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The Formula for Calculation of the Determination Coefficient (R Square) Simple Linear Regression

The coefficient of determination in regression analysis has an important function. Therefore, it is not surprising that various research papers using regression analysis will generally always bring up the value of the coefficient of determination. Based on this, Kanda data will write this topic to be discussed together. This article continues the previous week’s theme, which discussed manually calculating the coefficients bo and b1 in simple linear regression.

Before discussing how to calculate the coefficient of determination, would it be better to understand what the coefficient of determination (R square) is?. The coefficient of determination is a value to measure the ability of a model to explain how much variation in the independent variable can explain the variation in the dependent variable.

Based on the results of data analysis, the value of the coefficient of determination (R Square) will generally appear in the Model Summary table. Then maybe my friend will ask, “what is the unit of the coefficient of determination?” The value of the coefficient of determination is between 0 to 1. So, this coefficient of determination is unitless or has no units.

This range of values will show the goodness of a regression model. R Square value close to 1 indicates the model is getting better. On the other hand, the closer to 0 the value of R Square, the less good the model is. The coefficient of determination can be said to be a value that shows the contribution of the independent variable in explaining the variation of the dependent variable.

The value of R square will differ significantly in magnitude in research using time series data compared to analysis using cross-sectional data. Generally, the R square value of time-series data will be higher than the cross-section data. At least the R square value of 0.6 in the cross-sectional data is good, while in the time-series data, at least the R square of 0.8 has shown a good model. Until this stage, conceptually, it is hoped that you have a good understanding of the concept of R Square 😊.

Okay, then back to the title of the article discussed this time. I will provide information on calculating the value of the coefficient of determination (R Square). Referring to the book written by Koutsoyiannis (1977), the formula for calculating the value of the coefficient of determination (R2) is:

Based on this formula, you can see that in calculating the value of R square, you need the estimated coefficient value of b1, which has been discussed in last week’s article. Next, you need to calculate the sum of xy and the sum of y2. This calculation will be very easy to do with the help of a calculator or Microsoft Excel.

For those of you who want to practice calculating the value of the coefficient of determination in simple linear regression as in formulas using Microsoft Excel, I have prepared a video tutorial that will guide and make it easier for you to learn, as follows (video uses Indonesian, please use English subtitles):

Easy isn’t it? It turns out that calculating the value of the coefficient of determination is quite easy! Suppose you have obtained the calculated value, and are still curious about whether the calculation value is correct or not. In that case, you can compare it with the value of the coefficient of determination from data processing results using SPSS, SAS, and others. Of course, using the same data as when doing calculations manually 😊

Well, then you can interpret the value of the coefficient of determination. For example, from the calculation results obtained a coefficient of determination (R Square) of 0.845 then you can interpret: “The variation of the dependent variable (Y) of 84.5% can be explained by the variation of the independent variable (X), while the remaining 15.5% is explained by variations of other variables that are not included in this model”.

Now you know to calculate the coefficient of determination (R Square) independently. Hopefully, this article is useful for those of you who need it! Thank you for visiting my blog. I was hoping you could wait for an article update from me next week!

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