> n <- length(Y)
> 
> Y_corr <- (1/sqrt(n-1))*(Y-mean(Y))/sd(Y)       # Correlation transformation for Y
> X1_corr <- (1/sqrt(n-1))*(X1-mean(X1))/sd(X1)   # Correlation transformation for X1
> X2_corr <- (1/sqrt(n-1))*(X2-mean(X2))/sd(X2)   # Correlation transformation for X2
> 
> print(cbind(Y_corr,X1_corr,X2_corr))
            Y_corr     X1_corr      X2_corr
 [1,] -0.046367928  0.07782811 -0.102052117
 [2,] -0.108152604 -0.20197568 -0.079008091
 [3,]  0.384889109  0.35162753  0.243608280
 [4,] -0.168701586 -0.17075294 -0.194228224
 [5,] -0.001882962 -0.18156081  0.036212042
 [6,]  0.158139349  0.04900712  0.243608280
 [7,] -0.179822828 -0.15033807 -0.286404330
 [8,] -0.115566765 -0.12031620  0.013168015
 [9,] -0.225543488 -0.15754332 -0.125096144
[10,] -0.276206922 -0.28363515 -0.263360303
[11,]  0.370678634  0.31079779  0.266652307
[12,]  0.056812480  0.12946572 -0.009876011
[13,]  0.309511805  0.31680217  0.059256068
[14,] -0.226161335 -0.22959579 -0.309448356
[15,] -0.128541547 -0.11431183  0.151432174
[16,]  0.171731978  0.28437855  0.289696333
[17,] -0.219365020 -0.24880979 -0.148140170
[18,] -0.234193343 -0.12391883 -0.194228224
[19,]  0.313218885  0.33121266  0.220564254
[20,]  0.260701911  0.24835231  0.451004519
[21,] -0.095177822 -0.11671358 -0.263360303
> 
> dwaine.stdreg <- lm(Y_corr ~ X1_corr + X2_corr -1)   # Regression of Y* on X1*,X2*, no intercept
> summary(dwaine.stdreg)

Call:
lm(formula = Y_corr ~ X1_corr + X2_corr - 1)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.113831 -0.038406  0.004602  0.058298  0.124898 

Coefficients:
        Estimate Std. Error t value Pr(>|t|)    
X1_corr   0.7484     0.1061   7.056 1.03e-06 ***
X2_corr   0.2511     0.1061   2.368   0.0287 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.06619 on 19 degrees of freedom
Multiple R-squared: 0.9167,     Adjusted R-squared: 0.908 
F-statistic: 104.6 on 2 and 19 DF,  p-value: 5.544e-11 

> 
> (b1 <- (sd(Y)/sd(X1))*coef(dwaine.stdreg)[1])   # Compute b1 from b1*
X1_corr 
1.45456 
> (b2 <- (sd(Y)/sd(X2))*coef(dwaine.stdreg)[2])   # Compute b2 from b2*
X2_corr 
 9.3655 
> (b0 <- mean(Y) - b1*mean(X1) - b2*mean(X2))     # Comute b0 
  X1_corr 
-68.85707 
> 
> dwaine.reg <- lm(Y ~ X1 + X2)                        # Regression of Y on X1,X2
> summary(dwaine.reg)

Call:
lm(formula = Y ~ X1 + X2)

Residuals:
     Min       1Q   Median       3Q      Max 
-18.4239  -6.2161   0.7449   9.4356  20.2151 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) -68.8571    60.0170  -1.147   0.2663    
X1            1.4546     0.2118   6.868    2e-06 ***
X2            9.3655     4.0640   2.305   0.0333 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 11.01 on 18 degrees of freedom
Multiple R-squared: 0.9167,     Adjusted R-squared: 0.9075 
F-statistic:  99.1 on 2 and 18 DF,  p-value: 1.921e-10 

>