Chemistry 化学

Examples of Discussing Chemistry Experiment Graphs | Meaning of Regression Lines, Slopes, and Intercepts

In chemistry experiments, measured values are often organized into tables and graphs, and relationships are interpreted from them.
Graphs are particularly important when examining relationships such as absorbance and concentration, reaction time and changes in concentration, temperature and reaction rate, voltage and current, or titration volume and concentration.
By drawing a regression line on a graph, the trend in measured values can be expressed numerically, and experimental meaning can be interpreted from the slope and intercept.

However, simply writing in a report that “the graph became linear,” “the slope was large,” or “the intercept was shifted” results in a superficial discussion.
It is necessary to explain what the regression line represents, what units and meaning the slope has, why the intercept does not become 0, and how outliers and measurement errors affect the graph.
It is also important to explain how the regression equation and correlation coefficient are used.

This article clearly explains, as examples of discussions that can be used for chemistry experiment graphs, regression lines, slopes, intercepts, proportional relationships, calibration curves, correlation coefficients, outliers, errors, units, how to interpret graphs, discussions when the relationship is not linear, and points for improvement.

Note:
This article is a reference intended to assist with discussions of graphs prepared in basic chemistry experiments, analytical chemistry experiments, physical chemistry experiments, and materials chemistry experiments at universities and similar institutions.
For the actual method of drawing graphs, approximation methods, handling of correlation coefficients, significant figures, and notation of units, always follow the instructions in your university’s laboratory manual and those given by your instructor or TA.

Meaning of Creating Graphs in Chemistry Experiments

The purpose of creating graphs in chemistry experiments is to visually confirm relationships among measured values.
Trends that are difficult to understand from tables alone become easier to see in graphs, including linear relationships, curved relationships, proportional relationships, saturation, and outliers.
Graphs are used not simply to arrange experimental results but to identify regularities and characteristics of errors from the data.

Particularly in chemistry experiments, graphs are often used to confirm whether results follow theoretical equations.
For example, experiments may examine whether the relationship between absorbance and concentration is linear, whether reaction rate is proportional to concentration, or whether current is proportional to voltage.
The shape of the graph provides clues for determining whether the experimental results agree with theory.

Example Discussion:
By creating a graph, it is possible to visually confirm whether a linear relationship exists between the measured values.
In this experiment, because the value on the vertical axis increased at an approximately constant rate as the value on the horizontal axis increased, a proportional or linear relationship was considered to exist between the two.
Therefore, the graph is useful for determining the trend of the measured values.

Main Items to Include in the Results

Before writing a discussion of a graph, first organize the basic information related to the graph.
Checking the horizontal axis, vertical axis, units, measurement points, regression equation, slope, intercept, correlation coefficient, presence or absence of outliers, and other information makes the discussion easier to write.
Writing what was interpreted from the graph together with numerical values makes the discussion more persuasive.

Main Items to Include in the Results

  • Horizontal axis of the graph
  • Vertical axis of the graph
  • Units of each axis
  • Number of measurement points
  • Variation among measured values
  • Equation of the regression line
  • Slope
  • Intercept
  • Correlation coefficient or coefficient of determination
  • Presence or absence of outliers
  • Correspondence with the theoretical equation
  • Quality of linearity
  • Unknown quantity determined from the graph
  • Causes of error
  • Points for improvement

Example of How to Write the Results:
When a graph was prepared with concentration on the horizontal axis and absorbance on the vertical axis, the measurement points were distributed almost along a straight line.
The regression equation was expressed as y = ax + b, and the slope represents the magnitude of the change in absorbance relative to the change in concentration.
Because the intercept was not exactly 0, the effects of deviations in blank correction or measurement error may be considered.

What Is a Regression Line?

A regression line is a straight line drawn to best represent the overall trend of the measurement points.
Because experimental values contain measurement errors, it is uncommon for all points to lie perfectly on a single straight line.
Therefore, a line is determined that represents the overall trend while taking the variation in the measured values into account.

