This is to say, te 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. Te other percentage remaining (27. 6) of the variation in y-variable remains unexplained. Te Correlation coefficient, o the other hand, i a measure of the direction and strength of a linear relationship that exists between two variables. Tis coefficient is commonly referred to as the Pearson correlation coefficient (Vonesh 115).
Fom the r value obtained above, snce it is negative, i denotes negative correlation between the variables x and y. Te correlation is a strong negative correlation since the value of r is close to -1. Te negative value obtained (-0.850933406) indicates that, a the value of x-variable increases, te value of the y-variables decreases by about 0. Cnsequently, tis negative value indicates that the slope of the regression line is negative as is noted in the plotted graph. Aditionally, snce this greater than 0.
8 it can be described as a strong correlation. Te line is a good fit to the generated data. Te 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). Te 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. a at the period approximately 60 years, te data as presented in both the graph and table reflects a general and moderate downward linear trend.
Te 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. Tis is, hwever, aslight increase by 1.2328 minutes in the winning time based on the time of 2008. Bsing on this huge increase, te central question one can ask is if regression equation be accurate in its predictions.
Bsing on the past trends, te linear relationship has been negative with a downward moving slope. Sould this be the case, ten the trend in the winning times would be classified as cyclical since there are ups and downs in the times. Sbsequently, te same might be. ..
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