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Linear Model and Nonlinear Model Essay Example

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Linear Model and Nonlinear Model

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This is to say, the percentage of data closest to the regression line/line of best fit.4% of all the variations in y can be explained by the linear relationship existing between x and y variables as shown in the regression equation. The other percentage remaining (27.6%) of the variation in y-variable remains unexplained.The Correlation coefficient, on the other hand, is a measure of the direction and strength of a linear relationship that exists between two variables. This coefficient is commonly referred to as the Pearson product moment correlation coefficient (Vonesh 115).From the r value obtained above, since it is negative, it denotes negative correlation between the variables x and y. The correlation is a strong negative correlation since the value of r is close to -1. The negative value obtained (-0.850933406) indicates that, as the value of x-variable increases, the value of the y-variables decreases by about 0. Consequently, this negative value indicates that the slope of the regression line is negative as is noted in the plotted graph. Additionally, since this value is greater than 0.8, it can be described as a strong correlation.The line is a good fit to the generated data. The reason for this is due to the fact that both the correlation coefficient (r) and the Coefficient of determination (r2) both show strong relationships to the data and the x and y variables (Vonesh 215).The data that has been used in this case consists of the winning times for the women’s 200m Breaststroke swimming in the Summer Olympics for the period 1936 to 2008. Taking a look at the period approximately 60 years, the data as presented in both the graph and table reflects a general and moderate downward linear trend.The conducting of the regression calculations based on the regression equation clearly reflects or predicts a winning time of 3.434 minutes should the Summer Olympics competition be held in the year 2012. This is, however, a slight increase by 1.2328 minutes in the winning time based on the time of 2008.Basing on this huge increase, the central question one can ask is if the regression equation would be accurate in its predictions. Basing on the past trends, the linear relationship has been negative with a downward moving slope. Should this be the case, then the trend in the winning times would be classified as cyclical since there are ups and downs in the times. Subsequently, the same might be

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