Exploring Dependent Variables & Slope in Regression

A researcher is studying the relationship between hours studied and test scores. If the regression equation is y = 5x + 60, where y is the test score and x is the hours studied, what is the dependent variable?

• constant term

• test score

• regression coefficient

• hours studied

In the same study, if the slope of the regression line is 5, what does this indicate about the relationship between hours studied and test scores?

• The relationship is negative; more hours studied lead to lower test scores.

• The relationship is constant; hours studied do not affect test scores.

• The slope indicates no relationship between hours studied and test scores.

• The relationship is positive; more hours studied lead to higher test scores.

A car rental company finds that the cost of renting a car can be modeled by the equation y = 20x + 50, where y is the total cost and x is the number of days rented. Identify the dependent variable in this scenario.

• 20 (cost per day)

• y (total cost)

• x (number of days rented)

• 50 (fixed fee)

Using the equation from the car rental company, what does the intercept (50) represent in the context of this problem?

• The intercept (50) is the maximum rental duration allowed.

• The intercept (50) indicates the cost per mile driven.

• The intercept (50) represents the base fee for renting a car.

• The intercept (50) represents the discount for long-term rentals.

A fitness tracker company analyzes the relationship between daily steps taken and calories burned, resulting in the equation y = 0.04x + 200. What is the dependent variable here?

• calories burned

• caloric intake

• exercise duration

• daily steps taken

In the fitness tracker study, if the slope is 0.04, how many additional calories are burned for each additional step taken?

• 1 calorie

• 0.04 calories

• 0.5 calories

• 0.1 calories

A school is examining the correlation between the number of extracurricular activities students participate in and their GPA, resulting in the equation y = -0.2x + 3.5. What does the intercept (3.5) signify?

• The intercept shows the GPA of students with the highest number of activities.

• The intercept represents the maximum GPA achievable by students.

• The intercept signifies the expected GPA when no extracurricular activities are participated in.

• The intercept indicates the average number of extracurricular activities per student.

If the slope of the GPA regression line is -0.2, what does this suggest about the relationship between extracurricular activities and GPA?

• More extracurricular activities have no effect on GPA.

• The relationship is positive; more extracurricular activities lead to higher GPA.

• There is no relationship between extracurricular activities and GPA.

• The relationship is negative; more extracurricular activities are associated with lower GPA.

A local bakery tracks the relationship between the number of cupcakes sold and the revenue generated, resulting in the equation y = 2.5x + 100. Identify the dependent variable in this context.

• total cost of ingredients

• baking time for cupcakes

• revenue generated

• number of cupcakes sold

In the bakery's regression equation, what does the slope (2.5) tell us about the revenue generated per cupcake sold?

• The slope (2.5) means that the bakery loses $2.50 for each cupcake sold.

• The slope (2.5) shows that selling cupcakes decreases revenue by $2.50.

• The slope (2.5) indicates that each cupcake sold generates an additional $2.50 in revenue.

• The slope (2.5) indicates that the total revenue is fixed at $2.50 regardless of sales.