In many cases, the regression line is determined using the least-squares method.
In the least-squares method, the line is determined so that the overall differences between the individual measurement points and the line are minimized.
A regression line is not simply a line drawn by visual judgment but a line that numerically represents the entire set of measured values.

y = ax + b

a: slope, b: intercept

Example Discussion:
A regression line is a straight line that represents the overall trend while taking variation among the measurement points into account.
Because experimental values contain measurement errors, all points do not necessarily lie perfectly on the line.
Therefore, by using a regression line, the effect of individual measurement errors can be reduced and the relationship can be evaluated from the entire set of measured values.

Meaning of the Slope

The slope indicates how much the value on the vertical axis changes when the value on the horizontal axis changes by one unit.
When the regression line is expressed as y = ax + b, a is the slope.
In chemistry experiments, the slope often has physical or chemical meaning.

For example, when concentration is plotted on the horizontal axis and absorbance on the vertical axis in a calibration curve, the slope represents the increase in absorbance per unit concentration.
In a reaction-rate graph, the slope may represent the rate.
Because the meaning of the slope depends on what is plotted on the horizontal and vertical axes, it must always be considered together with its units.

Slope = Change in vertical-axis value / Change in horizontal-axis value

a = Δy / Δx

Example Discussion:
The slope of the regression line indicates how much the value on the vertical axis increases when the value on the horizontal axis increases by one unit.
In the calibration curve used in this experiment, a larger slope means that the measurement signal changes more greatly in response to a change in concentration, indicating higher sensitivity.
Therefore, the slope is not merely a numerical value but an important value representing the magnitude of the response of the measurement system.

Units of the Slope

The slope has units.
The unit of the slope is obtained by dividing the unit of the vertical axis by the unit of the horizontal axis.
For example, if the vertical axis is absorbance and the horizontal axis is concentration in mol/L, the unit of the slope is expressed as L/mol.
If the vertical axis is mass in g and the horizontal axis is time in s, the unit of the slope is g/s.

Considering the units of the slope makes it clear what the slope represents.
If only the numerical value of the slope is shown without units, its experimental meaning becomes difficult to understand.
In a report, it is important to always check the units when writing the slope.

Example Discussion:
The unit of the slope is obtained by dividing the unit of the vertical axis by the unit of the horizontal axis.
Therefore, when discussing the value of the slope, it is necessary to check not only the numerical magnitude but also the units.
Clarifying the units of the slope makes it easier to determine whether the value represents reaction rate, sensitivity, a proportionality constant, or another quantity.

Meaning of the Intercept

The intercept is the value indicated by the regression line on the vertical axis when the value on the horizontal axis is 0.
In the regression equation y = ax + b, b is the intercept.
In a graph that theoretically should pass through the origin, the intercept is expected to be close to 0.
However, in experiments, the intercept often deviates from 0.

Possible causes of an intercept deviating from 0 include insufficient blank correction, zero-point drift of the instrument, contamination of reagents, residual signals, measurement errors, and errors in concentration preparation.
The intercept is not a value that should simply be ignored but can provide clues for considering whether systematic error exists in the measurement system.

Example Discussion:
Theoretically, when the value on the horizontal axis is 0, the value on the vertical axis is also expected to be 0, but the intercept of the regression line deviated from 0.
Possible causes include incomplete blank correction, zero-point drift of the instrument, and residual signals caused by contamination of the sample or cell.
Therefore, deviation of the intercept may indicate systematic error contained in the measurement system.

Why the Intercept Does Not Become 0

In experimental graphs, even when a straight line theoretically should pass through the origin, the intercept may not become 0.
This is because experimental values contain errors.
Zero-point correction of the measuring instrument, impurities in reagents, blank values, background signals, contamination of containers, and operational errors can affect the intercept.

If the intercept is small, it may sometimes be considered to fall within the range of measurement error.
However, if the intercept is large, there may be a problem with the measurement method or correction rather than merely random error.
If the intercept has a large effect on the experimental result, the blank measurement and zero correction must be reviewed.

Example Discussion:
Possible reasons why the intercept did not become 0 include insufficient zero adjustment before measurement and incomplete correction of the blank sample.
In addition, if the sample cell or equipment is slightly contaminated, a signal may be detected even at concentration 0.
Therefore, to reduce deviation of the intercept, blank measurements and instrument calibration must be performed appropriately.

