared: 0.7498, Adjusted R-squared: 0.7486
## F-statistic: 595 on 2 and 397 DF, p-value: < 2.2e-16balance5.lm=lm(Balance~Rating+Limit, data=credit)
summary(balance5.lm)##
## Call:
## lm(formula = Balance ~ Rating + Limit, data = credit)
##
## Residuals:
## Min 1Q Median 3Q Max
## -707.8 -135.9 -9.5 124.0 817.6
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -377.53680 45.25418 -8.343 1.21e-15 ***
## Rating 2.20167 0.95229 2.312 0.0213 *
## Limit 0.02451 0.06383 0.384 0.7012
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 232.3 on 397 degrees of freedom
## Multiple R-squared: 0.7459, Adjusted R-squared: 0.7447
## F-statistic: 582.8 on 2 and 397 DF, p-value: < 2.2e-16Lab!
library(MASS)
library(ISLR)attach(Boston)
names(Boston)## [1] "crim" "zn" "indus" "chas" "nox" "rm" "age"
## [8] "dis" "rad" "tax" "ptratio" "black" "lstat" "medv"lm.fit=lm(medv~lstat, data=Boston)
summary(lm.fit)##
## Call:
## lm(formula = medv ~ lstat, data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.168 -3.990 -1.318 2.034 24.500
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 34.55384 0.56263 61.41 <2e-16 ***
## lstat -0.95005 0.03873 -24.53 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.216 on 504 degrees of freedom
## Multiple R-squared: 0.5441, Adjusted R-squared: 0.5432
## F-statistic: 601.6 on 1 and 504 DF, p-value: < 2.2e-16names(lm.fit)## [1] "coefficients" "residuals" "effects" "rank"
## [5] "fitted.values" "assign" "qr" "df.residual"
## [9] "xlevels" "call" "terms" "model"confint(lm.fit)## 2.5 % 97.5 %
## (Intercept) 33.448457 35.6592247
## lstat -1.026148 -0.8739505predict(lm.fit, data.frame(lstat=c(5,10,15)), interval="confidence")## fit lwr upr
## 1 29.80359 29.00741 30.59978
## 2 25.05335 24.47413 25.63256
## 3 20.30310 19.73159 20.87461predict(lm.fit, data.frame(lstat=c(5,10,15)), interval="prediction")## fit lwr upr
## 1 29.80359 17.565675 42.04151
## 2 25.05335 12.827626 37.27907
## 3 20.30310 8.077742 32.52846plot(lstat, medv)
abline(lm.fit)
plot(lstat, medv)
abline(lm.fit,lwd=3)
plot(lstat, medv, pch=20)
abline(lm.fit, col="red")
plot(lstat, medv)
abline(lm.fit,lwd=3, col="red", pch=20)
plot(lstat, medv)
abline(lm.fit,lwd=3, col="red", pch="+")
plot(1:20,1:20, pch=1:20)
par(mfrow=c(2,2))
plot(lm.fit)
plot(predict(lm.fit), residuals(lm.fit))
plot(predict(lm.fit), rstudent(lm.fit))
plot(hatvalues(lm.fit))
which.max(hatvalues(lm.fit))## 375
## 375lm.fit##
## Call:
## lm(formula = medv ~ lstat, data = Boston)
##
## Coefficients:
## (Intercept) lstat
## 34.55 -0.95Boston[375,]## crim zn indus chas nox rm age dis rad tax ptratio black
## 375 18.4982 0 18.1 0 0.668 4.138 100 1.137 24 666 20.2 396.9
## lstat medv
## 375 37.97 13.83.6.3 Multiple Linear Regression
lm.fit.boston1=lm(medv~lstat+age, data=Boston)
summary(lm.fit.boston1)##
## Call:
## lm(formula = medv ~ lstat + age, data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.981 -3.978 -1.283 1.968 23.158
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 33.22276 0.73085 45.458 < 2e-16 ***
## lstat -1.03207 0.04819 -21.416 < 2e-16 ***
## age 0.03454 0.01223 2.826 0.00491 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.173 on 503 degrees of freedom
## Multiple R-squared: 0.5513, Adjusted R-squared: 0.5495
## F-statistic: 309 on 2 and 503 DF, p-value: < 2.2e-16options(scipen=999)
lm.fit.boston2=lm(medv~., data=Boston)
summary(lm.fit.boston2)##
