12) The regression equation Credits = 15.4 - .07 Work was fitted from a sample of 21 statistics students. Credits is the number of college credits taken and Work is the number of hours worked per week at an outside job.
A) Interpret the slope.
B) Is the intercept meaningful? Explain.
C) Make a prediction of Credits when Work = 0 and when Work = 40.
What do these predictions tell you?
Substitute the values from C) into the equation and solve for each one to determine Credits.
Regression equation is predicted y = a + bx
...where a represents the y-intercept and b the slope.
I hope this will help get you started.
A) The slope (-0.07) in this regression equation represents the change in the number of college credits earned for every additional hour worked per week. So, for every additional hour worked, the number of college credits taken decreases by 0.07 units.
B) The intercept (15.4) in this regression equation is meaningful. It represents the estimated number of college credits taken when the number of hours worked per week outside of school is zero. In other words, it is the starting point or baseline number of college credits earned for students who do not work outside of school.
C) To make predictions, we can substitute the values of Work into the regression equation.
When Work = 0:
Credits = 15.4 - 0.07(0) = 15.4
This means that when a student does not work outside of school (Work = 0), the predicted number of college credits they will take is 15.4.
When Work = 40:
Credits = 15.4 - 0.07(40) = 12.2
This means that when a student works 40 hours per week outside of school, the predicted number of college credits they will take is 12.2.
These predictions tell us that as the number of hours worked per week increases, the number of college credits taken decreases. Furthermore, they also indicate that there is a limit to the reduction in credits, as the predicted number of credits does not go below zero.
A) The slope of -0.07 in the regression equation represents the change in the number of college credits (Credits) for each additional hour worked per week at an outside job (Work). In other words, for every additional hour worked per week, the number of college credits taken is expected to decrease by 0.07.
B) The intercept of 15.4 in the regression equation represents the expected number of college credits taken (Credits) when an individual does not work at an outside job (i.e., when Work = 0). However, it is important to note that an intercept value of 15.4 may not hold any meaningful interpretation in this particular context.
C) To make a prediction of Credits when Work = 0, we substitute Work = 0 into the regression equation: Credits = 15.4 - 0.07 * 0. This simplifies to: Credits = 15.4.
To make a prediction of Credits when Work = 40, we substitute Work = 40 into the regression equation: Credits = 15.4 - 0.07 * 40. This simplifies to: Credits = 12.6.
These predictions suggest that when an individual does not work at an outside job (Work = 0), they are expected to have 15.4 college credits. On the other hand, if an individual works 40 hours per week at an outside job, they are predicted to have 12.6 college credits. These predictions indicate that the number of college credits decreases as the number of hours worked at an outside job increases.