Regression Lines in Calibration Curves

A calibration curve is a graph prepared from measured values of standard solutions with known concentrations.
Concentration is plotted on the horizontal axis, and measurement signals such as absorbance or peak area are plotted on the vertical axis to determine a regression line.
By applying the measured value of an unknown sample to this line, the concentration of the unknown sample can be determined.

Linearity is extremely important in a calibration curve.
If concentration and signal are proportional within the measurement range, the concentration of the unknown sample can be determined relatively accurately.
However, if linearity breaks down at high concentrations or errors become large at low concentrations, the range of the calibration curve must be reviewed.

Example Discussion:
In a calibration curve, the relationship between the concentration of the standard solutions and the measurement signal is represented by a regression line, and the concentration of the unknown sample is determined.
Because the measurement points were distributed almost along the regression line, a linear relationship was considered to exist between concentration and signal within the measurement range.
However, because determining an unknown concentration outside the calibration curve range increases the error, the unknown sample must be evaluated within the range of the standard solutions.

Difference Between a Proportional Relationship and a Linear Relationship

A proportional relationship is one in which the value on the vertical axis is also 0 when the value on the horizontal axis is 0, and the graph is a straight line passing through the origin.
A linear relationship, on the other hand, does not necessarily need to pass through the origin.
When the regression line is expressed as y = ax + b, if b is 0, the relationship is proportional, while if b is not 0, the relationship is linear but cannot be called proportional.

In chemistry experiments, even when a proportional relationship is theoretically expected, an intercept may arise because of blank values or instrument drift.
Therefore, “the graph was linear” and “the values were proportional” must be distinguished.
A proportional relationship should be identified only after confirming whether the line passes through the origin.

Example Discussion:
Although the measurement points were distributed almost along a straight line, the intercept of the regression line was not 0, so strictly speaking, the relationship was considered linear rather than proportional.
For the relationship to be proportional, the value on the vertical axis must also be 0 when the value on the horizontal axis is 0, and the line must pass through the origin.
Therefore, when discussing a graph, it is necessary to check not only linearity but also the value of the intercept.

Meaning of the Correlation Coefficient and Coefficient of Determination

The correlation coefficient and coefficient of determination are indicators used to evaluate the degree to which measurement points show a linear relationship.
The coefficient of determination R2 indicates how well the regression line explains the variation in the measured values.
The closer R2 is to 1, the more closely the measurement points are considered to agree with the regression line.

However, a high R2 does not necessarily mean that the experimental result is correct.
If the number of measurement points is small or only a narrow range is measured, R2 may appear high.
In addition, the points may still lie on a straight line even when systematic error is present.
R2 is a guideline for linearity and does not indicate that the results are free from error.

Example Discussion:
Because the coefficient of determination R2 was close to 1, the measurement points agreed well with the regression line, and a strong linear relationship was considered to exist between the horizontal and vertical axes.
However, even when R2 is high, systematic errors such as deviations in blank correction or errors in concentration preparation may still be present.
Therefore, R2 must be treated as one indicator for judging linearity.

Discussion of Outliers

An outlier is a value that deviates greatly from the trend of the other measurement points.
If only one point is far from the regression line on a graph, that point may contain a measurement or operational error.
Possible causes include errors in concentration preparation, pipetting errors, contamination of the cell, reading errors, and insufficient sample mixing.

However, an outlier must not be excluded without a reason.
Clear justification is required to exclude an outlier.
Rather than deleting it simply because it does not fit the regression line, it should be handled carefully only when an abnormality in the experimental procedure or a difference in measurement conditions can be confirmed.

Example Discussion:
Because some measurement points deviated greatly from the regression line, those measurements may have contained errors in concentration preparation or measurement procedures.
In particular, contamination of the cell or insufficient mixing of the sample can greatly change the measured value.
However, when excluding an outlier, clear operational evidence must be provided rather than excluding it simply because it deviates from the line.

