Question

A researcher is studying reentry following imprisonment. She thinks that participation in educational programs in prison will increase the chances of employment upon release for formerly incarcerated individuals. To test her hypothesis, she first collected data from a random sample of formerly incarcerated inmates from prisons across the U.S. Then, she summarized the relationship between the number of educational programs participated in during prison and the number of calls from potential employers in the first month after release by calculating the following bivariate regression equation: y^=0.3+1.0(x). The next five questions (Q29 to Q33) are about this regression equation.

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

predicted number of calls from potential employers

number of educational programs

the intercept of the regression line

the slope of the regression line

the amount of variance explained

2. What does 1.0 refer to in the regression equation?

predicted number of calls from potential employers

number of educational programs

the intercept of the regression line

the slope of the regression line

the amount of variance explained

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

predicted number of calls from potential employers

number of educational programs

the intercept of the regression line

the slope of the regression line

the amount of variance explained

4. According to the regression equation, a formerly incarcerated adult who reports participating in two (2) educational programs is predicted to receive how many calls from potential employers?

2 calls

1.3 calls

0.3 calls

1.0 calls

2.3 calls

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 educational programs and number of calls from potential employers = 0.

True

False

Answer 1

Given, bivariate regression equation $\hat{y}$ = 0.3 + 1.0x

Answer 1:
In the regression equation, $\hat{y}$ denotes the predicted number of calls from potential employers

Hence, 1^st Option is correct

Answer 2:
Generally, in a regression equation the x - coefficient or the coefficient of the independent variable denotes the slope of the regression equation.

So, in the equation 1.0 refers to the slope of the regression line

Hence, 4^th Option is correct

Answer 3:
Here, x is the independent variable which refers to the number of educational programs

Hence,2^nd Option is correct

Answer 4:
Therefore, when x = 2

$\hat{y}$ = 0.3 + (1.0 x 2) = 2.3

Since, 2.3 calls have no meaning as there cannot be a 0.3 call, the incarcerated adult is predicted to receive 2 calls from potential employers

So, 1^st Option is correct

Answer 5:
The following statement of the null hypothesis is True