Question

r code for, any dataset will y, x1 and x2 will be okay

3- Refer to Brand preference data and problem in Assignment 5 (30 pts) a) Transform the variables by means of the correlation transformation and fit the standardized regression model (10pts). b) Interpret the standardized regression coefficient (5pts). c) Transform the estimated standardized regression coefficients back to the ones for the fitted regression model in the original variables (5pts). d) Calculate R2X1, R2X2, R212, R2,1/2, R?y2|1 and R2. Explain what each coefficient measures and interpret your results. (10pts)

Answer 1

### Sample Data
x1 <- c(2.75,2.5,2.5,2.5,2.5,2.5,2.5,2.25,2.25,2.25,2,2,2,1.75,1.75,1.75,1.75,1.75,1.75,1.75,1.75,1.75,1.75,1.75)
x2 <- c(5.3,5.3,5.3,5.3,5.4,5.6,5.5,5.5,5.5,5.6,5.7,5.9,6,5.9,5.8,6.1,6.2,6.1,6.1,6.1,5.9,6.2,6.2,6.1)
y <- c(1464,1394,1357,1293,1256,1254,1234,1195,1159,1167,1130,1075,1047,965,943,958,971,949,884,866,876,822,704,719) 

#check for linearity
# With x1
plot(x=x1, y=y) 
## with x2
plot(x=x2, y=y) 

### correlation of variable

cor.test( ~ y + x1,
          method = "pearson")

cor.test( ~ y + x2,
          method = "pearson")

### Linear Regression with Two variable (using transformation )
model <- lm(log(1+y) ~ x1 + x2)
summary(model)

## Residul Comparision 
x = residuals(model)
library(rcompanion)

plotNormalHistogram(x)