Quick Answer: Ramsey RESET Test Result

The Ramsey RESET Test checks whether the original regression model is correctly specified. The null hypothesis says the model has no major functional-form misspecification detected by fitted-value power terms. The alternative hypothesis says the model may be misspecified because the added fitted squared, fitted cubed, or higher-order fitted terms significantly improve prediction.

In this worked example, the model predicts G3 final grade using student-performance predictors such as prior grades and study-related variables. The Ramsey RESET Test is used after the basic regression model to ask a deeper diagnostic question: does the linear model capture the main structure, or are important nonlinear terms missing? The observed-versus-fitted chart, residuals-versus-fitted chart, fitted power terms chart, model fit comparison chart, RESET F reference curve, p-value decision chart, and RESET power-sensitivity chart are all used to support the decision.

What Is the Ramsey RESET Test?

Ramsey RESET Test, often called the Regression Equation Specification Error Test, is a diagnostic test for linear regression model specification. It asks whether the model may be missing nonlinear relationships or important terms. A regression model can have a high R-squared and still be misspecified if it leaves out nonlinear structure or uses the wrong functional form.

The test works by fitting the original regression model, saving the fitted values, then adding powers of those fitted values into an augmented model. If the added fitted power terms are statistically significant, the test suggests that the original model may be incomplete or misspecified.

The Ramsey RESET Test belongs in a broader regression-diagnostics workflow. It should be interpreted together with residual plots, observed-versus-fitted values, normality checks, heteroscedasticity checks, multicollinearity checks, outlier diagnostics, and theory-based model review. Useful related guides include Goldfeld-Quandt test, Q-Q plot normality check, P-P plot normality check, Levene test, and Brown-Forsythe test.

Ramsey RESET Test Formula

The original linear regression model can be written as:

After fitting this model, the predicted values are saved as ŷ. The Ramsey RESET Test then estimates an augmented model by adding fitted power terms:

The RESET decision tests whether the fitted power terms are jointly significant. If they are jointly significant, the original model may be missing nonlinear or omitted-variable structure.

Ramsey RESET F-Test Decision

If the RESET F-test is significant, the augmented model fits significantly better than the original model. This suggests possible omitted nonlinear terms, interactions, missing predictors, or incorrect functional form. If the test is not significant, the RESET test does not detect this type of misspecification.

Null and Alternative Hypotheses for Ramsey RESET Test

The Ramsey RESET Test has a clear hypothesis structure. The null hypothesis says the original regression model is adequately specified with respect to the fitted-power terms tested. The alternative hypothesis says the fitted power terms improve the model, suggesting misspecification.

Dataset and Regression Variables Used

The worked example uses a student performance regression model. The dependent variable is G3 final grade. Predictors may include earlier grades and student-background variables such as G1, G2, studytime, failures, absences and age. The Ramsey RESET Test checks whether the linear specification is adequate or whether fitted-value powers improve the model.

Before running the Ramsey RESET Test, review the model with descriptive statistics, frequency distribution, histogram interpretation, box plot interpretation, and coefficient of variation.

SPSS Output Interpretation for Ramsey RESET Test

The SPSS output PDF verifies the Ramsey RESET Test workflow. In SPSS, the RESET workflow is usually completed by fitting the original regression model, saving fitted values, computing fitted-value powers, fitting the augmented model, and comparing model fit. The RESET decision is based on whether the added fitted power terms significantly improve the model.

SPSS Ramsey RESET Workflow Table

SPSS Interpretation Logic

If the fitted power terms are significant in the augmented model, the SPSS interpretation should state that the original model may be misspecified. This does not automatically prove a specific omitted variable, but it does indicate that the linear specification may be incomplete. If the fitted power terms are not significant, the RESET test does not provide evidence of this type of misspecification.

How SPSS Output Connects with the Charts

The charts below explain the SPSS result visually. Observed-versus-fitted values show prediction alignment. Residuals-versus-fitted values show patterns not captured by the model. Fitted power terms show the variables added by RESET. Model fit comparison shows whether the augmented model improves fit. The RESET F reference curve and p-value chart summarize the formal decision. Power sensitivity shows how the test behaves when different fitted power terms are considered.

