Question

A researcher is studying reentry following imprisonment. She thinks that hanging out with friends with criminal records will increase the chances of getting rearrested for DUIs among formerly incarcerated individuals. To test her hypothesis, she first collected data from a random sample of formerly incarcerated adults. Then, she summarized the relationship between the number of criminal peers and the number of DUI arrests by calculating the following bivariate regression equation: y^=1.0+0.50(x).

1. What does  y^ refer to in the regression equation?

A. predicted number of DUI arrests

B. number of criminal peers

C. the intercept of the regression line

D. the slope of the regression line

E. the amount of variance explained

2. What does 0.50 refer to in the regression equation?

A. predicted number of DUI arrests

B. number of criminal peers

C. the intercept of the regression line

D. the slope of the regression line

E. the amount of variance explained

3. What does x refer to in the regression equation?

A. predicted number of DUI arrests

B. number of criminal peers

C. the intercept of the regression line

D. the slope of the regression line

E. the amount of variance explained

4. According to the regression equation, a formerly incarcerated adult who reports having four (4) friends with criminal records is predicted to have how many DUI arrests?

A. 0.5 arrests

B. 1.0 arrest

C. 3.0 arrests

D. 4.0 arrests

E. 0.0 arrests

5. After describing the bivariate relationship in this sample using the regression equation, the researcher then wants to test her hypothesis to make inferences about the existence of an association in the larger population. True or false: The following statement is an appropriate null hypothesis for this test. H₀: β for number of criminal peers and number of DUI arrests = 0.

A. True

B. False

Answer 1

The researcher wants to find out whether hanging out with criminal friends increases your chances of getting rearrested for DUIs among formerly incarcerated individuals.

Here, she wants to predict "the number of DUIs" by using the variable "number of criminal friends/peers".

Here, the dependent variable is "the number of DUIs" and the independent variable is " number of criminal friends/peers"

So, we have,

Y = the number of DUIs

X = number of criminal friends/peers

And the regression line is given as : =1.0+0.50X

where, is the predicted number of DUIs and X is the number of criminal peers.

1. predicted number of DUI arrests

2. the slope of the regression line

Explanation : The equation can be seen as Y = mx + c where c = intercept and m = slope. So m = 0.50 is the slope of the line .

3. number of criminal peers

4. Our equation is =1.0+0.50X and given X = 4 friends.

So,   = 1.0 + 0.50 * 4 = 1 + 2 = 3 DUIs i.e 3 arrents

5. False

Explanation:

The null hypothesis should be H₀: β for number of criminal peers and number of DUI arrests = 0.5

and the alternate hypothesis should he H₁: β for number of criminal peers and number of DUI arrests 0.5

because we have obtained β = 0.50, so we want to test this value for the population.