## Call:
## lm(formula = medv ~ ., data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.595 -2.730 -0.518 1.777 26.199
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 36.4594884 5.1034588 7.144 0.000000000003283 ***
## crim -0.1080114 0.0328650 -3.287 0.001087 **
## zn 0.0464205 0.0137275 3.382 0.000778 ***
## indus 0.0205586 0.0614957 0.334 0.738288
## chas 2.6867338 0.8615798 3.118 0.001925 **
## nox -17.7666112 3.8197437 -4.651 0.000004245643808 ***
## rm 3.8098652 0.4179253 9.116 < 0.0000000000000002 ***
## age 0.0006922 0.0132098 0.052 0.958229
## dis -1.4755668 0.1994547 -7.398 0.000000000000601 ***
## rad 0.3060495 0.0663464 4.613 0.000005070529023 ***
## tax -0.0123346 0.0037605 -3.280 0.001112 **
## ptratio -0.9527472 0.1308268 -7.283 0.000000000001309 ***
## black 0.0093117 0.0026860 3.467 0.000573 ***
## lstat -0.5247584 0.0507153 -10.347 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.745 on 492 degrees of freedom
## Multiple R-squared: 0.7406, Adjusted R-squared: 0.7338
## F-statistic: 108.1 on 13 and 492 DF, p-value: < 0.00000000000000022library(car)
vif(lm.fit.boston2)## crim zn indus chas nox rm age dis
## 1.792192 2.298758 3.991596 1.073995 4.393720 1.933744 3.100826 3.955945
## rad tax ptratio black lstat
## 7.484496 9.008554 1.799084 1.348521 2.941491lm.fit.boston2=lm(medv~.-age, data=Boston)
summary(lm.fit.boston2)##
## Call:
## lm(formula = medv ~ . - age, data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.6054 -2.7313 -0.5188 1.7601 26.2243
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 36.436927 5.080119 7.172 0.0000000000027155 ***
## crim -0.108006 0.032832 -3.290 0.001075 **
## zn 0.046334 0.013613 3.404 0.000719 ***
## indus 0.020562 0.061433 0.335 0.737989
## chas 2.689026 0.859598 3.128 0.001863 **
## nox -17.713540 3.679308 -4.814 0.0000019671100076 ***
## rm 3.814394 0.408480 9.338 < 0.0000000000000002 ***
## dis -1.478612 0.190611 -7.757 0.0000000000000503 ***
## rad 0.305786 0.066089 4.627 0.0000047505389684 ***
## tax -0.012329 0.003755 -3.283 0.001099 **
## ptratio -0.952211 0.130294 -7.308 0.0000000000010992 ***
## black 0.009321 0.002678 3.481 0.000544 ***
## lstat -0.523852 0.047625 -10.999 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.74 on 493 degrees of freedom
## Multiple R-squared: 0.7406, Adjusted R-squared: 0.7343
## F-statistic: 117.3 on 12 and 493 DF, p-value: < 0.00000000000000022summary(lm(medv~lstat*age, data=Boston))##
## Call:
## lm(formula = medv ~ lstat * age, data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.806 -4.045 -1.333 2.085 27.552
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 36.0885359 1.4698355 24.553 < 0.0000000000000002 ***
## lstat -1.3921168 0.1674555 -8.313 0.000000000000000878 ***
## age -0.0007209 0.0198792 -0.036 0.9711
## lstat:age 0.0041560 0.0018518 2.244 0.0252 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.149 on 502 degrees of freedom
## Multiple R-squared: 0.5557, Adjusted R-squared: 0.5531
## F-statistic: 209.3 on 3 and 502 DF, p-value: < 0.00000000000000022lm.fit.boston3=lm(medv~lstat+I(lstat^2))
summary(lm.fit.boston3)##
## Call:
## lm(formula = medv ~ lstat + I(lstat^2))
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.2834 -3.8313 -0.5295 2.3095 25.4148
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 42.862007 0.872084 49.15 <0.0000000000000002 ***
## lstat -2.332821 0.123803 -18.84 <0.0000000000000002 ***
## I(lstat^2) 0.043547 0.003745 11.63 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.524 on 503 degrees of freedom
## Multiple R-squared: 0.6407, Adjusted R-squared: 0.6393
## F-statistic: 448.5 on 2 and 503 DF, p-value: < 0.00000000000000022lm.fit.boston4=lm(medv~lstat)
anova(lm.fit, lm.fit.boston3)## Analysis of Variance Table
