Understanding Slope & Intercept in Linear Regression

A car rental company charges a base fee of $20 plus $0.15 per mile driven. Write the equation for the total cost (C) in terms of miles driven (m). What does the slope represent in this context?

• C = 15 + 0.20m; the slope represents the base fee.

• C = 20 + 0.15m; the slope (0.15) represents the cost per mile driven.

• C = 25 + 0.15m; the slope represents the fixed cost of the rental.

• C = 20 + 0.10m; the slope represents the total distance driven.

A student collects data on the number of hours studied (x) and the scores received on a test (y). The linear regression equation is y = 5x + 60. What does the y-intercept represent in this scenario?

• The y-intercept represents the number of hours studied before the test.

• The y-intercept indicates the maximum possible score on the test.

• The y-intercept shows the average score of all students.

• The y-intercept represents the expected test score when no hours are studied, which is 60.

A local gym tracks the number of members (x) and the monthly revenue (y). The regression line is given by y = 50x + 200. If the gym has 100 members, what is the expected revenue?

• 4500

• 5200

• 4800

• 6000

A researcher finds that the number of hours of sleep (x) affects test scores (y) with the equation y = 10x + 70. If a student scores 90 on the test, how many hours of sleep did they likely get?

• 2

• 3

• 1

• 4

A store's sales (y) can be predicted by the number of advertisements (x) with the equation y = 200 + 30x. What is the expected increase in sales for each additional advertisement?

• 20

• 50

• 10

• 30

A farmer notices that for every additional hour of watering (x), the crop yield (y) increases according to the equation y = 2x + 50. What is the crop yield if the farmer waters for 10 hours?

• 60

• 80

• 70

• 100

A school is analyzing the relationship between the number of students (x) and the number of teachers (y). The regression line is y = 0.2x + 5. If there are 200 students, how many teachers are expected?

• 25

• 30

• 45

• 60

A city planner finds that the number of bike lanes (x) correlates with the number of bike accidents (y) using the equation y = -0.5x + 30. What does the slope indicate about the relationship between bike lanes and accidents?

• The slope indicates that more bike lanes lead to more bike accidents.

• The slope shows that bike lanes have no effect on bike accidents.

• The slope suggests that fewer bike lanes result in fewer bike accidents.

• The slope indicates that more bike lanes are associated with fewer bike accidents.

A tech company finds that for every $1000 spent on advertising (x), sales (y) increase by $5000. If the company spends $3000, what is the expected increase in sales?

• 10000

• 20000

• 25000

• 15000

A student models the relationship between the temperature (x) in degrees Celsius and ice cream sales (y) with the equation y = 10x + 50. If the temperature is 25 degrees, how many ice creams are expected to be sold?

• 150

• 300

• 200

• 350