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王一安 2030005058 Problem1
侯香伶 2030005029 Problem2
陈韵扬 2030005011 Problem3
李文锐 2030005036 Problem4
陈郅涵 2030005013 Problem5
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Code Q1.R
#Y=Value
#X1=Lotsize
#X2=Bedrooms
#X3=Bathrooms
#X4=Rooms
#X5=Age
#X6=Taxes
#X7=Garage
#Problem 1
#(a)
A <- read.csv("RealEstate.csv",header = TRUE)
colnames(A)
Y <- A$Value
X1 <- A$LotSize
X2 <- A$Bedrooms
X3 <- A$Bathrooms
X4 <- A$Rooms
X5 <- A$Age
X6 <- A$Taxes
X7 <- A$Garage
summary(lm(Y~X1+X2+X3+X4+X5+X6+X7))#(b)
Estimated Regression Model:
(C) The R^2 and adjusted R^2 are all approximate 0.35, which means the fitting level is okay.
F statistic: The F value (8,+infty) is 2.93,and it is less than the model F-value = 25.91,so the model is significant at 0.05 level.
(D)
P-value: X5,X6 are not significant here. There are two independent variables are not significant in this model at 0.05 significant level.
(E)(F)
lm2 = lm(Y~X1+X2+X3+X4+X5+X6+X7)
windows()
par(mfrow=c(2,2))
plot(lm2)
#link:https://zhuanlan.zhihu.com/p/34627302
(a)
A <- read.csv("RealEstate.csv",header = TRUE)
colnames(A)
Y <- A$Value
X1 <- A$LotSize
X2 <- A$Bedrooms
X3 <- A$Bathrooms
X4 <- A$Rooms
X5 <- A$Age
X6 <- A$Taxes
X7 <- A$Garage
model<-lm(Y~X1+X2+X3+X4+X7,data=A)
summary(model)
windows()
par(mfrow=c(2,2))
plot(model)b),d)
according to Q1, the p-value of variables x1,x2,x3,x4,x7 are all<0.05,these are significant variables we should choose. so we need to use lm(y~x1+x2+x3+X4+x7) and the regression model is:
c) Since the p-values of the two models are same, the adjusted R-squared of them is similar, and the F-value of model in Question 1 is 25.91, the F-value of model in Question 2 is 33.89>25.91, so model in Question 2 is better than model in Question 1.
(e)(f)
summary(model)
windows()
par(mfrow=c(2,2))
plot(model)
(a)
lm1 = lm(Y~X1+X2+X3+X4+X5+X6+X7)
step(lm1,direction = "both")
(b)&(c)
Lm3<-lm(Y~X1+X2+X3+X4+X5+X7)
summary(lm3)
F-statistic in lm3 is 29.69, greater than F-statistic in lm1=25.91
New model lm3 is better than the model in Question 1
(d)
(e)&(f)
windows()
par(mfrow=c(2,2))
plot(lm3)
The final estimated regression model in Problem 3 is
The final estimated regression model in Problem 3 is
if one-car garage, z=1; else z=0.
(a)
A <- read.csv("RealEstate.csv",header = TRUE)
colnames(A)
Y <- A$Value
X1 <- A$LotSize
X2 <- A$Bedrooms
X3 <- A$Bathrooms
X4 <- A$Rooms
X5 <- A$Age
X6 <- A$Taxes
X7 <- A$Garage
X3_sqr<-X3^2
s4<-lm(Y~X1+X2+X3_sqr+X4+X5+X7)
summary(s4)(b)
The estimated regression model is
If one-car garage, z=1; else z=0.
(c)
Since the p-value of the new model is equal to the p-value of Q3, F-value of the new model is larger than F-value of Q3. Also, the adjusted R-squared of them is similar. We can conclude that this new model is better than the model in Q3.
(d)
From the p-value of each independent variable, the p-value of x5 is greater than alpha, but the p-value of other variables is smaller than alpha, so we can conclude that each independent variable is significant, except X5.
(e)&(f)
s4<-lm(Y~X1+X2+X3_sqr+X4+X5+X7)
windows()
par(mfrow=c(2,2))
plot(s4,main = "Graph of Q4")
The final estimated regression model in Problem 4 is
if one-car garage, z=1; else z=0.
A <- read.csv("RealEstate.csv",header = TRUE)
colnames(A)
Y <- A$Value
X1 <- A$LotSize
X2 <- A$Bedrooms
X3 <- A$Bathrooms
X4 <- A$Rooms
X5 <- A$Age
X6 <- A$Taxes
X7 <- A$Garage
(a)
X4_sqr<-X4^2
s5<-lm(Y~X1+X2+X3+X4_sqr+X5+X7)
summary(s5)
(b)
The estimated regression model is
if one-car garage, z=1;else z=0.
(c)
Since the p-value of the new model is equal to the p-value of Q4, F-value of the new model is smaller than F-value of Q4. Also, the adjusted R-squared of them is similar. We can conclude that this new model isn’t better than the model in Q4.
(d)
From the p-value of each independent variable, the p-value of x5 is greater than alpha, but the p-value of other variables is smaller than alpha, so we can conclude that each independent variable is significant, except X5.
(e)&(f)
s5<-lm(Y~X1+X2+X3r+X4_sqr+X5+X7)
windows()
par(mfrow=c(2,2))
plot(s5,main = "Graph of Q5")
M<- c("Q1","Q2","Q3","Q4","Q5")
pValue<- c("< 2.2E-16","< 2.2E-16","< 2.2E-16","< 2.2E-16","< 2.2E-16" )
Sig<- c("No","Yes","No", "No","No")
Rsqure <- c(0.3699, 0.3642, 0.3699, 0.3846,0.3617)
ProjectData <- data.frame(M, pValue , Sig, Rsqure)
colnames(ProjectData) <- c("Models","p-value of F-test","Sig. of all x-var.","R-Square" )
write.table(ProjectData,"/Users/chenzhihan/Desktop/R/ProjectData.txt")
write.csv(ProjectData,"/Users/chenzhihan/Desktop/R/ProjectData.csv")
By this table, we can find that the model in Problem 2 is the best. And all the variables are significant.
So the model is