What are the different types of mathematical relationships?
Is there a linear relationship between the volume and mass for a material? In physical science a "relationship" means how one variable changes with respect to another So that, to me, is something at the basic level we don't understand. For example, we might want to quantify the association between body mass index Define and provide examples of dependent and independent variables in a study In correlation analysis, we estimate a sample correlation coefficient, more. Definition of linear relationship: A relationship of direct proportionality that, when plotted on a graph, traces a straight line. In linear relationships, any given.
It is something that depends on other factors. For example, a test score could be a dependent variable because it could change depending on several factors such as how much you studied, how much sleep you got the night before you took the test, or even how hungry you were when you took it.
Usually when you are looking for a relationship between two things you are trying to find out what makes the dependent variable change the way it does. Inverse Relationship Now, let's look at the following equation: Note that as X increases Y decreases in a non-linear fashion.
This is an inverse relationship.
Example of an inverse relationship in science: When a higher viscosity leads to a decreased flow rate, the relationship between viscosity and flow rate is inverse.
Inverse relationships follow a hyperbolic pattern. Below is a graph that shows the hyperbolic shape of an inverse relationship. Quadratic formulas are often used to calculate the height of falling rocks, shooting projectiles or kicked balls.
Straight line graphs
A quadratic formula is sometimes called a second degree formula. Quadratic relationships are found in all accelerating objects e. Below is a graph that demostrates the shape of a quadratic equation. Inverse Square Law The principle in physics that the effect of certain forces, such as light, sound, and gravity, on an object varies by the inverse square of the distance between the object and the source of the force.
In physics, an inverse-square law is any physical law stating that a specified physical quantity or intensity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental cause for this can be understood as geometric dilution corresponding to point-source radiation into three-dimensional space.
This analysis assumes that there is a linear association between the two variables. If a different relationship is hypothesized, such as a curvilinear or exponential relationship, alternative regression analyses are performed. The figure below is a scatter diagram illustrating the relationship between BMI and total cholesterol.
Each point represents the observed x, y pair, in this case, BMI and the corresponding total cholesterol measured in each participant. Note that the independent variable BMI is on the horizontal axis and the dependent variable Total Serum Cholesterol on the vertical axis.
BMI and Total Cholesterol The graph shows that there is a positive or direct association between BMI and total cholesterol; participants with lower BMI are more likely to have lower total cholesterol levels and participants with higher BMI are more likely to have higher total cholesterol levels.
For either of these relationships we could use simple linear regression analysis to estimate the equation of the line that best describes the association between the independent variable and the dependent variable.
The simple linear regression equation is as follows: The Y-intercept and slope are estimated from the sample data, and they are the values that minimize the sum of the squared differences between the observed and the predicted values of the outcome, i. Do not put units into the table.
The units are stated in the first row of the table. In a table the units only appear in the first row, the head row. Graph[g] In the computer laboratory we will make a graph with volume on the x-axis and mass on the y-axis.
- 012 Lab 01: Mathematical models and measurements in Physical Science
- linear relationship
- Linear Relationship
Then we will run a mathematical decision analysis and make the appropriate calculations of the slope and the y-intercept using a spreadsheet. If the density relationship holds true, then the slope will be the density of the soap. Select the two columns containing the x and y data.
Note that the x data column is on the left, the y data is in the column on the right. Do not put blank columns or rows into the middle of a data table.
Correlation and Linear Regression
Data table Choose xy scatter graph in step one. Click next until you reach step four. In step four, add titles. Immediately after clicking on the Finish button, choose Insert: