Describe a Numeric-Numeric Relationship

Computes, prints and plots a comprehensive bivariate description for two quantitative variables. The function is dispatched automatically by desc(y ~ x, data) when both y and x are numeric.

Usage

.descNN(x, y, conf.level = 0.95)

# S3 method for class 'Desc.nn'
print(x, verbose = NULL, abs.sty = NULL, per.sty = NULL, ...)

# S3 method for class 'Desc.nn'
plot(x, main = x$meta$main, which = 1, verbose = NULL, ...)

Arguments

x

numeric predictor for .descNN(), or an object of class "Desc.nn" for the print and plot methods

verbose

integer controlling the amount of output (1, 2, or 3). NULL (default) falls back to x$meta$verbose \%||\% getOption("DescTools.verbose", 2).

abs.sty

format style for counts. NULL falls back to getOption("DescTools.abs.sty").

per.sty

format style for proportions. NULL falls back to getOption("DescTools.per.sty").

...

further arguments passed to the underlying plot functions

main

main title for the plot. Defaults to the title stored in x$meta$main.

which

integer vector selecting which plots to draw. See Details. NULL (default) selects plots automatically based on verbose.

y

numeric response variable

conf.level

confidence level for interval estimates (default 0.95)

Value

.descNN() returns an object of class c("Desc.nn", "Desc"). Its lm$intercept and lm$slope components contain:

est

point estimate of the coefficient

lci

lower confidence interval bound

uci

upper confidence interval bound

p

p-value

The print and plot methods return x invisibly.

Details

Print output by verbose level:

verbose = 1

Summary (n, missings), Pearson r and Spearman r each with confidence interval and effect size label, linear regression coefficients (estimate, CI, significance) and R².

verbose = 2 (default)

All of the above, plus residual standard error and Shapiro-Wilk test on residuals.

verbose = 3

All of the above, plus Breusch-Pagan test for heteroscedasticity and Cook's distance summary.

Confidence intervals are reported throughout instead of standard errors and t-values, using confint() for regression coefficients and corCI() (Fisher z-transform) for correlations.

Effect size labels for correlations follow Cohen (1988):

negligible	|r| < 0.10
small	0.10 \(\le\) |r| < 0.30
moderate	0.30 \(\le\) |r| < 0.50
large	|r| \(\ge\) 0.50

Plot options via which:

which = 1

Scatterplot with linear regression line and confidence band.

which = 2

Scatterplot with Loess smoother and confidence band (via lines.loess()).

which = 3

Residual plot: residuals vs. fitted values.

which = 4

Q-Q plot of residuals.

Default which by verbose level:

• verbose = 1: which = 1

• verbose = 2: which = 1:2

• verbose = 3: which = 1:4

References

Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum Associates.

Breusch, T.S. and Pagan, A.R. (1979). A simple test for heteroscedasticity and random coefficient variation. Econometrica, 47, 1287–1294.

See also

desc() for the generic entry point, desc.nq() for numeric ~ categorical, desc.qn() for categorical ~ numeric, desc.qq() for categorical ~ categorical, lumen::corCI(), lumen::bpTest(), stats::lm(), stats::cor.test()

Other desc: desc(), desc.Date(), desc.factor(), desc.nq, desc.numeric(), desc.qn, desc.qq, desc.table(), desc.ts()

Examples

# basic usage via desc()
desc(mpg ~ wt, mtcars)
#> ────────────────────────────────────────────────────────────────────────────── 
#> mpg ~ wt (mtcars) (Desc.nn)
#> 
#> Summary:
#> pairs: 32, valid: 32 (100.0%), missings: 0 (0.0%)
#> 
#> 
#> Pearson  r:  -0.868  (-0.934, -0.744)  ***  large
#> Spearman r:  -0.886  (-0.943, -0.778)  ***  large
#> 
#> Linear regression:
#>   Intercept:    6.0473  (  5.4168,   6.6777)  ***
#>   Slope:       -0.1409  ( -0.1710,  -0.1108)  ***
#>   R²: 0.753   adj. R²: 0.745   p: <0.001
#>   Residual SE: 0.4945 on 30 df
#>   Shapiro-Wilk on residuals: W = 0.919,  p = 0.02
#> 


# more detail
desc(mpg ~ wt, mtcars, verbose = 3)
#> ────────────────────────────────────────────────────────────────────────────── 
#> mpg ~ wt (mtcars) (Desc.nn)
#> 
#> Summary:
#> pairs: 32, valid: 32 (100.0%), missings: 0 (0.0%)
#> 
#> 
#> Pearson  r:  -0.868  (-0.934, -0.744)  ***  large
#> Spearman r:  -0.886  (-0.943, -0.778)  ***  large
#> 
#> Linear regression:
#>   Intercept:    6.0473  (  5.4168,   6.6777)  ***
#>   Slope:       -0.1409  ( -0.1710,  -0.1108)  ***
#>   R²: 0.753   adj. R²: 0.745   p: <0.001
#>   Residual SE: 0.4945 on 30 df
#>   Shapiro-Wilk on residuals: W = 0.919,  p = 0.02
#> 


# store result and plot separately
d <- desc(mpg ~ wt, mtcars, plotit = FALSE)
print(d, verbose = 1)
#> ────────────────────────────────────────────────────────────────────────────── 
#> mpg ~ wt (mtcars) (Desc.nn)
#> 
#> Summary:
#> pairs: 32, valid: 32 (100.0%), missings: 0 (0.0%)
#> 
#> 
#> Pearson  r:  -0.868  (-0.934, -0.744)  ***  large
#> Spearman r:  -0.886  (-0.943, -0.778)  ***  large
#> 
#> Linear regression:
#>   Intercept:    6.0473  (  5.4168,   6.6777)  ***
#>   Slope:       -0.1409  ( -0.1710,  -0.1108)  ***
#>   R²: 0.753   adj. R²: 0.745   p: <0.001
#>   Residual SE: 0.4945 on 30 df
#>   Shapiro-Wilk on residuals: W = 0.919,  p = 0.02
#> 
plot(d, which = 1:2)


# pipe
desc(mpg ~ wt, mtcars) |> plot(which = 3)