Discussion of Variation Among Measurement Points

Measurement points vary around the regression line because experimental values contain random errors.
Random errors include reading errors, slight differences in pipetting, temperature changes, instrument noise, and differences in sample mixing.
The smaller the variation, the higher the reproducibility of the measurement is considered to be.

When the variation is large, the reliability of the regression line decreases.
As a result, the values determined from the slope and intercept also contain greater uncertainty.
To reduce variation, it is effective to standardize the measurement procedure, perform multiple measurements under the same conditions, and use the mean.

Example Discussion:
Possible causes of the variation of measurement points around the regression line include random errors in pipetting, insufficient sample mixing, and reading errors of the measuring instrument.
The larger the variation, the lower the reliability of the slope and intercept obtained from the regression line.
Therefore, to improve the reproducibility of the measured values, it is effective to standardize the operating conditions, perform multiple measurements, and use the mean.

Discussion When the Relationship Is Not Linear

A graph may become curved even when a linear relationship is theoretically expected.
Possible causes include an excessively wide measurement range, saturation of reactions or absorption at high concentrations, decomposition of the sample, nonlinear detector response, and changes in temperature or pH.
In calibration curves, linearity may break down on the high-concentration side.

If the relationship is not linear, the data should not be forcibly fitted to a straight line.
Instead, transformation according to the theoretical equation or review of the measurement range is necessary.
Depending on the experiment, methods such as taking logarithms, taking reciprocals, or using only the low-concentration range may be considered.
It is important to consider the range in which linearity holds.

Example Discussion:
A possible reason why the measurement points deviated from a straight line and formed a curve is that the measurement range was too wide and the measurement signal became saturated on the high-concentration side.
In this case, fitting the entire range with a single straight line produces large errors in the slope and intercept.
Therefore, it is necessary to select the concentration range in which linearity holds and prepare the calibration curve within that range.

Regression Through the Origin and Regression Without Fixing the Origin

When fitting a graph, a straight line may be drawn through the origin, or the intercept may be allowed to vary freely.
If it is theoretically clear that the value on the vertical axis must be 0 when the value on the horizontal axis is 0, regression through the origin may be used.
However, if experimental values contain blank or background signals, regression without forcing the line through the origin may represent the experimental results better.

Whether the line should pass through the origin must be determined based on theory and the measurement method rather than appearance.
Forcing the line through the origin removes the intercept, but it may result in an unreasonable fit when the measured values as a whole are considered.
In a report, it is useful to explain which type of regression was used and why.

Example Discussion:
Although a relationship passing through the origin is theoretically expected, the experimental values may contain blank signals or zero-point drift of the instrument.
Therefore, using a regression line with a freely varying intercept may better represent the trend of the actual measured values.
Whether regression through the origin should be used must be determined by considering the theoretical equation and characteristics of the measurement system.

Discussion of Determining an Unknown Quantity from a Graph

In chemistry experiments, regression lines may be used to determine unknown quantities.
Examples include determining the concentration of an unknown sample from a calibration curve, determining reaction rate from the slope, and determining a proportionality constant or molar absorption coefficient from the slope.
In such cases, the reliability of the regression line directly affects the precision of the unknown quantity.

When determining an unknown quantity, check whether the value of the unknown sample lies within the calibration curve range.
Extrapolating outside the range of the standard solutions may result in large errors.
Because errors in the slope and intercept also affect the unknown quantity, the linearity of the graph and variation among measurement points must also be discussed.

When y = ax + b, x = (y – b) / a

Example Discussion:
The concentration of the unknown sample was determined by substituting the measured value into the regression equation of the calibration curve.
In this method, the accuracy of the slope and intercept of the regression line affects the calculated unknown concentration.
In addition, if the measured value of the unknown sample lies outside the calibration curve range, errors caused by extrapolation become large, so evaluation within the range of the standard solutions is desirable.

When the Slope Deviates from the Theoretical Value

The slope of the regression line may deviate from a theoretical or literature value.
Possible causes include errors in preparing the concentration of standard solutions, insufficient calibration of the measuring instrument, temperature changes, deterioration of reagents, incomplete reaction, and differences in detector sensitivity.
Because the slope represents the overall response, it is easily affected by systematic error.