Python Chart-by-Chart Interpretation

The Python charts provide the main visual explanation of the Ramsey RESET Test. They show the original model fit, residual structure, fitted power terms, model fit comparison, RESET F-test reference curve, p-value decision and sensitivity to fitted power choices.

Python Chart 1: Observed vs Fitted Values

This chart checks how closely the original regression model predicts the observed outcome. If points follow the diagonal reference pattern closely, the fitted values are aligned with observed values. If there is curvature, systematic spread, or large deviations, the model may not capture the full relationship.

For the Ramsey RESET Test, observed-versus-fitted alignment is the first visual clue. A model can fit well overall but still miss nonlinear patterns. Therefore, this chart should be interpreted with residuals-versus-fitted and fitted power terms rather than alone.

Python Chart 2: Residuals vs Fitted Values

This chart is one of the most important diagnostics for the Ramsey RESET Test. Residuals should be scattered randomly around zero. Curves, waves, funnels, or systematic patterns suggest that the model may be missing nonlinear terms, interactions, or other structure.

If the residuals show a clear pattern, the RESET test may become significant because fitted squared or cubed terms can capture some of the missing structure. If the residual pattern is random, the RESET test is less likely to detect misspecification.

Python Chart 3: Fitted Power Terms

This chart explains the mechanics of the Ramsey RESET Test. The original fitted values are transformed into powers such as fitted squared and fitted cubed. These power terms are added to the model to test whether they explain additional variation in the outcome.

If fitted power terms add meaningful explanatory power, the model may be missing nonlinear structure. The chart helps readers understand that RESET is not a vague model-checking tool; it specifically tests whether powers of fitted values reveal patterns that the original model failed to capture.

Python Chart 4: Model Fit Comparison

This chart compares model fit before and after adding the RESET fitted power terms. If the augmented model improves fit noticeably and the improvement is statistically significant, the RESET decision supports possible misspecification in the original model.

The correct interpretation is not that the fitted powers should always become the final model. Instead, they are diagnostic indicators. A significant improvement means the analyst should consider better theory-based nonlinear terms, transformations, interactions, or omitted variables.

Python Chart 5: RESET F Reference Curve

This chart explains the formal F-test decision. The RESET F statistic is compared with the reference F distribution. If the observed F statistic falls far into the upper tail, the p-value becomes small, and the test rejects the null hypothesis of correct specification.

The F reference curve helps readers understand that the RESET decision is a formal statistical comparison, not only a visual judgment. It shows where the observed statistic lies relative to what would be expected if the added fitted power terms did not matter.

Python Chart 6: P-value Decision

This chart summarizes the decision rule. If the p-value is less than .05, reject the null hypothesis that the original model is adequately specified under the fitted-power diagnostic. If the p-value is greater than .05, the RESET test does not find evidence of specification error through the tested fitted powers.

The p-value decision should always be reported with the visual charts. A significant p-value tells the analyst that follow-up work is needed, but the residual plots and model comparison help explain what type of follow-up may be useful.

Python Chart 7: RESET Power Sensitivity

This chart shows the sensitivity of the RESET result to the fitted power terms included in the augmented model. A test that includes only fitted squared values may behave differently from a test that includes squared and cubed fitted values. Sensitivity analysis helps determine whether the misspecification signal is stable or dependent on one chosen power term.

If the RESET decision remains significant across several power settings, the evidence of misspecification is stronger. If the result changes depending on the power choice, the analyst should interpret the result more cautiously and inspect the residual plots carefully.

R Chart-by-Chart Validation

The R charts validate the Python and SPSS Ramsey RESET Test interpretation using a separate workflow. The same seven diagnostic views appear again: observed versus fitted values, residuals versus fitted values, fitted power terms, model fit comparison, RESET F reference curve, p-value decision and RESET power sensitivity.

R Chart 1: Observed vs Fitted Values

The R observed-versus-fitted chart validates the Python model-fit view. It shows whether fitted values track observed G3 values reasonably well and whether there are visible prediction patterns that may require further diagnostic review.

