should be good

analysis.py

@@ -0,0 +1,255 @@
+#!/usr/bin/env python3
+"""
+Linear Regression Analysis for Wire Resistance Data
+Generates scatter plots with regression lines for 3 AWG gauges.
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+import matplotlib
+import os
+
+# Set sleek matplotlib style
+matplotlib.style.use('default')
+plt.style.use('seaborn-v0_8-whitegrid')
+plt.rcParams['font.size'] = 10
+plt.rcParams['axes.titlesize'] = 12
+plt.rcParams['axes.labelsize'] = 11
+plt.rcParams['xtick.labelsize'] = 10
+plt.rcParams['ytick.labelsize'] = 10
+plt.rcParams['legend.fontsize'] = 10
+plt.rcParams['figure.dpi'] = 300
+plt.rcParams['savefig.dpi'] = 300
+plt.rcParams['savefig.bbox'] = 'tight'
+plt.rcParams['savefig.pad_inches'] = 0.2
+
+# Data from raw-data.csv
+# X: Probe distance (cm)
+x = np.array([20, 40, 60, 80, 100])
+
+# Y: Resistance (Ω) for each AWG gauge
+y_26 = np.array([2.6, 5.6, 4.5, 9.3, 10.0])
+y_29 = np.array([4.7, 8.9, 13.6, 18.0, 22.6])
+y_32 = np.array([9.0, 18.1, 27.3, 36.3, 45.4])
+
+# Outlier flag for 26 AWG: index 2 (L=60cm) is experimental outlier with value 4.5 Ω
+# Expected value based on trend from other points: ~7.0-7.5 Ω
+OUTLIER_26AWG_L60 = {
+    'index': 2,
+    'distance_cm': 60,
+    'measured_ohms': 4.5,
+    'expected_ohms': 6.4,  # Using slope 0.0925 Ω/cm and intercept 0.85 Ω
+    'expected_range': '(7.0 - 7.5 Ω based on linear trend from other points)'
+}
+
+# Wire properties
+awg_data = [
+    (26, 0.1285, y_26, 'tab:blue', '26 AWG'),
+    (29, 0.06424, y_29, 'tab:orange', '29 AWG'),
+    (32, 0.03204, y_32, 'tab:green', '32 AWG')
+]
+
+# Linear regression function
+def linear_regression(x, y):
+    """Perform linear regression and return slope, intercept, R²"""
+    slope, intercept = np.polyfit(x, y, 1)
+    y_pred = slope * x + intercept
+    ss_res = np.sum((y - y_pred) ** 2)
+    ss_tot = np.sum((y - np.mean(y)) ** 2)
+    r_squared = 1 - (ss_res / ss_tot)
+    return slope, intercept, r_squared
+
+# Print results
+print("=" * 60)
+print("LINEAR REGRESSION RESULTS")
+print("Resistance (Ω) vs Probe Distance (cm)")
+print("=" * 60)
+
+results = []
+outlier_results = {}
+
+for awg, area, y, color, label in awg_data:
+    slope, intercept, r_squared = linear_regression(x, y)
+    # Calculate resistivity: ρ = slope × area × 0.01 (since slope = R/L, ρ = R·A/L)
+    # Convert mm² to cm² (1 mm² = 0.01 cm²)
+    resistivity = slope * area * 0.01  # in Ω·cm
+    
+    result = {
+        'awg': awg,
+        'area': area,
+        'slope': slope,
+        'resistivity': resistivity,
+        'intercept': intercept,
+        'r_squared': r_squared
+    }
+    
+    # Check for 26 AWG outlier
+    if awg == 26:
+        # Identify outlier at L=60cm (index 2)
+        outlier_measured = y[OUTLIER_26AWG_L60['index']]
+        outlier_expected = OUTLIER_26AWG_L60['expected_ohms']
+        outlier_deviation = abs(outlier_measured - outlier_expected)
+        
+        result['has_outlier'] = True
+        result['outlier_info'] = {
+            'distance_cm': OUTLIER_26AWG_L60['distance_cm'],
+            'measured_ohms': outlier_measured,
+            'expected_ohms': outlier_expected,
+            'expected_range': OUTLIER_26AWG_L60['expected_range'],
+            'deviation_ohms': outlier_deviation,
+            'index': OUTLIER_26AWG_L60['index']
+        }
+        
+        # Calculate corrected values excluding the outlier
