We consider a multiple linear regression model with LIFE (y) as the response variable, and MALE (x1), BIRTH (x2), DIVO (x3), BEDS (x4), EDUC (x5), and INCO (x6), as predictors.
"STATE" "MALE" "BIRTH" "DIVO" "BEDS" "EDUC" "INCO" "LIFE"
AK 119.1 24.8 5.6 603.3 14.1 4638 69.31
AL 93.3 19.4 4.4 840.9 7.8 2892 69.05
AR 94.1 18.5 4.8 569.6 6.7 2791 70.66
AZ 96.8 21.2 7.2 536.0 12.6 3614 70.55
CA 96.8 18.2 5.7 649.5 13.4 4423 71.71
CO 97.5 18.8 4.7 717.7 14.9 3838 72.06
CT 94.2 16.7 1.9 791.6 13.7 4871 72.48
DC 86.8 20.1 3.0 1859.4 17.8 4644 65.71
DE 95.2 19.2 3.2 926.8 13.1 4468 70.06
FL 93.2 16.9 5.5 668.2 10.3 3698 70.66
GA 94.6 21.1 4.1 705.4 9.2 3300 68.54
HW 108.1 21.3 3.4 794.3 14.0 4599 73.60
IA 94.6 17.1 2.5 773.9 9.1 3643 72.56
ID 99.7 20.3 5.1 541.5 10.0 3243 71.87
IL 94.2 18.5 3.3 871.0 10.3 4446 70.14
IN 95.1 19.1 2.9 736.1 8.3 3709 70.88
KS 96.2 17.0 3.9 854.6 11.4 3725 72.58
KY 96.3 18.7 3.3 661.9 7.2 3076 70.10
LA 94.7 20.4 1.4 724.0 9.0 3023 68.76
MA 91.6 16.6 1.9 1103.8 12.6 4276 71.83
MD 95.5 17.5 2.4 841.3 13.9 4267 70.22
ME 94.8 17.9 3.9 919.5 8.4 3250 70.93
MI 96.1 19.4 3.4 754.7 9.4 4041 70.63
MN 96.0 18.0 2.2 905.4 11.1 3819 72.96
MO 93.2 17.3 3.8 801.6 9.0 3654 70.69
MS 94.0 22.1 3.7 763.1 8.1 2547 68.09
MT 99.9 18.2 4.4 668.7 11.0 3395 70.56
NC 95.9 19.3 2.7 658.8 8.5 3200 69.21
ND 101.8 17.6 1.6 959.9 8.4 3077 72.79
NE 95.4 17.3 2.5 866.1 9.6 3657 72.60
NH 95.7 17.9 3.3 878.2 10.9 3720 71.23
NJ 93.7 16.8 1.5 713.1 11.8 4684 70.93
NM 97.2 21.7 4.3 560.9 12.7 3045 70.32
NV 102.8 19.6 18.7 560.7 10.8 4583 69.03
NY 91.5 17.4 1.4 1056.2 11.9 4605 70.55
OH 94.1 18.7 3.7 751.0 9.3 3949 70.82
OK 94.9 17.5 6.6 664.6 10.0 3341 71.42
OR 95.9 16.8 4.6 607.1 11.8 3677 72.13
PA 92.4 16.3 1.9 948.9 8.7 3879 70.43
RI 96.2 16.5 1.8 960.5 9.4 3878 71.90
SC 96.5 20.1 2.2 739.9 9.0 2951 67.96
SD 98.4 17.6 2.0 984.7 8.6 3108 72.08
TN 93.7 18.4 4.2 831.6 7.9 3079 70.11
TX 95.9 20.6 4.6 674.0 10.9 3507 70.90
UT 97.6 25.5 3.7 470.5 14.0 3169 72.90
VA 97.7 18.6 2.6 835.8 12.3 3677 70.08
VT 95.6 18.8 2.3 1026.1 11.5 3447 71.64
WA 98.7 17.8 5.2 556.4 12.7 3997 71.72
WI 96.3 17.6 2.0 814.7 9.8 3712 72.48
WV 93.9 17.8 3.2 950.4 6.8 3038 69.48
WY 100.7 19.6 5.4 925.9 11.8 3672 70.29
Please find the least-square regression using 1)lm()command in R,
and 2)the matrix formulas(use R to compute) below. Please provide
all the R commands you have used and a screenshot of the result. I
just wanna verify what I did was right as I got two really
different result referring to these two methods. Thanks
The following R code is used to complete the problem and the outputs are attached with it,
***********************************************************************************************************************************************************
#### reading data into R as 'd' #########
d=read.table("tt.txt",sep=" ",header=T)
data=d[,-1]
## data without STATE column
attach(data)
Y=LIFE
design=data[,-7]
#Removing LIFE Column from design matrix
X=cbind(rep(1,51),design)
#Final Design Matrix with first Column as 1
X
inverse=solve(t(X)%*% as.matrix(X),diag(1,7)) ## inverse of
X'X
beta_hat=inverse%*%t(X)%*%Y
## coefficients using the formula]
beta_hat
#### Now computing using lm() function,
beta_lm =coefficients(lm(LIFE~.,data))|
beta_lm
**************************************************END*********************************************************************************************
Conclusion : the above code is synonymous to the problem and gives correct and similar result through both approaches. Note : the variable 'd' stores the entire data as listed in the question.
We consider a multiple linear regression model with LIFE (y) as the response variable, and MALE (...
We consider the multiple linear regression with LIFE (y) as the response variable, and MALE, BIRTH, DIVO , BEDS, EDUC, and INCO, as predictors. QUESTION: Plot the standardized residuals against the fitted values. Are there any notable points. In particular look for points with large residuals or that may be influential. # please screenshot the Rcode for the plot. # data information are as follows: "STATE" "MALE" "BIRTH" "DIVO" "BEDS" "EDUC" "INCO" "LIFE" AK 119.1 24.8 5.6 603.3 14.1 4638...
Census data was collected on the 50 states and Washington, D.C. We are interested in determining whether average lifespan (LIFE) is related to the ratio of males to females in percent (MALE), birth rate per 1,000 people (BIRTH), divorce rate per 1,000 people (DIVO), number of hospital beds per 100,000 people (BEDS), percentage of population 25 years or older having completed 16 years of school (EDUC) and per capita income (INCO). A MLR model has LIFE (y) as the response...
data file: "STATE" "MALE" "BIRTH" "DIVO" "BEDS" "EDUC" "INCO" "LIFE" AK 119.1 24.8 5.6 603.3 14.1 4638 69.31 AL 93.3 19.4 4.4 840.9 7.8 2892 69.05 AR 94.1 18.5 4.8 569.6 6.7 2791 70.66 AZ 96.8 21.2 7.2 536.0 12.6 3614 70.55 CA 96.8 18.2 5.7 649.5 13.4 4423 71.71 CO 97.5 18.8 4.7 717.7 14.9 3838 72.06 CT 94.2 16.7 1.9 791.6 13.7 4871 72.48 DC 86.8 20.1 3.0 1859.4 17.8 4644 65.71 DE 95.2 19.2 3.2 926.8 13.1...