R Chart 2: Residuals vs Fitted Values

The R residual plot confirms whether residual patterns are random or systematic. A random cloud supports the linear specification. A curve or structured pattern suggests that the model may be missing nonlinear or omitted terms, which is exactly the type of issue the Ramsey RESET Test is designed to detect.

R Chart 3: Fitted Power Terms

The R fitted-power chart validates how the augmented model is built. It confirms that the RESET test adds functions of the fitted values rather than randomly adding unrelated terms. This helps readers understand the test logic clearly.

R Chart 4: Model Fit Comparison

The R model fit comparison confirms whether adding fitted power terms improves fit. If the augmented model improves fit only slightly and the p-value is not significant, specification may be acceptable under this test. If improvement is clear and significant, the original model requires follow-up.

R Chart 5: RESET F Reference Curve

The R F reference curve validates the formal RESET decision. The chart shows how extreme the observed RESET F statistic is under the null hypothesis. This makes the p-value decision more transparent for readers.

R Chart 6: P-value Decision

The R p-value chart confirms the decision rule used in Python. The chart should be read together with the residual plot and model comparison. A significant result points to possible specification error; a nonsignificant result means this RESET version did not detect fitted-power misspecification.

R Chart 7: RESET Power Sensitivity

The R sensitivity chart confirms whether the RESET decision is stable across fitted-power choices. Stable significance across powers strengthens the misspecification warning. A decision that changes across powers should be interpreted cautiously and followed by theory-based model review.

SPSS, R, Python and Excel Workflows for Ramsey RESET Test

The Ramsey RESET Test can be performed in SPSS, R, Python and Excel-style workflows. The core logic is always the same: fit the original model, save fitted values, create fitted power terms, fit an augmented model, and test whether the fitted powers significantly improve model fit.

SPSS Workflow

R Workflow

Python Workflow

Excel Workflow

Code Blocks for Ramsey RESET Test

SPSS Syntax for Ramsey RESET Test

* Ramsey RESET Test workflow in SPSS.
* Dependent variable: G3.
* Predictors: G1 G2 studytime failures absences age.

TITLE "Ramsey RESET Test Regression Specification Check".

REGRESSION
  /DEPENDENT G3
  /METHOD=ENTER G1 G2 studytime failures absences age
  /STATISTICS COEFF OUTS R ANOVA COLLIN TOL CHANGE
  /SAVE PRED(pred_original) RESID(resid_original)
  /CRITERIA=PIN(.05) POUT(.10).

* Create fitted power terms.
COMPUTE pred_sq = pred_original ** 2.
COMPUTE pred_cu = pred_original ** 3.
VARIABLE LABELS pred_sq "Squared fitted value for Ramsey RESET".
VARIABLE LABELS pred_cu "Cubed fitted value for Ramsey RESET".
EXECUTE.

* Augmented RESET model.
REGRESSION
  /DEPENDENT G3
  /METHOD=ENTER G1 G2 studytime failures absences age pred_sq pred_cu
  /STATISTICS COEFF OUTS R ANOVA COLLIN TOL CHANGE
  /CRITERIA=PIN(.05) POUT(.10).

* Inspect residuals from original model.
EXAMINE VARIABLES=resid_original
  /PLOT BOXPLOT HISTOGRAM NPPLOT
  /STATISTICS DESCRIPTIVES
  /CINTERVAL 95
  /MISSING LISTWISE
  /NOTOTAL.

OUTPUT EXPORT
  /CONTENTS EXPORT=VISIBLE
  /PDF DOCUMENTFILE="Ramsey-RESET-Test-SPSS-Output.pdf".