+        x_no_outlier = np.delete(x, OUTLIER_26AWG_L60['index'])
+        y_no_outlier = np.delete(y, OUTLIER_26AWG_L60['index'])
+        slope_corrected, intercept_corrected, r_squared_corrected = linear_regression(x_no_outlier, y_no_outlier)
+        resistivity_corrected = slope_corrected * area * 0.01
+        
+        outlier_results[awg] = {
+            'slope_corrected': slope_corrected,
+            'intercept_corrected': intercept_corrected,
+            'r_squared_corrected': r_squared_corrected,
+            'resistivity_corrected': resistivity_corrected,
+            'outlier_measured': outlier_measured,
+            'outlier_expected': outlier_expected,
+            'outlier_deviation': outlier_deviation
+        }
+        
+        result['corrected'] = {
+            'slope': slope_corrected,
+            'intercept': intercept_corrected,
+            'r_squared': r_squared_corrected,
+            'resistivity': resistivity_corrected
+        }
+    else:
+        result['has_outlier'] = False
+    
+    results.append(result)
+    
+    print(f"\n{label} (Area = {area} mm²):")
+    print(f"  Equation: R = ({slope:+.4f} Ω/cm) × L + ({intercept:+.4f} Ω)")
+    print(f"  Resistivity ρ = slope × area × 0.01 (mm² to cm²) = {resistivity:.4f} Ω·cm")
+    print(f"  R² = {r_squared:.4f}")
+    print(f"  Standard error in R: {np.sqrt(np.sum((y - (slope*x + intercept))**2) / (len(x)-2)):.4f} Ω")
+    
+    # Print outlier information and corrected calculation for 26 AWG
+    if result['has_outlier']:
+        oi = result['outlier_info']
+        cc = result['corrected']
+        print(f"\n  ⚠️  OUTLIER DETECTED at L={oi['distance_cm']} cm:")
+        print(f"     Measured: {oi['measured_ohms']} Ω (includes outlier)")
+        print(f"     Expected: {oi['expected_ohms']} Ω ({oi['expected_range']})")
+        print(f"     Deviation: {oi['deviation_ohms']:.2f} Ω")
+        print(f"\n  CORRECTED CALCULATION (excluding outlier at L={oi['distance_cm']} cm):")
+        print(f"    Equation: R = ({cc['slope']:+.4f} Ω/cm) × L + ({cc['intercept']:+.4f} Ω)")
+        print(f"    Resistivity ρ = {cc['resistivity']:.4f} Ω·cm")
+        print(f"    R² = {cc['r_squared']:.4f}")
+        print(f"    Standard error in R: {np.sqrt(np.sum((y_no_outlier - (cc['slope']*x_no_outlier + cc['intercept']))**2) / (len(x_no_outlier)-2)):.4f} Ω")
+        print(f"\n  SUMMARY:")
+        print(f"    With outlier:   slope={slope:.4f} Ω/cm, R²={r_squared:.4f}")
+        print(f"    Without outlier: slope={cc['slope']:.4f} Ω/cm, R²={cc['r_squared']:.4f}")
+
+print("\n" + "=" * 60)
+
+# Create single figure with all 3 wires on same plot
+fig, ax = plt.subplots(1, 1, figsize=(10, 6))
+
+# Store regression results for legend
+all_slopes = []
+all_intercepts = []
+all_r_squared = []
+
+for awg, area, y, color, label in awg_data:
+    slope, intercept, r_squared = linear_regression(x, y)
+    all_slopes.append(slope)
+    all_intercepts.append(intercept)
+    all_r_squared.append(r_squared)
+    
+    # Scatter plot for this wire
+    ax.scatter(x, y, color=color, s=100, edgecolors='black', linewidth=1, zorder=3, label=f'{label}')
+    
+    # Regression line
+    x_line = np.linspace(10, 110, 100)
+    y_line = slope * x_line + intercept
+    ax.plot(x_line, y_line, color=color, linestyle='-', linewidth=2.5, alpha=0.8, zorder=2)
+
+# Format axes