For example, if the concentration is prepared higher than the actual intended value, the slope of the calibration curve may appear smaller than it should be.
Conversely, under instrument conditions that produce a larger measurement signal, the slope may become larger.
Deviation of the slope may indicate not merely random error but a shift in the entire measurement system.

Example Discussion:
Possible reasons why the slope of the obtained regression line was smaller than the theoretical value include errors in preparing the concentrations of the standard solutions and insufficient sensitivity of the measuring instrument.
Because the slope represents the magnitude of the response on the vertical axis to changes on the horizontal axis, systematic shifts in concentration or measurement signals have a large effect on it.
Therefore, when discussing deviation of the slope, both sample preparation and instrument calibration must be checked.

When the Intercept Deviates Greatly

When the intercept deviates greatly, a constant background signal may have been added to all measured values.
Possible causes include absorbance in the blank sample, contamination of the sample cell, insufficient zero adjustment of the instrument, and impurities in solvents or reagents.
The intercept may have a large effect on quantification on the low-concentration side.

When the intercept is large, the intercept must be correctly accounted for when determining an unknown quantity.
In addition, if the intercept is large in a graph that should pass through the origin, there is a high possibility of a problem with the experimental procedure or measurement conditions.
It is important to review blank correction and instrument calibration.

Example Discussion:
If the intercept showed a large positive value, this means that a measurement signal existed even at concentration 0.
Possible causes include absorption by the blank sample, contamination of the cell, zero-point drift of the instrument, and impurities in the reagents.
Because deviation of the intercept affects the quantitative value of the unknown sample, blank correction and zero adjustment must be performed appropriately.

Discussion of Semilogarithmic and Log-Log Graphs

Depending on the experiment, a relationship that appears curved on an ordinary graph may become linear by taking logarithms.
For example, in a first-order reaction, the relationship between the logarithm of concentration and time may become linear.
In addition, a power-law relationship may sometimes be analyzed as a linear relationship by using a log-log graph.

When using a logarithmic graph, it must be made clear that the values on the vertical or horizontal axis are logarithmic values rather than the original values.
The meaning of the slope also changes from that in an ordinary graph.
Because obtaining a straight line does not necessarily mean a simple proportional relationship, it is important to interpret the transformation used in relation to the theoretical equation.

Example Discussion:
Although the relationship was curved on the ordinary graph, the measurement points approached a straight line when the vertical axis was converted to logarithmic values.
This suggests that the measured values may have changed exponentially.
The slope after logarithmic transformation must be interpreted not as a simple amount of change in the original graph but as a value corresponding to a theoretical equation, such as a rate constant.

Differences in Appearance Caused by Graph Axis Settings

The appearance of measured values changes greatly depending on the axis range and scale used in a graph.
If the axis range is too wide, variation may appear small.
Conversely, if the range is too narrow, small differences may appear large.
Therefore, it is important not to judge only from the visual appearance of the graph but also to check numerical values and the regression equation.

In addition, if the units or scale intervals on the horizontal and vertical axes are inappropriate, the trend of the data may be misinterpreted.
In chemistry laboratory reports, axis labels, units, and measurement ranges should be clearly indicated, and the graph should be prepared so that the necessary range is easy to view.

Example Discussion:
Because the appearance of a graph changes depending on the axis range and scale settings, it is not appropriate to judge linearity or variation based only on appearance.
If the axis range is too wide, deviations among the measurement points appear small, while if it is too narrow, errors are exaggerated.
Therefore, the regression equation, coefficient of determination, and residuals must also be evaluated.

Causes of Error When Creating Graphs

Causes of error when creating graphs include errors in entering measured values, errors in unit conversion, incorrect selection of axes, reversing the horizontal and vertical axes, handling of outliers, incorrect selection of the regression range, and incorrect judgment about whether the regression line should pass through the origin.
Because graphs are created by processing measured values, errors and misunderstandings may arise during the graph-creation stage.

Unit conversion errors in particular directly affect the value of the slope.
For example, confusing mg/L with mol/L greatly changes the meaning of the slope.
In addition, reversing the horizontal and vertical axes also reverses the interpretation of the slope.
After creating the graph, it is necessary to always check the axes, units, and regression equation.