Python Code for Ramsey RESET Test

import pandas as pd
import statsmodels.api as sm
from statsmodels.stats.diagnostic import linear_reset

df = pd.read_csv("dataset.csv")

dependent = "G3"
predictors = ["G1", "G2", "studytime", "failures", "absences", "age"]

model_data = df[[dependent] + predictors].apply(pd.to_numeric, errors="coerce").dropna()

X = sm.add_constant(model_data[predictors])
y = model_data[dependent]

original_model = sm.OLS(y, X).fit()

# Ramsey RESET Test using fitted powers
reset_result = linear_reset(original_model, power=3, use_f=True)

print(original_model.summary())
print(reset_result)

# Manual augmented model with fitted squared and cubed
model_data["fitted"] = original_model.fittedvalues
model_data["fitted_sq"] = model_data["fitted"] ** 2
model_data["fitted_cu"] = model_data["fitted"] ** 3

X_aug = sm.add_constant(model_data[predictors + ["fitted_sq", "fitted_cu"]])
augmented_model = sm.OLS(y, X_aug).fit()

print(augmented_model.summary())

print("Original R-squared:", original_model.rsquared)
print("Augmented R-squared:", augmented_model.rsquared)
print("RESET F statistic:", reset_result.statistic)
print("RESET p-value:", reset_result.pvalue)

if reset_result.pvalue < 0.05:
    print("Reject correct specification: possible model misspecification.")
else:
    print("Do not reject correct specification under RESET test.")

R Code for Ramsey RESET Test

# Ramsey RESET Test in R

df <- read.csv("dataset.csv")

vars_needed <- c("G3", "G1", "G2", "studytime", "failures", "absences", "age")
df_model <- df[vars_needed]
df_model[] <- lapply(df_model, as.numeric)
df_model <- na.omit(df_model)

model_original <- lm(G3 ~ G1 + G2 + studytime + failures + absences + age, data = df_model)

summary(model_original)

# install.packages("lmtest")
library(lmtest)

reset_result <- resettest(model_original, power = 2:3, type = "fitted")

print(reset_result)

# Manual augmented model
df_model$fitted <- fitted(model_original)
df_model$fitted_sq <- df_model$fitted^2
df_model$fitted_cu <- df_model$fitted^3

model_augmented <- lm(G3 ~ G1 + G2 + studytime + failures + absences + age + fitted_sq + fitted_cu,
                      data = df_model)

summary(model_augmented)

anova(model_original, model_augmented)

Excel Formula Block for Ramsey RESET Test

Step 1:
Run the original regression using Excel Data Analysis ToolPak.

Step 2:
Save predicted values from the original model.

Step 3:
Create fitted squared:
=Predicted_Value^2

Step 4:
Create fitted cubed:
=Predicted_Value^3

Step 5:
Run the augmented regression:
Dependent variable = G3
Predictors = original predictors + fitted squared + fitted cubed

Step 6:
Compare original and augmented models:
Original R²
Augmented R²
Adjusted R²
F statistics
Significance of fitted squared and fitted cubed terms

Step 7:
Interpret:
If fitted power terms significantly improve fit, the original model may be misspecified.
If fitted power terms do not improve fit, RESET does not detect fitted-power misspecification.

APA Reporting Wording for Ramsey RESET Test

APA reporting for the Ramsey RESET Test should include the test name, model being checked, fitted power terms used, F statistic if available, p-value, decision, and follow-up interpretation. Do not simply write that the model is “good” or “bad.” The RESET test is a specification diagnostic, not a complete model-quality certificate.

APA-Style Full Report

If RESET Is Significant

If RESET Is Not Significant

Common Mistakes in Ramsey RESET Test Interpretation

When to Use Ramsey RESET Test

Use the Ramsey RESET Test after fitting a linear regression model when you want to check whether the model may have an incorrect functional form. It is especially useful when residual plots suggest curvature, when theory suggests possible nonlinear relationships, or when a model fits poorly despite relevant predictors.

The Ramsey RESET Test should be used with other regression diagnostics. For heteroscedasticity, review the Goldfeld-Quandt test. For normality, review the Q-Q plot normality check, P-P plot normality check, Kolmogorov-Smirnov test, Lilliefors test, D’Agostino-Pearson test, and Ryan-Joiner test.

Downloads and Resources for Ramsey RESET Test

The SPSS output PDF below verifies the Ramsey RESET Test workflow used for this guide. Use it as the supporting output file for SPSS interpretation, original model review, fitted power terms, augmented model comparison and reporting.

Related Statistical Guides

Use these related guides to connect the Ramsey RESET Test with regression diagnostics, assumption checks, normality tests, variance checks, descriptive analysis and reporting.