Berekening en interpretatie van de lineaire correlatiecoëfficiënt

Consider the data set of carbon dioxide levels versus the annual temperature over a specific period. The scatter plot of the data points shows a probable linear pattern between the two variables.

To confirm a straight-line pattern, the linear correlation coefficient, r, is calculated.

First, x square, y square, and the product of x and y are determined and then added. The number of data points is 7.

From these values, the coefficient of correlation is calculated.

The meaning of the correlation coefficient value can be interpreted using the critical value table.

At a significance level of 0.05, and n equals 7, the critical value comes out to be 0.754.

Since the modulus of r is more than the critical value, there is sufficient evidence to support the conclusion that there is a linear correlation between the variables.

The r square value indicates that 76.2% of the variation in annual temperature can be explained by the linear relationship between carbon dioxide levels and annual temperature.