Suppose a doctor measures the height, x, and head circumference, y, of 8 childre

Question

Suppose a doctor measures the height, x, and head circumference, y, of 8 children and obtains the data below. The completion coefficient is 0.956 and the least squares regression line is y = 0.237x + 10.997. Complete parts (a) and (b) below. (a) Compute the coefficient of determination, R^2. R^2 = % (b) Interpret the coefficient of determination and comment on the adequacy of the linear model. A. R^2 of the variation in head circumference is explained by the least-squares regression equation. The linear model appears to be appropriate. B. R^2 of the variation in head circumference is not explained by the least-squares regression equation. The linear modal appears to be appropriate. D. R^2 of the variation in head circumference is not explained by the least-squares regression equation. The linear model appears to be not appropriates.

Explanation / Answer

Here' the answer to the problem:

a) The R^2 is the square of R , which is the coefficient of correlation. Square it and you will get the Coefficient of determination. R^2.

So, it' .956^2 = .914

b)

R^2 is the %of variation that can be explained by the indep. variable. The model seems to be right since the R^2 is quiet high and therefore the indep. variable covers almost all the correlation/determination for prediction.The model' predictive strength is quiet high.

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