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Run a Linear Regression

Source: R/linear_regression.R
linear_regression.Rd

linear_regression() performs bivariate or multiple linear regression with SPSS-compatible output. Wraps stats::lm() and adds standardized coefficients (Beta), a formatted ANOVA table, and a model summary matching SPSS REGRESSION output.

Supports two interface styles:

  • Formula interface: linear_regression(data, life_satisfaction ~ age + education)

  • SPSS-style: linear_regression(data, dependent = life_satisfaction, predictors = c(age, education))

Usage

linear_regression(
  data,
  formula = NULL,
  dependent = NULL,
  predictors = NULL,
  weights = NULL,
  use = c("listwise", "pairwise"),
  standardized = TRUE,
  conf.level = 0.95
)

Arguments

data

Your survey data (a data frame or tibble). If grouped (via dplyr::group_by()), separate regressions are run for each group.

formula

A formula specifying the model (e.g., y ~ x1 + x2). If provided, dependent and predictors are ignored.

dependent

The dependent variable (unquoted). Used with predictors when no formula is given.

predictors

Predictor variable(s) (unquoted, supports tidyselect). Used with dependent when no formula is given.

weights

Optional survey weights (unquoted variable name). When specified, weighted least squares (WLS) is used, matching SPSS WEIGHT BY.

use

How to handle missing data: "listwise" (default) drops any case with a missing value on any variable (matching SPSS /MISSING LISTWISE). "pairwise" computes the regression from a pairwise covariance/correlation matrix, retaining more cases (matching SPSS /MISSING PAIRWISE).

standardized

Logical. If TRUE (default), standardized coefficients (Beta) are calculated and included in the output.

conf.level

Confidence level for coefficient intervals (default 0.95).

Value

An object of class "linear_regression" containing:

coefficients

Tibble with B, Std.Error, Beta, t, p, CI_lower, CI_upper

model_summary

List with R, R_squared, adj_R_squared, std_error

anova

Tibble with Sum of Squares, df, Mean Square, F, Sig.

descriptives

Tibble with Mean, Std.Deviation, N for all variables

model

The underlying lm object

formula

The formula used

n

Sample size (listwise complete cases)

dependent

Name of the dependent variable

predictor_names

Names of predictor variables

weighted

Logical indicating whether weights were used

weight_name

Name of the weight variable (or NULL)

Use summary() for the full SPSS-style output with toggleable sections.

Details

Understanding the Results

The output includes four sections matching SPSS REGRESSION output:

  • Model Summary: R, R-squared, Adjusted R-squared, and Standard Error of the Estimate. R-squared tells you how much variance in the dependent variable is explained by the predictors.

  • ANOVA: Tests whether the overall model is significant. A significant F-test means at least one predictor matters.

  • Coefficients: B (unstandardized), Beta (standardized), t-value, p-value, and confidence intervals for each predictor.

  • Descriptives: Mean, SD, and N for all variables in the model.

Interpreting coefficients:

  • B (unstandardized): For each 1-unit increase in the predictor, the dependent variable changes by B units

  • Beta (standardized): Allows comparison across predictors with different scales. Larger absolute Beta = stronger effect

  • p-value: Values below 0.05 indicate statistically significant predictors

When to Use This

Use linear_regression() when:

  • Your dependent variable is continuous (e.g., income, satisfaction score)

  • You want to predict an outcome from one or more predictors

  • You need standardized coefficients to compare predictor importance

For binary outcomes (yes/no, 0/1), use logistic_regression instead.

Technical Details

Missing Data: By default, listwise deletion is used (matching SPSS REGRESSION /MISSING LISTWISE). Set use = "pairwise" to match SPSS /MISSING PAIRWISE, which computes the regression from a pairwise covariance matrix. Pairwise deletion retains more cases and produces results closer to SPSS output when data has varying patterns of missingness.

Weights: When weights are specified, they are treated as frequency weights (matching SPSS WEIGHT BY behavior). The model is fitted using weighted least squares via lm(weights = ...).

Standardized Coefficients: Beta = B * (SD_x / SD_y). This matches the SPSS standardized coefficient output. Not available for the intercept.

Grouped Analysis: When data is grouped via dplyr::group_by(), a separate regression is run for each group (matching SPSS SPLIT FILE BY).

See also

logistic_regression for binary outcome variables.

describe for checking variable distributions before regression.

pearson_cor for checking bivariate correlations.

summary.linear_regression for detailed output with toggleable sections.

