Impliment
getwd()
## [1] "C:/Users/Shalini/Documents"
mydata <- read.csv("G:/Datasets_BA 2/wc-at.csv")
View(mydata)
summary(mydata)
## Waist AT
## Min. : 63.5 Min. : 11.44
## 1st Qu.: 80.0 1st Qu.: 50.88
## Median : 90.8 Median : 96.54
## Mean : 91.9 Mean :101.89
## 3rd Qu.:104.0 3rd Qu.:137.00
## Max. :121.0 Max. :253.00
plot(mydata)
colnames(mydata)
## [1] "Waist" "AT"
sd(mydata$waist)
## [1] NA
sd(mydata$AT)
## [1] 57.29476
var(mydata$Waist)
## [1] 183.8496
var(mydata$AT)
## [1] 3282.69
hist(mydata$Waist)
hist(mydata$AT)
qqnorm(mydata$Waist)
qqline(mydata$Waist)
qqnorm(mydata$AT)
qqline(mydata$AT)
cor(mydata$Waist,mydata$AT)
## [1] 0.8185578
model <- lm(mydata$AT~mydata$Waist)
summary(model)
##
## Call:
## lm(formula = mydata$AT ~ mydata$Waist)
##
## Residuals:
## Min 1Q Median 3Q Max
## -107.288 -19.143 -2.939 16.376 90.342
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -215.9815 21.7963 -9.909 <2e-16 ***
## mydata$Waist 3.4589 0.2347 14.740 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 33.06 on 107 degrees of freedom
## Multiple R-squared: 0.67, Adjusted R-squared: 0.667
## F-statistic: 217.3 on 1 and 107 DF, p-value: < 2.2e-16
confint(model,level=0.95)
## 2.5 % 97.5 %
## (Intercept) -259.190053 -172.77292
## mydata$Waist 2.993689 3.92403
predict(model,interval="predict")
## Warning in predict.lm(model, interval = "predict"): predictions on current data refer to _future_ responses
## fit lwr upr
## 1 42.568252 -23.7607107 108.89721
## 2 35.131704 -31.3249765 101.58838
## 3 66.953210 0.9383962 132.96802
## 4 74.389758 8.4385892 140.34093
## 5 42.222366 -24.1122081 108.55694
## 6 32.537559 -33.9671546 99.04227
## 7 63.840237 -2.2056980 129.88617
## 8 72.487385 6.5213726 138.45340
## 9 3.656083 -63.5036005 70.81577
## 10 37.207020 -29.2125284 103.62657
## 11 32.710502 -33.7909536 99.21196
## 12 43.432966 -22.8821078 109.74804
## 13 36.861134 -29.5645231 103.28679
## 14 57.268404 -8.8518878 123.38870
## 15 50.350685 -15.8605336 116.56190
## 16 22.160981 -44.5537679 88.87573
## 17 46.718883 -19.5452517 112.98302
## 18 40.492936 -25.8701771 106.85605
## 19 39.282335 -27.1012331 105.66590
## 20 46.545940 -19.7208032 112.81268
## 21 49.831856 -16.3867039 116.05042
## 22 63.840237 -2.2056980 129.88617
## 23 60.381377 -5.7022296 126.46498
## 24 92.548770 26.6894200 158.40812
## 25 67.644982 1.6367253 133.65324
## 26 102.233576 36.3862036 168.08095
## 27 83.555735 17.6622091 149.44926
## 28 62.456693 -3.6039202 128.51731
## 29 81.480420 15.5758571 147.38498
## 30 69.374412 3.3819768 135.36685
## 31 72.833271 6.8700310 138.79651
## 32 88.744024 22.8729233 154.61513
## 33 98.082945 32.2335934 163.93230
## 34 93.240542 27.3829016 159.09818
## 35 136.822170 70.8074775 202.83686
## 36 110.880725 45.0222774 176.73917
## 37 98.774717 32.9260237 164.62341
## 38 140.281029 74.2316072 206.33045
## 39 60.727263 -5.3524301 126.80696
## 40 57.268404 -8.8518878 123.38870
## 41 72.833271 6.8700310 138.79651
## 42 46.891826 -19.3697083 113.15336
## 43 62.456693 -3.6039202 128.51731
## 44 83.209849 17.3145658 149.10513
## 45 71.103842 5.1264122 137.08127
## 46 154.462353 88.2365608 220.68815
## 47 110.188953 44.3321471 176.04576
## 48 110.880725 45.0222774 176.73917
## 49 59.689606 -6.4019262 125.78114
## 50 58.306062 -7.8017094 124.41383
## 51 