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## What is a regression analysis and what is it used for?

A good example of a sport that uses a regression analysis is baseball. There are several situations that are taken into account when making pitching decisions. A majority of the time a manager will choose to pitch his starting pitcher in the game, but if he is coming off an injury or if he has been performing poorly lately he may not start him. Or, if the opposing team is hitting well against his pitcher, he may choose not to start him. In any of these cases, the manager would be making a decision based on the game situation. There are different statistical models that can be used to predict how a pitcher will perform in a specific situation. If a manager is using one of these statistical models to choose who to pitch and when, then he is performing what is known as a regression analysis.

## The different types of regression models

There are different types of regression models that allow you to predict the performance of future games based on past performances. One of these types is a linear model. A linear model is used when the relationship between a variable and another one is straight, (or homogeneous) and when the variables are on a straight line. After the relationship between two variables has been determined, the relation can be summarized in a simple equation such as y = mx + b. In this equation the x stands for the independent variable and y is the dependent one. The slope m is the regression coefficient that measures how sensitive to change the dependent variable y is with respect to a change in the independent one x. In cases where there is a significant positive relationship between two variables, both variables tend to increase or decrease together. If a regression coefficient is equal or very close to one it means that there is a very high correlation between the two variables and that the equation y = mx + b is an accurate description of the relationship. The independent variable is not always x, in some cases it could be y, z or z´. In this last case, the equation would be y´ = my + b with m > 0. In this case the equation can be simplified to y = my + b. The regression model can also describe the relationship between an independent variable and a dependent variable which may not be linear, but it is of a similar form.

## The steps involved in conducting a regression analysis

The first step in conducting a regression analysis is to decide which variables are related to each other. Next, the values of these two variables must be found and recorded. Once those steps are completed, the researcher must determine if the relationship between the two variables is truly significant. If it is not significant then the analysis must be repeated using different variables for the same purpose. If the two variables are significant, then a standard formula can be used to determine the level of significance. Lastly, confidence levels must be set and the results are interpreted.

The first step in conducting a regression analysis is to decide which variables are related to each other. There are two types of relationships between variables: linear and non-linear. If the variables are linearly related then they form a straight line when graphed; if they are non-linearly related they form an ellipse or some other shape. The variables can be related even if they form an ellipse, but the major distinction between linear and non-linear relationships is that linear relationships are easier to understand than non-linear relationships.

## How to interpret the results of a regression analysis

If a regression analysis is performed correctly, then when the dependent variable is higher than x it should also be higher than y and vice versa. All of the points on the line must be in order with the lowest value being on the left and the highest being on the right.

The slope of the line is determined by the constant β, which is not affected by x or y. The slope of the line is different from typical mathematics where an exponent and a coefficient are used to represent slope.

The intercept of the regression line must also be interpreted. The value of b0 should be interpreted as “the expected value” if x=0 and y=0.

## What are some potential problems with using regression analysis

One potential problem with using regression analysis is that the line being drawn may not cover all of the points on the graph or it may be too high. This is a big problem because it poses a threat to the validity of your data and if you don’t notice this problem then your results will not make sense. Another potential problem is that the data you are using to perform the analysis may have too much of an extreme range. This problem can cause your line to be too low or too high which again is a threat to the validity of your data and your results will not make sense. Another potential problem is that there may be an outlier in your data set. This is a big problem because the outlier could throw off the line being used to predict the values and you may get an inaccurate prediction. Finally, by not testing for these problems or by not checking your results for accuracy you are risking the validity of your data and therefore accuracy of your results.

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