Introduction > Step-by-Step Statistics > Now You've Mastered the Basics > Testing for Relationships

Testing for Relationships Regression analyses are used to determine relationships between your treatment(s) and experimental units and can be used to predict future observations. Before you conduct a regression analysis, it's important to check that your explanatory variable is continuous. You will come across linear or multiple regressions. Linear Regression This is used to test if there is a relationship between one variable and another. For example, you could be researching the correlation between calf birth weight and final weight of the cow. Using linear regression an equation can be written which describes the relationship between the two variables. How well the equation fits the raw data is measured by the value. Generally, an greater than 0.5 is acceptable. The equation can then be used to predict the final weight given a birth weight, although be cautious about the faith you invest in predicting beyond your original raw data. For example, in the graph below, you should be cautious when predicting the final weight of cows if the birth rate was lower than 34kg and higher than 57kg. Exercise Have a go at performing a linear regression Multiple Regression You may be interested in the effects of several variables, such as the effect of birth weight, birth length and final weight. In this case, you'd use a multiple regression analyse to determine the influence of birth length and birth weight on the final weight of the animal. This is used to predict relationships between several variables. To use multiple regression, run the initial analysis with all your variables present in every combination. For example, if you were investigating the effects of birth weight and birth length on the final weight of cows, your explanatory variables would be entered as:      weight+length+weight*length. The results of the analysis will rank the variables in terms of the probability of the explanatory variable affecting the response variable. The least significant explanatory variable should be removed and the data re-analysed. This process should be repeated until you're left with explanatory variables with P<0.05. This is known as the top-down approach. To ensure the robustness of your analysis, you should then repeat your analysis using the bottom-up approach. This involves running your statistics with your response variable and one explanatory variable. Explanatory variables should then be added one at a time and the data re-analysed at each step. Insignificant variables should be removed and you should end up with the same equation as produced using the top-down approach.

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