What happens if we run a model based on the z-scores of independent variables instead of the raw values?

Create the z-scores of disp and wt

mtcars$zdisp = (mtcars$disp - mean(mtcars$disp))/sd(mtcars$disp)
mtcars$zwt = (mtcars$wt - mean(mtcars$wt))/sd(mtcars$wt)

Run the two models and look at the summaries

What is the same and what is different?

mod1 = lm(mpg ~ disp + wt,data=mtcars)
modz = lm(mpg ~ zdisp + zwt, data = mtcars)

summary(mod1)
## 
## Call:
## lm(formula = mpg ~ disp + wt, data = mtcars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4087 -2.3243 -0.7683  1.7721  6.3484 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 34.96055    2.16454  16.151 4.91e-16 ***
## disp        -0.01773    0.00919  -1.929  0.06362 .  
## wt          -3.35082    1.16413  -2.878  0.00743 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.917 on 29 degrees of freedom
## Multiple R-squared:  0.7809, Adjusted R-squared:  0.7658 
## F-statistic: 51.69 on 2 and 29 DF,  p-value: 2.744e-10
summary(modz)
## 
## Call:
## lm(formula = mpg ~ zdisp + zwt, data = mtcars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4087 -2.3243 -0.7683  1.7721  6.3484 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  20.0906     0.5156  38.967  < 2e-16 ***
## zdisp        -2.1968     1.1390  -1.929  0.06362 .  
## zwt          -3.2786     1.1390  -2.878  0.00743 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.917 on 29 degrees of freedom
## Multiple R-squared:  0.7809, Adjusted R-squared:  0.7658 
## F-statistic: 51.69 on 2 and 29 DF,  p-value: 2.744e-10
pred1 = predict(mod1)
predz = predict(modz)

dfres = data.frame(pred1,predz)
head(dfres)
##                      pred1    predz
## Mazda RX4         23.34543 23.34543
## Mazda RX4 Wag     22.49097 22.49097
## Datsun 710        25.27237 25.27237
## Hornet 4 Drive    19.61467 19.61467
## Hornet Sportabout 17.05281 17.05281
## Valiant           19.37863 19.37863

Create and examine the predictions

pred1 = predict(mod1)
predz = predict(modz)

dfres = data.frame(pred1,predz)
head(dfres)
##                      pred1    predz
## Mazda RX4         23.34543 23.34543
## Mazda RX4 Wag     22.49097 22.49097
## Datsun 710        25.27237 25.27237
## Hornet 4 Drive    19.61467 19.61467
## Hornet Sportabout 17.05281 17.05281
## Valiant           19.37863 19.37863

Repeat this exercise using the logarithmic transformation.