Exploring Dependent Variables and Regression Slopes

A car rental company charges a base fee of $20 plus $0.15 per mile driven. If the total cost for a customer is $50, what is the dependent variable in this scenario?

• base fee

• miles driven

• rental duration

• total cost

In a study of plant growth, researchers found that for every additional hour of sunlight, the height of the plants increased by 2 cm. If the slope of the regression line is 2, what does this slope represent?

• The slope represents the total height of the plants after a certain period.

• The slope represents the increase in plant height (2 cm) for each additional hour of sunlight.

• The slope indicates the amount of water needed for plant growth.

• The slope shows the average temperature increase for each hour of sunlight.

A school is analyzing the relationship between study hours and test scores. If the regression equation is y = 5x + 60, what does the y-intercept represent in this context?

• The y-intercept represents the maximum possible test score a student can achieve.

• The y-intercept indicates the number of study hours needed to achieve a passing score.

• The y-intercept represents the predicted test score for a student who studies 0 hours, which is 60.

• The y-intercept shows the average test score of all students regardless of study hours.

A fitness tracker shows that for every 100 calories burned, a person runs an average of 1 mile. If the regression equation is y = 1x + 0, what is the slope and what does it indicate?

• The slope is 1, indicating that for every 100 calories burned, 0.5 miles are run.

• The slope is 0, indicating no calories are burned per mile.

• The slope is 2, indicating that for every mile run, 200 calories are burned.

• The slope is 1, indicating that for every mile run, 100 calories are burned.

A local bakery found that for every additional cupcake sold, their profit increases by $1. If the regression line is represented by the equation y = 1x + 50, what is the dependent variable?

• number of cupcakes sold

• profit

• total sales revenue

• cost of ingredients

In a survey, it was found that the average number of hours students sleep affects their grades. If the regression equation is y = -3x + 90, what does the slope tell us about the relationship between sleep and grades?

• The slope of -3 indicates that more sleep is associated with lower grades.

• The slope of -3 suggests that sleep has no impact on grades.

• The slope of -3 shows that less sleep leads to better grades.

• The slope of -3 indicates that more sleep is associated with higher grades.

A researcher is studying the effect of temperature on ice cream sales. If the regression equation is y = 10x + 200, what does the y-intercept represent in this scenario?

• The y-intercept represents the average temperature at which ice cream is sold.

• The y-intercept represents the baseline ice cream sales when the temperature is 0 degrees.

• The y-intercept shows the increase in sales for every degree above freezing.

• The y-intercept indicates the maximum ice cream sales at high temperatures.

A gym tracks the relationship between the number of classes attended and weight loss. If the regression line is y = -2x + 30, what does the slope indicate about the relationship?

• The slope of -2 means that attending more classes has no effect on weight loss.

• The slope of -2 suggests that weight loss increases by 2 units for every class not attended.

• The slope of -2 indicates that each additional class attended results in a weight loss decrease of 2 units.

• The slope of -2 indicates that each additional class attended results in a weight gain of 2 units.

A company found that for every $100 increase in advertising, sales increase by $500. If the regression equation is y = 5x + 2000, what is the meaning of the y-intercept?

• The y-intercept (2000) indicates the baseline sales when advertising is $0.

• The y-intercept (2000) indicates the sales increase for every $100 spent on advertising.

• The y-intercept (2000) represents the maximum possible sales.

• The y-intercept (2000) shows the total advertising budget.

In a study of hours spent studying and exam scores, the regression equation is y = 4x + 50. If a student studies for 5 hours, what will be their predicted exam score?

• 70

• 60

• 80

• 90