Example Discussion:
Possible causes of error when creating the graph include incorrect entry of measured values, unit conversion errors, and incorrect axis settings.
Because the slope in particular depends on the units of the vertical and horizontal axes, incorrect units prevent the experimental meaning from being interpreted correctly.
Therefore, after creating the graph, the axis labels, units, regression equation, and measurement range must be checked.

When a Graph Can Be Considered Good

A graph can be considered good when the axis labels and units are clear, the measurement points are displayed appropriately, and the regression line represents the trend of the data well.
In addition, if the measurement range is appropriate, there are few outliers, the coefficient of determination is high, and the graph corresponds to the theoretical equation, it can be considered a reliable graph.

However, a visually clean straight line is not necessarily a good graph.
If there are few measurement points or the range is too narrow, linearity cannot be sufficiently confirmed.
A good graph is one in which not only the appearance but also the measurement conditions, correspondence with theory, and handling of errors are appropriate.

Example Discussion:
In this graph, the measurement points were distributed almost along the regression line, and the coefficient of determination was also high, so a good linear relationship was considered to exist between the horizontal and vertical axes.
In addition, the axis labels and units were clear, and experimental meaning could be interpreted from the slope and intercept.
Therefore, this graph was considered generally appropriate for representing the trend of the measured values.

Example Discussions When the Experiment Did Not Go Well

When the graph does not work well, consider the cause based on results such as large variation among measurement points, points deviating from the regression line, a greatly shifted intercept, a low coefficient of determination, a slope that differs from theory, or a curved rather than linear relationship.
Organizing the possible causes into measurement procedures, sample preparation, instruments, temperature, pH, concentration range, and graph-creation methods makes the discussion easier.

Example Discussion:
Possible reasons for the large variation among the measurement points and poor agreement with the regression line include errors in preparing the sample concentration and reading errors of the measuring instrument.
In particular, slight differences in pipetting and dilution directly affect the values on the horizontal axis.
Therefore, to reduce variation in the measured values, the samples must be prepared carefully and measured multiple times under the same conditions.

Another Example Discussion:
Possible reasons why the intercept deviated greatly include insufficient blank correction and inappropriate zero adjustment of the instrument.
If a signal is detected even at concentration 0, the regression line does not pass through the origin and errors also occur in the quantitative value of the unknown sample.
Therefore, it is important to perform blank measurements before measurement and confirm the zero adjustment of the instrument.

Another Example Discussion:
If the measurement points on the high-concentration side deviated from the regression line, the measurement signal may have become saturated and the proportional relationship between concentration and signal may have broken down.
In such a case, fitting the entire concentration range with a single straight line produces large errors in the slope and the calculation of the unknown concentration.
Therefore, it is necessary to select the concentration range in which linearity is maintained and prepare the calibration curve within that range.

How to Write Points for Improvement

In a discussion of chemistry experiment graphs, writing not only about problems with the graph but also about how they can be improved makes the report easier to organize.
Points for improvement can be organized into measurement procedures, sample preparation, instrument calibration, graph-creation methods, and data processing.

Improvements to Measurement and Sample Preparation

  • Prepare standard solutions accurately
  • Use pipettes and volumetric flasks correctly
  • Mix samples thoroughly
  • Perform blank correction before measurement
  • Check the zero adjustment of the measuring instrument
  • Perform multiple measurements under the same conditions
  • Keep temperature and pH constant
  • Avoid contamination of cells and equipment

Improvements to Graph Creation and Analysis

  • Set the horizontal and vertical axes correctly
  • Clearly indicate axis labels and units
  • Perform regression within the range in which linearity holds
  • If an outlier is excluded, provide justification
  • Include the regression equation
  • Explain the meaning of the slope and intercept
  • Show the coefficient of determination as a guideline for linearity
  • Evaluate unknown samples within the calibration curve range

Example of How to Write Points for Improvement:
To improve the linearity of the graph, it is necessary to accurately prepare the concentrations of the standard solutions and confirm blank correction and zero adjustment before measurement.
In addition, it is important to exclude high-concentration regions in which measured values deviate from the straight line and determine the regression line within the range in which linearity holds.
If an outlier is present, its operational cause must be checked and handled with justification.

