Fifteen specimens of human sera were tested comparatively for tuberculin antibod

Question

Fifteen specimens of human sera were tested comparatively for tuberculin antibody by two methods The logarithms of the titers obtained by the two methods were as follows: 21. Find the regression equation describing the relationship between the two variables, compute r, and test H0 : 0 by both the F test and the t test. 21. The regression equation is B=1.28+0.851 A SE Coef 0.3935 0.1601 Coef Predictor Constant 1.2763 0.8513 3.24 5.32 0.006 0.000 S = 02409 R-Sq 685% R-Sg (adj) 66.1% Analysis of Variance MS Source Regression Residual Error 13 Total DF 1.64181.6418 28.29 0.000 0.7545 0.0580 2.3963 14

Explanation / Answer

The regression equation is B = 1.2763 + 0.8513A

since Slope = 0.8513 which is greater than 0, thus both variables are positive correlation i.e. A increases B also increase and vice-versa
If A increase 1 unit then B also increase 0.8513 units

r^2 = 1.6418/2.3963 = 0.6851

H0: Beta1 =0
H1: Beta1 not = 0
P-value of A is 0.000< alpha 0.05, so we reject H0
Thus we conclude that A is significant. i.e. the population regression coefficient of A is not equal to zero

P-value of regression is 0.000<alpha 0.05, so we reject H0
Thus we conclude that the regression equation is best fit to the given data

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