Create Normal Quantile-Quantile Plot for Logarithmic Model in R

How to create normal quantile-quantile plot for a logarithmic model in R?

A logarithmic model is the type of model in which we take the log of the dependent variable and then create the linear model in R. If we want to create the normal quantile-quantile plot for a logarithmic model then plot function can be used with the model object name and which = 2 argument must be introduced to get the desired plot.

Example1

Live Demo

> x1<-rnorm(100,5,1)
> x1

Output

[1]  4.735737 3.631521 5.522580 5.538314 5.580952 4.341072 4.736899 2.455681
[9]  4.042295 5.534034 4.717607 6.146558 4.466849 5.444437 5.390151 4.491595
[17] 4.227620 4.223362 5.452378 5.690660 5.321716 5.269895 2.810042 4.295378
[25] 5.767740 3.939896 6.213647 4.608487 5.094318 4.621997 4.801568 6.329819
[33] 4.339835 3.172058 6.031193 5.123346 5.673534 5.668435 5.754537 4.164556
[41] 6.630504 5.209786 7.171595 4.713524 4.382267 5.204943 5.895252 4.413933
[49] 5.491437 3.806081 6.283097 4.892824 3.698107 4.758340 3.612643 4.670258
[57] 5.376201 6.440996 3.589660 4.990421 6.649452 5.549918 4.224869 5.604002
[65] 4.667142 5.522634 4.820425 4.278682 4.611169 3.801012 4.774964 4.678297
[73] 4.087518 5.705981 5.812739 4.585449 3.328274 3.626282 4.637604 3.707011
[81] 5.661713 4.671823 6.033384 3.553500 3.945178 3.065177 4.260533 5.226990
[89] 4.852304 4.995663 5.229401 6.588605 5.375225 6.089018 4.199044 6.520236
[97] 5.569930 7.400434 6.291279 4.593149

Example

Live Demo

> y1<-rpois(100,10)
> y1

Output

[1] 10 13 10 11 12 10 7 10 15 6 6 7 8 11 14 16 7 11 14 11 7 7 9 7 7
[26] 13 8 11 12 14 13 8 12 6 9 15 10 8 9 12 11 12 9 10 12 15 11 14 12 13
[51] 8 8 19 10 7 9 9 16 13 8 8 6 9 11 11 18 11 12 12 15 7 12 10 8 10
[76] 10 14 11 5 9 6 11 13 8 9 10 6 6 13 12 14 12 9 11 11 8 9 12 13 5

> Model1<-lm(log(y1)~x1)
> summary(Model1)

Call:

lm(formula = log(y1) ~ x1)

Residuals:

Min 1Q Median 3Q Max
-0.69827 -0.19657 0.01667 0.19465 0.61978

Coefficients:

Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.39474 0.15197 15.758 <2e-16 ***
x1 -0.01895 0.03011 -0.629 0.531
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2895 on 98 degrees of freedom

Multiple R-squared: 0.004024, Adjusted R-squared: -0.006139

F-statistic: 0.3959 on 1 and 98 DF, p-value: 0.5307

Creating the normal quantile-quantile plot:

> plot(Model1,which=2)

Output:

Example2

Live Demo

> x2<-rpois(100,5)
> x2

Output

[1]  3 7 13 4 6 2 4 3 2 7 4 6 3 11 6 5 5 6 6 2 3 7 8 3 1
[26] 8 5 2 2 3 7 6 7 4 7 2 4 3 4 2 5 2 4 5 3 5 8 5 3 3
[51] 6 2 8 3 4 7 3 5 5 3 7 4 7 6 6 6 10 5 4 3 5 7 3 3 5
[76] 4 9 3 7 8 7 2 6 5 7 5 6 6 5 3 9 9 5 4 2 5 5 5 6 4

Example2

Live Demo

> y2<-rpois(100,12)
> y2

Output

[1]  16 8 10 12 11 11 6 15 3 12 8 11 9 12 8 18 7 13 10 17 15 17 15 10 11
[26] 12 16 12 17 13 11 17 16 14 15 10 12 9 10 14 9 6 12 17 14 9 10 9 13 5
[51] 16 12 17 11 10 12 13 18 12 14 19 9 14 11 14 12 6 7 6 16 9 10 11 15 10
[76] 11 8 13 7 16 19 18 8 13 15 11 7 12 7 9 9 14 14 13 15 10 14 11 13 11

> Model2<-lm(log(y2)~x2)
> summary(Model2)

Call:

lm(formula = log(y2) ~ x2)

Residuals:

Min 1Q Median 3Q Max
-1.31858 -0.17210 0.04939 0.21912 0.50892

Coefficients:

Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.409861 0.081191 29.681 <2e-16 ***
x2 0.003665 0.014863 0.247 0.806
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.327 on 98 degrees of freedom

Multiple R-squared: 0.00062, Adjusted R-squared: -0.009578

F-statistic: 0.0608 on 1 and 98 DF, p-value: 0.8057

Creating the normal quantile-quantile plot:

> plot(Model2,which=2)

Output: