# (Answered) MATH225N Week 8 Assignment: Linear Regression Equations

Question

Annie owns a tutoring service. For each tutoring session, she charges \$75 plus \$35 per hour of work. A linear equation that expresses the total amount of money Annie earns per tutoring session is y=75+35x. What are the independent and dependent variables? What is the y-intercept and the slope?

# Question

Which of the following lines has slope zero? Select all correct answers.

Question

The scatter plot below shows data relating IQ and the number of hours people spend on the Internet each week. Which of the following patterns does the scatter plot show?

Question

The scatter plot below shows data relating total income and the number of children a family has. Which of the following patterns does the scatter plot show?

Question

Which of the following lines has a negative slope? Select all correct answers.

Question

What percent of aluminum in the soil must there be for the daffodils to grow only by 5 centimeters?

Question

George is an avid plant lover and is concerned about the lack of daffodils that grow in his backyard. He finds the growth of the daffodils, G, is dependent on the percent of aluminum measured in the soil, x, and can be modeled by the function

G(x)=16−4x.

Draw the graph of the growth function by plotting its G-intercept and another point.

Question

Using the linear relationship graphed above, estimate the percent of new machines if there is 12% defects in the shoes at various production facilities.

Question

A shoe designer explored the relationship between the percent of defects and the percent of new machines at various production facilities throughout the state. The designer collects information from 6 of their facilities, shown in the table below.

Use the graph below to plot the points and develop a linear relationship between the percent of defects and the percent of new machines.

 Facility Number % of Defects % of New Machines 1 25 32 2 20 40 3 15 50 4 10 65 5 5 70 6 0 85

## Solution:

Question

Annie owns a tutoring service. For each tutoring session, she charges \$75 plus \$35 per hour of work. A linear equation that expresses the total amount of money Annie earns per tutoring session is y=75+35x. What are the independent and dependent variables? What is the y-intercept and the slope?

Correct answer: The independent variable (x) is the amount, in dollars, Annie earns for a tutoring session. The dependent variable (y) is the amount of time Annie tutors.
Annie charges a one-time fee of \$35 (this is when x=0), so the y-intercept is 35. Annie earns \$75 for each hour she works, so the slope is 75.