#Essentials to Business Analytics
# Question 1
x<-c(17.9,16.2,15.0,16.0,17.3,13.2,16.3,17.2,17.7,14.2)
y<-c(2200,6350,8470,6300,4100,8700,6100,2680,3500,8100)
plot(x,y,col="blue",lwd=5,main="Bicycle World Weight and Price",xlab="Weight",ylab = "Price")
abline(lm(y ~ x))
model3<-lm(y ~ x)
model3
##
## Call:
## lm(formula = y ~ x)
##
## Coefficients:
## (Intercept) x
## 28818 -1439
summary(model3)
##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1387.1 -715.9 164.6 679.9 1237.1
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 28818.0 3267.3 8.820 2.15e-05 ***
## x -1439.0 202.1 -7.121 9.99e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 942.3 on 8 degrees of freedom
## Multiple R-squared: 0.8637, Adjusted R-squared: 0.8467
## F-statistic: 50.7 on 1 and 8 DF, p-value: 9.994e-05
data<-data.frame(x,y,xdev=(x-mean(x)),ydev=(y-mean(y)),xdevydev=((x-mean(x))*(y-mean(y))),xdev2=(x-mean(x))^2,ydev2=(y-mean(y))^2)
data
## x y xdev ydev xdevydev xdev2 ydev2
## 1 17.9 2200 1.8 -3450 -6210 3.24 11902500
## 2 16.2 6350 0.1 700 70 0.01 490000
## 3 15.0 8470 -1.1 2820 -3102 1.21 7952400
## 4 16.0 6300 -0.1 650 -65 0.01 422500
## 5 17.3 4100 1.2 -1550 -1860 1.44 2402500
## 6 13.2 8700 -2.9 3050 -8845 8.41 9302500
## 7 16.3 6100 0.2 450 90 0.04 202500
## 8 17.2 2680 1.1 -2970 -3267 1.21 8820900
## 9 17.7 3500 1.6 -2150 -3440 2.56 4622500
## 10 14.2 8100 -1.9 2450 -4655 3.61 6002500
SSy <- sum(data$ydev2)
SSy^2
## [1] 2.716578e+15
# Graph indidcates a negative linear relationship between Weight and Price
# Estimated Regression Model would be y = b0+B1*x --> y=-1439(x)+28818
# Question 2
x<-c(20,20,40,30,60,40)
y<-c(21,19,15,16,14,17)
plot(x,y, col="green",lwd=5,main="# of defective parts to Line Speed",xlab="Line Speed",ylab="Defective Parts")
abline(lm(y~ x))
model4<-lm(y ~ x)
model4
##
## Call:
## lm(formula = y ~ x)
##
## Coefficients:
## (Intercept) x
## 22.1739 -0.1478
xmean<-mean(x)
ymean<-mean(y)
points(xmean,ymean,col="Red",lwd=10)
summary(model4)
##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
## 1 2 3 4 5 6
## 1.7826 -0.2174 -1.2609 -1.7391 0.6957 0.7391
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 22.17391 1.65275 13.416 0.000179 ***
## x -0.14783 0.04391 -3.367 0.028135 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.489 on 4 degrees of freedom
## Multiple R-squared: 0.7391, Adjusted R-squared: 0.6739
## F-statistic: 11.33 on 1 and 4 DF, p-value: 0.02813
SSE<-c(1.78,.217,1.739,.695,.7391)^2
sum(SSE)
## [1] 7.268904
#Essentials to Business Analytics
# Question 3
x<-c(13,10,20,28,32,17,24,31,40,38)
y<-c(17,22,30,37,47,30.5,32.4,39,51.5,40)
plot(x,y,col="purple",lwd=5,main="Annual Maintenance Expense - Weekly usage",xlab = "Weekly usage hours",ylab="Annual Maintenance (100s)")
abline(lm(y~ x))
xmean<-mean(x)
ymean<-mean(y)
points(xmean,ymean,col="red", lwd=10)
model5<-lm(lm(y~ x))
summary(model5)
##
## Call:
## lm(formula = lm(y ~ x))
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.7504 -1.0566 0.0997 2.6192 5.9710
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.5145 3.7473 2.806 0.022990 *
## x 0.9536 0.1383 6.897 0.000125 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.252 on 8 degrees of freedom
## Multiple R-squared: 0.856, Adjusted R-squared: 0.8381
## F-statistic: 47.57 on 1 and 8 DF, p-value: 0.0001249
w<-10.5145+x*.95
SSE<-(y-w)^2
sum(SSE)
## [1] 144.7592
# Question 8
x<-c(22,29,36,47,63,77,73,87,92,101,110,28,59,68,68,91,42,65,110)
y<-c(16.2,16,13.8,11.5,12.5,12.9,11.2,13,11.8,10.8,8.3,12.5,11.1,15,12.2,13,15.6,12.7,8.3)
plot(x,y,col="orange",lwd=5,main="Miles to Price Comparrison", ylab = "Price(1000s)",xlab = "Miles(1000s)")
#There is a negitive linear relationship between Price and Miles
lm(y~x)
##
## Call:
## lm(formula = y ~ x)
##
## Coefficients:
## (Intercept) x
## 16.46976 -0.05877
# Estimated Regression Equation - y= -.05877(x) + 16.46976
A<-(-.05877*x)+16.46976
t.test(A)
##
## One Sample t-test
##
## data: A
## t = 33.793, df = 18, p-value < 2.2e-16
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## 11.76754 13.32773
## sample estimates:
## mean of x
## 12.54764
t.test(y)
##
## One Sample t-test
##
## data: y
## t = 24.8, df = 18, p-value = 2.284e-15
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## 11.48440 13.61033
## sample estimates:
## mean of x
## 12.54737