Question

Please help me interpret the regression SAS output. Please state the hypothesis(reject or not reject), significance of the adjusted R-sq, state the regression equation for the data. Lastly please state the regression equation for each stim dummy category (1=Yes 0=No)

11.3.3 One purpose of a study by Connor et al. (A-8) was to examine reactive aggression among children and adolescents referred to a residential treatment center. The researchers used the Proactive/Reactive Rating Scale, obtained by presenting three statements to clinicians who examined the subjects. The respondents answered, using a scale from 1 to 5, with 5 indicating that the statement almost always applied to the child. An example of a reactive aggression statement is, “When this child has been teased or threatened, he or she gets angry easily and strikes back.” The reactive score was the average response to three statements of this type. With this variable as the outcome variable, researchers also examined the following: VERBALIQ (verbal IQ) and STIM (stimulant use for attention deficit hyperactivity disorder symptoms, 1=Yes, O=No). Perform a multiple linear regression to find the effects of verbal IQ and STIM in predicting reactive aggression in the following sample of 68 subjects and complete the SAS Lab Report by using (a)-(h) steps.

Answer 1

The least square regression equation is,

Reactive score = 4.75732 - 0.01944 Verbal IQ + 0.67641 stim_dummy

Test for overall significance of the model:

Hypothesis:

HO: Bu = B2 = 0

$H_a : At \ least \ one \ \beta_i \neq 0 \ \ i = 1,2$

This hypothesis is tested using F test.

F = 4.84 and p-value = 0.0110

Since p-value is less than 0.05, we reject null hypothesis at 5% level of significance and conclude that fitted regression model is statistically significant.

Adjusted R² = 0.1028 which is very low. It means fitted model will explain only 10.28% of variation in the reactive score.

Separate regression equation according to dummy variable.

When stim_dummy = 1, regression equation is,

Reactive score = 4.75732 - 0.01944 Verbal IQ + 0.67641 (1)

Reactive score = 5.43373 - 0.01944 Verbal IQ

When stim_dummy = 0 , regression equation is,

Reactive score = 4.75732 - 0.01944 Verbal IQ + 0.67641 (0)

Reactive score = 4.75732 - 0.01944 Verbal IQ

Answer 2

1)       One purpose of a study by Connor et al. was to examine reactive aggression among children and adolescents referred to a residential treatment center. The researchers used the Proactive/Reactive Rating Scale, obtained by presenting three statements to clinicians who examined the subjects. The respondents answered, using a scale from 1 to 5, with 5 indicating that the statement almost always applied to the child. An example of a reactive aggression statement is, “When this child has been teased or threatened, he or she gets angry easily and strikes back.” The reactive score was the average response to three statements of this type. With this variable as the outcome variable, researchers also examined the following: AGE (years), VERBALIQ (verbal IQ), STIM (stimulant use), AGEABUSE (age when first abused), CTQ (a measure of hyperactivity in which higher scores indicate higher hyperactivity), TOTALHOS (total hostility as measured by an evaluator, with higher numbers indicating higher hostility).
The data is available in an attached file.

 

a.        In the first part of this question, use the response variable “reactive score” and the explanatory variable “VERBALIQ” to answer the following:

1.        Prepare an ANOVA table to test whether we have linear relationship between the two variables and find the regression equation.

 

2.        Test the null hypothesis that  at the .05 level of significance.

 

 

3.      Construct a 95% confidence interval for. Interpret the interval in words.

 

4.      Find the coefficient of determination and interpret it in words.

 

 

5.      Test the regression assumptions.

 

 

 

 

b.        In the remaining section of the question, use all the variables listed in the question. Perform stepwise regression to find the variables most useful in predicting reactive aggression in the sample of 60 subjects.

 

 

Infectious Disease The degree of clinical