# (Solved) Math225 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

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 last minute purchases if 40% of the customers wait more than 7 minutes in line.

Question

A department store manager explored the relationship between the percent of customers that wait more than 7 minutes in line and the percent of customers that purchase last minute items at checkout. The manager collects information from 5 checkout lines, shown in the table below.

Use the graph below to plot the points and develop a linear relationship between the percent of waiting customers and the percent of last minute purchases.

 Line % of Waiting Customers % of Last Minute Purchases 1 25 3 2 35 11 3 50 16 4 60 20 5 70 30

Question

How many pages of notes did a student take if they had 12 problems marked incorrect on the statistics midterm?

Question

The number of questions marked incorrect on a statistics midterm, y, is dependent on the pages of notes a student wrote over the semester, x, and can be modeled by the function

y(x)=30−3.5x.

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

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

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:

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?

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

What percent of aluminum in the soil must there be for the…Please click the icon below to download the solution at \$5