Linear Regression Equations week 8 PDF

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Linear Regression Equations week 8 1. 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? 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. 2. 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.

Correct! You nailed it.

$$0, 16 $$4, 0 Example Correct Answer

$$0, 16 $$7, −12 The function G(x)=16−4x is a linear equation, so its graph is a straight line that can be drawn by plotting 2 points and connecting them. Its G intercept occurs when x=0, so

G(0)=16, and (0,16) is the G -intercept.

To find another point, plug in another x value into the function G(x). For example, when x=7 , we have

G(7)=16−4(7)=−12. So, (7,−12) is another point on the graph of G(x) .

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

Round your final answer to the nearest whole number.

•

03 percent$3\ \text{percent}$3 percent

For the daffodils to grow only by 5 centimeters, the growth must be 5. So, we must find the percent of aluminum in the soil, x , so that G(x)=5. For G(x)=5 , we have

16−4x−4xxxx=5=−11=−11−4=2.75≈3.

4. The scatter plot below shows data relating competitive chess players' ratings and their IQ. Which of the following patterns does the scatter plot show?

no pattern 5. 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?

Negative linear pattern with deviations 6. 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.

Well done! You got it right.

$$0, 30 $$2, 23 Example Correct Answer

$$0, 30 $$2, 23 The function y(x)=30−3.5x is a linear equation, so its graph is a straight line that can be drawn by plotting 2 points and connecting them. Its y intercept occurs when x=0, so

y(0)=30, and (0,30) is the y -intercept. To find another point, plug in another x value into the function y(x). For example, when x=2 , we have

y(2)=30−3.5(2)=23. 7. How many pages of notes did a student take if they had 12 problems marked incorrect on the statistics midterm? 5 8. 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.

The percent of defects is the x -coordinate, while the percent of new machines is the y coordinate. So, the table of values corresponds to the points

(25,32), (20,40), (15,50), (10,65), (5,70), (0,85). 9. Using the linear relationship graphed above, estimate the percent of new machines if there is 12% defects in the shoes at various production facilities. 58% 10. 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.

(25,3), (35,11), (50,16), (60,20), (70,30). 11. 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. 12% 12. A government agency explored the relationship between the percent of public colleges and the percent of freshmen that stay home during college. The researcher collects information from 5 states, shown in the table below.

Use the graph below to plot the points and develop a linear relationship between the percent of public colleges and the percent of freshmen that stay home during college.

(15,20), (35,30), (50,45), (55,65), (60,70) 13. Using the linear relationship graphed above, estimate the percent of freshmen that stay instate if there are 45% public colleges. 50% 14. Describe the relationship between the independent variable, x, and the dependent variable,

y, if the correlation is positive. As the independent variable, x, increases, the dependent variable, y increases.

15. Which of the following patterns does the scatter plot show?

Correct answer: Negative linear pattern with deviations

16. Horace keeps track of the amount of time he studies and the score he gets on his quiz. The data are shown in the table below. Which of the scatter plots below accurately records the data? Hours studying

Quiz score

1

4

2

6

3

7

4

8

5

9

17. An owner of multiple online clothing stores explored the relationship between the percent of on-call service representatives and the percent of purchases over $75 at the same stores. The owner collects information from 6 of their online stores, shown in the table below. Use the graph below to plot the points and develop a linear relationship between the percent of on-call service representatives and the percent of purchases over $75.

(20,20), (35,25), (50,40), (55,35), (60,40), (75,54).

18. Using the linear relationship graphed above, estimate the percent of over $75 purchases if there are 40% on-call service representatives. 30%...