Difference Between a Superficial Discussion and a Good Discussion

In a discussion of a graph, simply writing that “the graph became linear,” “the slope was large,” or “the intercept was shifted” results in a superficial discussion.
A good discussion explains what the slope and intercept mean experimentally and how they relate to errors and theoretical equations.

Superficial Discussion Good Discussion
The graph became linear. Because the measurement points were distributed almost along the regression line, a linear relationship was considered to exist between the horizontal and vertical axes within the measurement range.
The slope was large. A large slope indicates that the response on the vertical axis is large relative to changes in the value on the horizontal axis, and in a calibration curve it means that measurement sensitivity is high.
The intercept was not 0. Possible reasons why the intercept deviated from 0 include insufficient blank correction, zero-point drift of the instrument, and background signals caused by contamination of the sample cell.
The points varied. The variation among measurement points was considered to have been caused by random errors such as errors in concentration preparation, instrument noise, and insufficient sample mixing.
The graph was not linear. The measurement signal may have become saturated on the high-concentration side, or the measurement range may have been too wide and exceeded the range in which the theoretical linear relationship holds.

Examples of Expressions That Can Be Used in Reports

The following expressions can be used when writing the results and discussion of chemistry experiment graphs.
Adjust the necessary parts according to your own experimental results.

  • Because the measurement points were distributed almost along the regression line, a linear relationship was considered to exist between the two variables.
  • The slope of the regression line represents the change in the vertical-axis value when the horizontal-axis value changes by one unit.
  • A larger slope means that the response to the change in the measured quantity is larger.
  • Possible reasons why the intercept deviated from 0 include blank correction and zero-point drift of the instrument.
  • Because the coefficient of determination R2 was close to 1, the regression line represented the trend of the measured values well.
  • Outliers may have been caused by errors in concentration preparation or measurement procedures.
  • If linearity breaks down on the high-concentration side, saturation of the measurement signal may be a possible cause.
  • The value of an unknown sample must be determined within the calibration curve range.
  • When discussing the slope and intercept, the units and experimental meaning must be checked.
  • To increase the reliability of the graph, it is important to perform multiple measurements and check for outliers and variation.

Points to Check When Discussing Chemistry Experiment Graphs

Checking the following points before writing the report makes the discussion easier to write.

  • Are the horizontal and vertical axes set correctly?
  • Are the axis labels and units clearly indicated?
  • Is the regression equation written?
  • Is the meaning of the slope explained?
  • Have the units of the slope been checked?
  • Is the meaning of the intercept explained?
  • Have the reasons why the intercept deviates from 0 been considered?
  • Are the coefficient of determination and correlation coefficient handled appropriately?
  • Has the presence or absence of outliers been checked?
  • Has the range in which linearity holds been considered?
  • Is the unknown quantity determined within the calibration curve range?
  • Do the points for improvement correspond to the causes of error?

Summary

Chemistry experiment graphs are important for visually showing relationships among measured values and confirming correspondence with theoretical equations and trends in the measured values.
A regression line represents the overall trend of the measurement points, and the slope indicates the magnitude of the response on the vertical axis to changes on the horizontal axis.
The intercept is the value on the vertical axis when the horizontal-axis value is 0 and provides a clue for considering systematic errors such as blank correction and zero-point drift.

The slope and intercept are not merely numerical values but have meanings corresponding to the experimental conditions and measurement method.
The slope has units and may represent sensitivity in a calibration curve, rate in a reaction-rate graph, or a proportionality constant in a physical-property measurement.
If the intercept deviates from 0, background signals, instrument calibration, and contamination of reagents or cells should be considered.

In a report, rather than simply writing that “the graph became linear,” organize and discuss the regression equation, slope, intercept, units, coefficient of determination, outliers, range of linearity, method of determining unknown quantities, causes of error, and points for improvement.
Discussion of graphs is an essential part of understanding experimental results numerically and connecting theory with measured values.

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