As X increases Y will increase proportionally. If we plot the X-y graph a straight line will be formed. In nature data is not exact so points will not always fall on the line. The points fall close enough to the straight line to conclude that this is a linear or direct relationship. Independent variable - An independent variable is exactly what it sounds like. It is a variable that stands alone and isn't changed by the other variables you are trying to measure. For example If time is one of your variables , it is the independent variable.
Time is always the independent variable. Dependent variable -- Just like an independent variable, a dependent variable is exactly what it sounds like. 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. 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. A direct relationship is proportional in the sense that when one variable increases, so does the other. Using the example from the last section, the higher from which you drop a ball, the higher it bounces back up.
A circle with a bigger diameter will have a bigger circumference. If you increase the independent variable x , such as the diameter of the circle or the height of the ball drop , the dependent variable increases too and vice-versa.
Pi is always the same, so if you double the value of D , the value of C doubles too. The gradient of the graph tells you the value of the constant. Inverse relationships work differently. If you increase x , the value of y decreases. For example, if you move more quickly to your destination, your journey time will decrease. In this example, x is your speed and y is the journey time. Doubling your speed halves the journey time, and increasing the speed by ten times makes the journey time ten times shorter.
As you start to increase x , y decreases really quickly, but as you continue increasing x the rate of decrease of y gets slower. In this case, y is inversely related to x. At first an increase of 3 in x decreases y by 2, but then an increase of 6 in x only decreases y by 1. This is why inverse relationships are declining curves that get shallower the further you move along them. In direct relationships, an increase in x leads to a correspondingly sized increase in y , and a decrease has the opposite effect.
A positive correlation exists when one variable decreases as the other variable decreases, or one variable increases while the other increases. The direction of the relationship between two variables is identified by the sign of the correlation coefficient for the variables. A residual is a measure of how well a line fits an individual data point. This vertical distance is known as a residual.
For data points above the line, the residual is positive, and for data points below the line, the residual is negative. If you have a positive value for residual, it means the actual value was MORE than the predicted value. The person actually did better than you predicted. Under the line, you OVER-predicted, so you have a negative residual.
A residual value is a measure of how much a regression line vertically misses a data point. You can think of the lines as averages; a few data points will fit the line and others will miss. A residual plot has the Residual Values on the vertical axis; the horizontal axis displays the independent variable. A residual is the difference between an observed value of the response variable y and the predicted value of y.
If it is positive, then the observed value is greater than the predicted value. A residual is the sum of the observed y-value of a data point and the predicted y-value on a regression line for the x-coordinate of the data point. A residual is positive when the point is below the line, negative when it is above the line, and zero when the observed y-value equals the predicted y-value. In statistical models, a residual is the difference between the observed value and the mean value that the model predicts for that observation.
Residual values are especially useful in regression and ANOVA procedures because they indicate the extent to which a model accounts for the variation in the observed data. To determine the residual percentage on depreciation, you would divide the original amount of the item by the current depreciated cost or the amount of money recovered after selling the item.
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