##
## Model 1: medv ~ lstat
## Model 2: medv ~ lstat + I(lstat^2)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 504 19472
## 2 503 15347 1 4125.1 135.2 < 0.00000000000000022 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1par(mfrow=c(2,2))
plot(lm.fit.boston4)
lm.fit5=lm(medv~poly(lstat,5))
summary(lm.fit5)##
## Call:
## lm(formula = medv ~ poly(lstat, 5))
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.5433 -3.1039 -0.7052 2.0844 27.1153
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 22.5328 0.2318 97.197 < 0.0000000000000002 ***
## poly(lstat, 5)1 -152.4595 5.2148 -29.236 < 0.0000000000000002 ***
## poly(lstat, 5)2 64.2272 5.2148 12.316 < 0.0000000000000002 ***
## poly(lstat, 5)3 -27.0511 5.2148 -5.187 0.00000031 ***
## poly(lstat, 5)4 25.4517 5.2148 4.881 0.00000142 ***
## poly(lstat, 5)5 -19.2524 5.2148 -3.692 0.000247 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.215 on 500 degrees of freedom
## Multiple R-squared: 0.6817, Adjusted R-squared: 0.6785
## F-statistic: 214.2 on 5 and 500 DF, p-value: < 0.00000000000000022summary(lm(medv~log(rm), data=Boston))##
## Call:
## lm(formula = medv ~ log(rm), data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -19.487 -2.875 -0.104 2.837 39.816
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -76.488 5.028 -15.21 <0.0000000000000002 ***
## log(rm) 54.055 2.739 19.73 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.915 on 504 degrees of freedom
## Multiple R-squared: 0.4358, Adjusted R-squared: 0.4347
## F-statistic: 389.3 on 1 and 504 DF, p-value: < 0.000000000000000223.6, qualitative predictors
attach(Carseats)## The following object is masked _by_ .GlobalEnv:
##
## Advertising## The following object is masked from Advertising:
##
## Salesnames(Carseats)## [1] "Sales" "CompPrice" "Income" "Advertising" "Population"
## [6] "Price" "ShelveLoc" "Age" "Education" "Urban"
## [11] "US"lm.fit.carseats1=lm(Sales~.+Income:Advertising+Price:Age, data=Carseats)
summary(lm.fit.carseats1)##
## Call:
## lm(formula = Sales ~ . + Income:Advertising + Price:Age, data = Carseats)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.9208 -0.7503 0.0177 0.6754 3.3413
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.5755654 1.0087470 6.519 0.000000000222 ***
## CompPrice 0.0929371 0.0041183 22.567 < 0.0000000000000002 ***
## Income 0.0108940 0.0026044 4.183 0.000035665275 ***
## Advertising 0.0702462 0.0226091 3.107 0.002030 **
## Population 0.0001592 0.0003679 0.433 0.665330
## Price -0.1008064 0.0074399 -13.549 < 0.0000000000000002 ***
## ShelveLocGood 4.8486762 0.1528378 31.724 < 0.0000000000000002 ***
## ShelveLocMedium 1.9532620 0.1257682 15.531 < 0.0000000000000002 ***
## Age -0.0579466 0.0159506 -3.633 0.000318 ***
## Education -0.0208525 0.0196131 -1.063 0.288361
## UrbanYes 0.1401597 0.1124019 1.247 0.213171
## USYes -0.1575571 0.1489234 -1.058 0.290729
## Income:Advertising 0.0007510 0.0002784 2.698 0.007290 **
## Price:Age 0.0001068 0.0001333 0.801 0.423812
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.011 on 386 degrees of freedom
## Multiple R-squared: 0.8761, Adjusted R-squared: 0.8719
## F-statistic: 210 on 13 and 386 DF, p-value: < 0.00000000000000022contrasts(ShelveLoc)## Good Medium
## Bad 0 0
## Good 1 0
## Medium 0 1