Predictor Coef St. dev. T P. Analysis of Variance

Constant 81.17 43.50 1.87 0.104

X1 0.4929 0.4749 1.04 0.334

X2 0.4741 0.3641 1.30 0.234

S = 16.32 R-SQ = 30.2%

Analysis of Variance

Source DF SS MS F P

Regression 2 805.2 402.6 1.51 0.285

Residual Error 7 1864.9 266.4

Total 9 2670.1

Source DF SEQ. SS

X1 1 353.4

X2 1 451.8

We now proceed to interpret the results in table 4.2 and use them to make further statistical inferences.

a) The equation of the fitted linear regression is

This means that the mean blood pressure increases by 0.493 if weight

increases by 1 kilogram and age remains fixed.

Similarly, a 1-year increase in age with the weight held fixed will increase the mean blood pressure by 0.474.

b) The estimated regression coefficients and the corresponding estimated standard errors are

estimated standard error

estimated standard error

estimated standard error

Further, the error standard deviation estimated by with

degrees of freedom .

These results are useful in interval estimation and hypothesis tests about the regression coefficients.

c) In Table 4.2, the result or tells us that

30.2% of the variability of y is explained by the fitted multiple regression of

y on and . The analysis of variance shows the decomposition of the total variability into the two components

Thus,

and is estimated by , so .

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