A public health researcher wants to use regression to predict the sun safety kno

Question

A public health researcher wants to use regression to predict the sun safety knowledge of pre-school children. The researcher randomly sampled 35 pre-schoolers, assigned them to one of two groups, and then measured the following three variables:

SUNSCORE:    y = Score on sun-safety comprehension test

READING:        x1= Reading comprehension score

GROUP:            x2= 1 if child received a Be Sun Safe demonstration, 0 if not

Use the following information to answer the multiple regression questions.

Printout C:  UNWEIGHTED LEAST SQUARES LINEAR REGRESSION OF SUNSCORE

PREDICTOR

VARIABLES    COEFFICIENT    STD ERROR     STUDENT'S T P     

CONSTANT 4.23186 0.82079 5.16       0.0000

READING 0.00631 0.00194 3.25 0.0027   

READSQ .00000425 .00000087 4.87 0.0000   

GROUP 2.04026 0.45579 4.48 0.0001    

RSQUARED           0.7757      RESID. MEAN SQUARE (MSE)    1.79234

ADJUSTED RSQUARED 0.7546      STANDARD DEVIATION          1.33878

SOURCE        DF SS MS F P

REGRESSION     3     198.310      66.1033    36.88   0.0000

RESIDUAL 32     57.3548      1.79234

TOTAL 35     255.665

In terms of the predictive ability of the model, which of the following is the single most important value on Printout C to consider?

Explanation / Answer

In order to judge significance of the model, both R-square and F can be used. R-square is the proportion of variation of the dependent variable explained by the set of independent variables. F-test is used to check the significance of the model. For R -square we can't compare its value with any critical values, it will keep on increasing as we keep on including new independent variables. But F can be compared with the critical values in order to judge significance of the model. Thus F is more important. (Ans).

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