+ax.set_xlabel('Probe Distance (cm)', fontsize=12, fontweight='bold')
+ax.set_ylabel('Resistance (Ω)', fontsize=12, fontweight='bold')
+ax.set_title('Resistance vs Probe Distance for Different Wire Gauges', fontsize=14, fontweight='bold', pad=15)
+
+# Add legend
+ax.legend(loc='upper left', fontsize=10, framealpha=0.9)
+
+# Add equations legend
+eq_text = '26 AWG: R = {:.4f}L + {:.4f}\n'.format(all_slopes[0], all_intercepts[0])
+eq_text += '29 AWG: R = {:.4f}L + {:.4f}\n'.format(all_slopes[1], all_intercepts[1])
+eq_text += '32 AWG: R = {:.4f}L + {:.4f}'.format(all_slopes[2], all_intercepts[2])
+ax.text(0.98, 0.98, eq_text, transform=ax.transAxes, fontsize=9,
+        verticalalignment='top', horizontalalignment='right')
+
+# Grid
+ax.grid(True, linestyle='--', alpha=0.7)
+ax.set_axisbelow(True)
+
+# Limit axes
+ax.set_xlim(15, 105)
+y_max_data = max(np.max(y_26), np.max(y_29), np.max(y_32))
+y_max_lines = max(all_slopes[0]*110+all_intercepts[0], 
+                  all_slopes[1]*110+all_intercepts[1], 
+                  all_slopes[2]*110+all_intercepts[2])
+ax.set_ylim(0, max(y_max_data, y_max_lines) * 1.1)
+
+# Save figure
+output_file = 'wire_resistance_regression.png'
+plt.savefig(output_file, format='png', bbox_inches='tight')
+print(f"\nFigure saved as: {output_file}")
+
+# Also save as PDF for higher quality
+output_pdf = 'wire_resistance_regression.pdf'
+plt.savefig(output_pdf, format='pdf', bbox_inches='tight')
+print(f"Figure saved as: {output_pdf}")
+
+plt.close()
+
+# Print LaTeX inclusion code
+print("\n" + "=" * 60)
+print("LATEX INCLUSION CODE (add to your .tex file)")
+print("=" * 60)
+print("""
+\\begin{figure*}
+ \\centering
+ \\includegraphics[width=\\textwidth]{wire_resistance_regression}
+ \\caption{Linear regression analysis of resistance vs probe distance for three wire gauges. Each subplot shows experimental data points (circles) and the best-fit linear regression line. The regression equation and R² value are displayed in each plot. Note: 26 AWG data contains an experimental outlier at L=60cm (4.5 Ω vs expected ~6.4 Ω).}
+ \\label{fig:wire_regression}
+\\end{figure*}
+""")
+
+# Print summary table for LaTeX
+print("\n" + "=" * 60)
+print("LATEX TABLE CODE (for regression parameters)")
+print("=" * 60)
+print("""
+\\begin{table}
+ \\caption{Linear regression parameters and calculated resistivity for each wire gauge. Note: 26 AWG data excluded outlier at L=60cm (measured 4.5 Ω vs expected 6.4 Ω) due to experimental uncertainty.}
+ \\label{tab:regression_params}
+ \\begin{tabular}{ccccc}
+   \\hline
+   AWG & Area (mm$^2$) & Slope (Ω/cm) & Resistivity (Ω·cm) & R² \\
+   \\hline
+""")
+for res in results:
+    if res['has_outlier'] and 'corrected' in res:
+        # Print 26 AWG with both values
+        print(f"   {res['awg']} & {res['area']} & {res['slope']:.6f} (with outlier) & {res['resistivity']:.6f} & {res['r_squared']:.6f} \\\\")
+        print(f"      & & {res['corrected']['slope']:.6f} (corrected) & {res['corrected']['resistivity']:.6f} & {res['corrected']['r_squared']:.6f} \\\\")
+    else:
+        print(f"   {res['awg']} & {res['area']} & {res['slope']:.6f} & {res['resistivity']:.6f} & {res['r_squared']:.6f} \\\\")
+print("""   \\hline
+ \\end{tabular}
+ \\begin{tablenotes}
+  \\item Note: 26 AWG corrected values exclude outlier at L=60cm (measured 4.5 Ω, expected 6.4 Ω).
+ \\end{tablenotes}
+\\end{table}
+""")

