An adjusted value of 2 based on the number of degrees of freedom is calculated using the formula shown below, where n is the number of data pairs and k is the number of independent variables 1-[(1-2)(n-1) Data were found on eight pre-owned My results (n=400) show a significant ( p = 8 10 5) but weak correlation (Spearman's = .20). Note that R2 could theoretically be smaller than zero if the SSR is larger than the SST. Firstly find the correlation coefficient (or maybe it is mentioned in the question for e.g, r = This is possible if the regression line goes against the trend. The coefficient of determination (commonly denoted R 2) is the proportion of the variance in the response variable that can be explained by the explanatory variables in a regression model. This value is the same as we found in example 1 using the other formula. We apply the lm function to a formula that describes the variable eruptions by the variable waiting, and save the linear regression model in a new variable eruption.lm . Formula 1: r = n ( x y) ( x) ( y) [ n x 2 ( x) 2] [ n y 2 ( y) 2] Where, n is the total number of observations. Find the coefficient of determination for the