Chapter 24 Simple Regression Analysis
Univariate regression analysis (with one predictor) can be useful to get an estimate of the increase in the dependent variable as a function of the predictor variable. The approach differs for continuous or categorical predictors, and both will be shown.
24.1.1 Example dataset
This example uses the Rosetta Stats example dataset “pp15” (see Chapter 1 for information about the datasets and Chapter 3 for an explanation of how to load datasets).
24.2 Input: jamovi
In the “Analyses” tab, click the “Regression” button and from the menu that appears, select “Linear Regression” as shown in Figure 24.1.
In the box at the left, select the dependent variable and move it to the box labelled “Dependent variable” using the button labelled with the rightward-pointing arrow as shown in Figure 24.2.
Then, select the predictor variable and move it to the box labelled “Covariates” if it is a continuous variable, and to the box labelled “Factors” if it is a categorical variable, as shown in Figure 24.3.
The results will immediately be shown in the right-hand “Results” panel. You can scroll down to specify additional analyses, for example to order more details about the coefficient by opening the “Model Coefficients” section as shown in Figure 24.4.
For example, to request the confidence interval for the slope coefficient and the standardized (scaled) coefficient, check the corresponding check boxes as shown in Figure 24.5.
24.3 Input: R
In R, there are roughly three approaches. Many analyses can be done with base R without installing additional packages. The
rosetta package accompanies this book and aims to provide output similar to jamovi and SPSS with simple commands. Finally, the tidyverse is a popular collection of packages that try to work together consistently but implement a different underlying logic that base R (and so, the
24.3.1 R: base R
In base R, the
lm (linear model) function can be combined with the
summary function to show the most important results. With a continuous predictor, the code is as follows.
<- result lm( ~ highDose_attitude, xtcUseDosePref data=dat );summary( result);
With a categorical predictor, the code is essentially the same, since R automatically treats variables that are factors as categorical, and numeric vectors as continuous variables.
<- result lm( ~ hasJob, xtcUseDosePref data=dat );summary( result);
24.3.2 R: rosetta
rosetta package, the
regr function wraps base R’s
lm function to present output similar to that provided by other statistics programs in one command.
::regr( rosetta~ highDose_attitude, xtcUseDosePref data=dat );
lm in base R, the command is the same for a continuous predictor as it is for a categorical predictor (i.e. by replacing
A scatter plot can be requested using argument
::regr( rosetta~ highDose_attitude, xtcUseDosePref data=dat, plot=TRUE );
24.4 Input: SPSS
For SPSS, there are two approaches: using the Graphical User Interface (GUI) or specify an analysis script, which in SPSS are called “syntax”.
24.4.2 SPSS: Syntax
In SPSS, the
REGRESSION command is used (don’t forget the period at the end (
.), the command terminator):
REGRESSION /DEPENDENT xtcUseDosePref /METHOD ENTER highDose_attitude /STATISTICS COEF CI(95) R ANOVA .
With a categorical predictor the code is essentially the same, since SPSS “sees” whether the predictor is continuous or categorical.
REGRESSION /DEPENDENT xtcUseDosePref /METHOD ENTER gender /STATISTICS COEF CI(95) R ANOVA .
24.6 Output: R
24.6.1 R: base R
Call: lm(formula = xtcUseDosePref ~ highDose_attitude, data = pp15) Residuals: Min 1Q Median 3Q Max -144.58 -58.56 -11.85 41.44 348.60 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 56.394 24.890 2.266 0.0251 * highDose_attitude 32.956 6.704 4.916 2.56e-06 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 88.8 on 133 degrees of freedom (694 observations deleted due to missingness) Multiple R-squared: 0.1538, Adjusted R-squared: 0.1474 F-statistic: 24.16 on 1 and 133 DF, p-value: 2.559e-06
24.6.2 R: rosetta
22.214.171.124 Regression analysis
|Formula:||xtcUseDosePref ~ highDose_attitude|
|Multiple R-squared:||[.06; .28] (point estimate = 0.15, adjusted = 0.15)|
Test for significance:
(of full model)
|F[1, 133] = 24.16, p < .001|
Raw regression coefficients
|95% conf. int.||estimate||se||t||p|
|a These are unstandardized beta values, called ‘B’ in SPSS.|
Scaled regression coefficients
|95% conf. int.||estimate||se||t||p|
|a These are standardized beta values, called ‘Beta’ in SPSS.|