mnras_template.tex

@@ -51,7 +51,6 @@
 % Only include extra packages if you really need them. Avoid using amssymb if newtxmath is enabled, as these packages can cause conflicts. newtxmatch covers the same math symbols while producing a consistent Times New Roman font. Common packages are:
 \usepackage{graphicx}	% Including figure files
 \usepackage{amsmath}	% Advanced maths commands
-\usepackage{pdflscape}	% Landscape environment
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
@@ -83,7 +82,7 @@ $^{2}$Physics, Plano East Senior High School, 3000 Los Rios Blvd, Plano, TX 7507
 }
 
 % These dates will be filled out by the publisher
-\date{Accepted XXX. Received YYY; in original form ZZZ}
+\date{\today}
 
 % Prints the current year, for the copyright statements etc. To achieve a fixed year, replace the expression with a number. 
 \pubyear{\the\year{}}
@@ -145,22 +144,44 @@ Refer back to them as e.g. equation~(\ref{eq:quadratic}).
 \subsection{Results and Discussion}
 
 
-\begin{landscape}
- \begin{table}
-  \caption{Resistance measurements for different wire cross-sectional areas at varying probe distances. All resistance values measured in $\Omega$.}
-  \label{tab:resistance}
-  \begin{tabular}{cccccc}
-    \hline
-    Area & \multicolumn{5}{c}{Probe distance} \\
-    (mm$^2$) & 20 cm & 40 cm & 60 cm & 80 cm & 100 cm \\
-    \hline
-    0.1285 (26 AWG) & 2.6 $\Omega$ & 5.6 $\Omega$ & 4.5 $\Omega$ & 9.3 $\Omega$ & 10.0 $\Omega$ \\
-    0.06424 (29 AWG) & 4.7 $\Omega$ & 8.9 $\Omega$ & 13.6 $\Omega$ & 18.0 $\Omega$ & 22.6 $\Omega$ \\
-    0.03204 (32 AWG) & 9.0 $\Omega$ & 18.1 $\Omega$ & 27.3 $\Omega$ & 36.3 $\Omega$ & 45.4 $\Omega$ \\
-    \hline
-  \end{tabular}
- \end{table}
-\end{landscape}
+\begin{table*}
+ \caption{Resistance measurements for different wire cross-sectional areas at varying probe distances. All resistance values measured in $\Omega$.}
+ \label{tab:resistance}
+ \begin{tabular}{lrrrrr}
+   \hline
+   Area & \multicolumn{5}{c}{Probe distance} \\
+   (mm$^2$) & 20 cm & 40 cm & 60 cm & 80 cm & 100 cm \\
+   & ($\Omega$) & & & & \\
+   \hline
+   0.1285 (26 AWG) & 2.6 & 5.6 & 4.5 & 9.3 & 10.0 \\
+   0.06424 (29 AWG) & 4.7 & 8.9 & 13.6 & 18.0 & 22.6 \\
+   0.03204 (32 AWG) & 9.0 & 18.1 & 27.3 & 36.3 & 45.4 \\
+   \hline
+ \end{tabular}
+\end{table*}
+
+
+\begin{figure*}
+ \centering
+ \includegraphics[width=\textwidth]{wire_resistance_regression}
+ \caption{Linear regression analysis of resistance vs probe distance for three wire gauges. Experimental data points (circles) and best-fit regression lines are shown for each AWG gauge. Regression equations: 26 AWG: R = 0.0925L + 0.8500, 29 AWG: R = 0.2245L + 0.0900, 32 AWG: R = 0.4550L - 0.0800 (R, L in $\Omega$, cm). Note: 26 AWG data contains experimental outlier at L=60 cm (4.5 $\Omega$ vs expected 6.4 $\Omega$).}
+ \label{fig:wire_regression}
+\end{figure*}
+
+
+\begin{table*}
+ \caption{Linear regression parameters and calculated resistivity for all three wire gauges. Note: 26 AWG data contains experimental outlier at L=60 cm.}
+ \label{tab:regression_params}
+ \begin{tabular}{ccccc}
+     \hline
+     AWG & Area (mm$^2$) & Slope ($\Omega$/cm) & Resistivity ($\Omega\cdot$cm) & R$^2$ \\
+     \hline
+     26 & 0.1285 & 0.092500 & 0.000119 & 0.854343 \\
+     29 & 0.06424 & 0.224500 & 0.000144 & 0.999747 \\
+     32 & 0.03204 & 0.455000 & 0.000146 & 1.000000 \\
+     \hline
+   \end{tabular}
+\end{table*}
 
 
 \section{Conclusions}

raw-data.csv

@@ -0,0 +1,14 @@
+26,0.1285,,,,,,,
+29,0.06424,,,,,,,
+32,0.03204,,,,,,BASE RES,1.45
+,,,,,,,at room temp,1.4501595
+,,,,,,,,
+,,,,,,,,
+,,,,,,,,
+,,,Area,,,,,
+,,x,0.1285,0.06424,0.03204,,,
+,,20,2.6,4.7,9.0,,,
+,,40,5.6,8.9,18.1,,,
+,,60,4.5,13.6,27.3,,,
+,,80,9.3,18.0,36.3,,,
+,,100,10.0,22.6,45.4,,,