94.624085 28.7694706 160.47870
## 52 73.870929 7.9158100 139.82605
## 53 78.713332 12.7922191 144.63445
## 54 45.162396 -21.1255054 111.45030
## 55 55.193088 -10.9531208 121.33930
## 56 55.884860 -10.2525800 122.02230
## 57 87.706367 21.8313711 153.58136
## 58 82.518078 16.6191807 148.41697
## 59 79.750990 13.8363291 145.66565
## 60 73.525043 7.5672497 139.48284
## 61 52.426001 -13.7565798 118.60858
## 62 77.675674 11.7478144 143.60353
## 63 60.035492 -6.0520617 126.12304
## 64 158.612984 92.3252791 224.90069
## 65 197.698095 130.6020356 264.79416
## 66 198.735753 131.6127559 265.85875
## 67 117.798443 51.9163563 183.68053
## 68 148.928178 82.7776990 215.07866
## 69 147.198748 81.0701043 213.32739
## 70 154.116467 87.8956245 220.33731
## 71 154.116467 87.8956245 220.33731
## 72 133.363311 67.3800865 199.34653
## 73 119.527873 53.6378248 185.41792
## 74 129.904451 63.9494297 195.85947
## 75 157.575326 91.3035349 223.84712
## 76 129.904451 63.9494297 195.85947
## 77 140.281029 74.2316072 206.33045
## 78 143.739889 77.6524810 209.82730
## 79 150.657608 84.4844833 216.83073
## 80 161.034186 94.7082219 227.36015
## 81 142.010459 75.9424508 208.07847
## 82 164.493045 98.1096934 230.87640
## 83 164.493045 98.1096934 230.87640
## 84 171.410764 104.9030239 237.91850
## 85 159.304756 93.0062808 225.60323
## 86 143.739889 77.6524810 209.82730
## 87 167.951905 101.5079578 234.39585
## 88 159.304756 93.0062808 225.60323
## 89 202.540498 135.3163441 269.76465
## 90 161.034186 94.7082219 227.36015
## 91 121.257303 55.3584733 187.15613
## 92 148.928178 82.7776990 215.07866
## 93 122.986732 57.0783023 188.89516
## 94 110.880725 45.0222774 176.73917
## 95 119.527873 53.6378248 185.41792
## 96 147.198748 81.0701043 213.32739
## 97 150.657608 84.4844833 216.83073
## 98 126.445592 60.5155029 192.37568
## 99 98.774717 32.9260237 164.62341
## 100 138.551600 72.5199497 204.58325
## 101 150.657608 84.4844833 216.83073
## 102 161.380072 95.0485136 227.71163
## 103 181.787342 115.0691257 248.50556
## 104 133.363311 67.3800865 199.34653
## 105 130.250337 64.2926425 196.20803
## 106 106.730093 40.8795247 172.58066
## 107 136.130398 70.1222603 202.13854
## 108 157.229440 90.9628890 223.49599
## 109 159.304756 93.0062808 225.60323
model <- lm(mydata$AT~log(mydata$Waist))
summary(model)
##
## Call:
## lm(formula = mydata$AT ~ log(mydata$Waist))
##
## Residuals:
## Min 1Q Median 3Q Max
## -98.473 -18.273 -2.374 14.538 90.400
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1328.34 95.92 -13.85 <2e-16 ***
## log(mydata$Waist) 317.14 21.26 14.92 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 32.8 on 107 degrees of freedom
## Multiple R-squared: 0.6753, Adjusted R-squared: 0.6723
## F-statistic: 222.6 on 1 and 107 DF, p-value: < 2.2e-16
model <- lm(log(mydata$AT)~log(mydata$Waist))
summary(model)
##
## Call:
## lm(formula = log(mydata$AT) ~ log(mydata$Waist))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.96388 -0.21762 0.01988 0.21214 0.79811
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -12.4607 0.9820 -12.69 <2e-16 ***
## log(mydata$Waist) 3.7476 0.2176 17.22 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3358 on 107 degrees of freedom
## Multiple R-squared: 0.7348, Adjusted R-squared: 0.7324
## F-statistic: 296.5 on 1 and 107 DF, p-value: < 2.2e-16