Other regression: logistic_regression()

Examples

library(dplyr)
data(survey_data)

# Bivariate regression
linear_regression(survey_data, life_satisfaction ~ age)
#> Linear Regression: life_satisfaction ~ age
#>   R2 = 0.001, adj.R2 = 0.000, F(1, 2419) = 2.00, p = 0.158 , N = 2421

# Multiple regression
linear_regression(survey_data, income ~ age + education + life_satisfaction)
#> Linear Regression: income ~ age + education + life_satisfaction
#>   R2 = 0.471, adj.R2 = 0.470, F(3, 2111) = 625.48, p < 0.001 ***, N = 2115

# SPSS-style interface
linear_regression(survey_data,
                  dependent = life_satisfaction,
                  predictors = c(trust_government, trust_media, trust_science))
#> Linear Regression: life_satisfaction ~ trust_government + trust_media + trust_science
#>   R2 = 0.002, adj.R2 = 0.000, F(3, 2062) = 1.16, p = 0.322 , N = 2066

# Weighted regression
linear_regression(survey_data, life_satisfaction ~ age, weights = sampling_weight)
#> Linear Regression: life_satisfaction ~ age [Weighted]
#>   R2 = 0.001, adj.R2 = 0.000, F(1, 2435) = 2.08, p = 0.150 , N = 2437

# Grouped by region
survey_data |>
  dplyr::group_by(region) |>
  linear_regression(life_satisfaction ~ age)
#> Linear Regression: life_satisfaction ~ age [Grouped: region]
#>   region = East: R2 = 0.002, adj.R2 = -0.000, F(1, 463) = 0.88, p = 0.350 , N = 465
#>   region = West: R2 = 0.001, adj.R2 = 0.000, F(1, 1954) = 1.20, p = 0.274 , N = 1956

# --- Three-layer output ---
result <- linear_regression(survey_data, life_satisfaction ~ age + income)
result              # compact one-line overview
#> Linear Regression: life_satisfaction ~ age + income
#>   R2 = 0.201, adj.R2 = 0.200, F(2, 2112) = 265.60, p < 0.001 ***, N = 2115
summary(result)     # full detailed SPSS-style output
#> 
#> Linear Regression Results
#> -------------------------
#> - Formula: life_satisfaction ~ age + income
#> - Method: ENTER (all predictors)
#> - N: 2115
#> 
#>   Model Summary
#>   ------------------------------------------------------------
#>   R                              0.448
#>   R Square                       0.201
#>   Adjusted R Square              0.200
#>   Std. Error of Estimate         1.026
#>   ------------------------------------------------------------
#> 
#>   ANOVA
#>   ------------------------------------------------------------------------------
#>   Source           Sum of Squares    df      Mean Square          F     Sig.
#>   ------------------------------------------------------------------------------
#>   Regression              559.609     2          279.804    265.598    0.000 ***
#>   Residual               2224.965  2112            1.053                     
#>   Total                  2784.574  2114                                      
#>   ------------------------------------------------------------------------------
#> 
#>   Coefficients
#>   ----------------------------------------------------------------------------------------
#>   Term                               B  Std.Error     Beta          t     Sig. 
#>   ----------------------------------------------------------------------------------------
#>   (Intercept)                    2.321      0.092              25.237    0.000 ***
#>   age                           -0.001      0.001   -0.010     -0.508    0.611 
#>   income                         0.000      0.000    0.448     23.037    0.000 ***
#>   ----------------------------------------------------------------------------------------
#> 
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
summary(result, collinearity = FALSE)  # hide VIF/Tolerance
#> 
#> Linear Regression Results
#> -------------------------
#> - Formula: life_satisfaction ~ age + income
#> - Method: ENTER (all predictors)
#> - N: 2115
#> 
#>   Model Summary
#>   ------------------------------------------------------------
#>   R                              0.448
#>   R Square                       0.201
#>   Adjusted R Square              0.200
#>   Std. Error of Estimate         1.026
#>   ------------------------------------------------------------
#> 
#>   ANOVA
#>   ------------------------------------------------------------------------------
#>   Source           Sum of Squares    df      Mean Square          F     Sig.
#>   ------------------------------------------------------------------------------
#>   Regression              559.609     2          279.804    265.598    0.000 ***
#>   Residual               2224.965  2112            1.053                     
#>   Total                  2784.574  2114                                      
#>   ------------------------------------------------------------------------------
#> 
#>   Coefficients
#>   ----------------------------------------------------------------------------------------
#>   Term                               B  Std.Error     Beta          t     Sig. 
#>   ----------------------------------------------------------------------------------------
#>   (Intercept)                    2.321      0.092              25.237    0.000 ***
#>   age                           -0.001      0.001   -0.010     -0.508    0.611 
#>   income                         0.000      0.000    0.448     23.037    0.000 ***
#>   ----------------------------------------------------------------------------------------
#> 
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05