[Top Answer] MATH225N – Week 8 Assignment Linear Regression Equations

Description

Week 8: Regression

 

Week	Assignments	Due Date
Week 8	Graded Discussion	Suggested Due Date— Initial Post:  Wednesday of Week 8   Due Date— Responses:  Sunday of Week 8 [Have two posts on two different days]
	Knewton Homework Assignments Coefficient of Determination Correlation and Causation Linear Regression Equations Performing Linear Regressions with Technology – Excel Predictions Using Linear Regression	Sunday of Week 8
	Week 8 final exam

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Week 8 Assignment – Linear Regression Equations

Activity 1

Question

Alice owns a snow shoveling business. For each driveway, she charges $50 plus $70 per hour of work. A linear equation that expresses the total amount of money Alice earns per driveway is y=70x+50. What are the independent and dependent variables? What is the y-intercept and the slope?

• The independent variable (x) is the amount of time Alice shovels snow. The dependent variable (y) is the amount, in dollars, Alice earns for a driveway.
• Alice charges a one-time fee of $50 (this is when x=0), so the y-intercept is 50. Alice earns $70 for each hour she works, so the slope is 70.
• The independent variable (x) is the amount of time Alice shovels snow. The dependent variable (y) is the amount, in dollars, Alice earns for a driveway.
• Alice charges a one-time fee of $70 (this is when x=0), so the y-intercept is 70. Alice earns $50 for each hour she works, so the slope is 50.
• The independent variable (x) is the amount, in dollars, Alice earns for a driveway. The dependent variable (y) is the amount of time Alice shovels snow.
• Alice charges a one-time fee of $50 (this is when x=0), so the y-intercept is 50. Alice earns $70 for each hour she works, so the slope is 70.
• The independent variable (x) is the amount, in dollars, Alice earns for a driveway. The dependent variable (y) is the amount of time Alice shovels snow.
• Alice charges a one-time fee of $70 (this is when x=0), so the y-intercept is 70. Alice earns $50 for each hour she works, so the slope is 50.

Answer

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Activity 2

Question

Olivia owns a house painting service. For each house, she charges $95 plus $60 per hour of work. A linear equation that expresses the total amount of money Olivia earns per house is y=60x+95. What are the independent and dependent variables? What is the y-intercept and the slope?

• The independent variable (x) is the amount of time Olivia paints a house. The dependent variable (y) is the amount, in dollars, Olivia earns for a house.
• Olivia charges a one-time fee of $95 (this is when x=0), so the y-intercept is 95. Olivia earns $60 for each hour she works, so the slope is 60.
• The independent variable (x) is the amount, in dollars, Olivia earns for a house. The dependent variable (y) is the amount of time Olivia paints a house.
• Olivia charges a one-time fee of $60 (this is when x=0), so the y-intercept is 60. Olivia earns $95 for each hour she works, so the slope is 95.
• The independent variable (x) is the amount of time Olivia paints a house. The dependent variable (y) is the amount, in dollars, Olivia earns for a house.
• Olivia charges a one-time fee of $60 (this is when x=0), so the y-intercept is 60. Olivia earns $95 for each hour she works, so the slope is 95.
• The independent variable (x) is the amount, in dollars, Olivia earns for a house. The dependent variable (y) is the amount of time Olivia paints a house.
• Olivia charges a one-time fee of $95 (this is when x=0), so the y-intercept is 95. Olivia earns $60 for each hour she works, so the slope is 60.

Answer

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Activity 3

Question

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

Select the correct answer below:

• positive linear pattern
• positive linear pattern with deviations
• negative linear pattern
• negative linear pattern with deviations
• no pattern

Answer

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Activity 4

Question

Rosetta owns a wedding photography business. For each wedding, she charges $100 plus $50 per hour of work. A linear equation that expresses the total amount of money Rosetta earns per wedding is y=50x+100. What are the independent and dependent variables? What is the y-intercept and the slope?

Select the correct answer below:

• The independent variable (x) is the amount of time Rosetta shoots photos. The dependent variable (y) is the amount, in dollars, Rosetta earns for a wedding.
• Rosetta charges a one-time fee of $100 (this is when x=0), so the y-intercept is 100. Rosetta earns $50 for each hour she works, so the slope is 50.
• The independent variable (x) is the amount, in dollars, Rosetta earns for a wedding. The dependent variable (y) is the amount of time Rosetta shoots photos.
• Rosetta charges a one-time fee of $100 (this is when x=0), so the y-intercept is 100. Rosetta earns $50 for each hour she works, so the slope is 50.
• The independent variable (x) is the amount of time Rosetta shoots photos. The dependent variable (y) is the amount, in dollars, Rosetta earns for a wedding.
• Rosetta charges a one-time fee of $50 (this is when x=0), so the y-intercept is 50. Rosetta earns $100 for each hour she works, so the slope is 100.
• The independent variable (x) is the amount, in dollars, Rosetta earns for a wedding. The dependent variable (y) is the amount of time Rosetta shoots photos.
• Rosetta charges a one-time fee of $50 (this is when x=0), so the y-intercept is 50. Rosetta earns $100 for each hour she works, so the slope is 100.

Answer

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Activity 5

Question

Lexie owns a lawn mowing service. For each lawn, she charges $85 plus $20 per hour of work. A linear equation that expresses the total amount of money Lexie earns per lawn is y=85+20x. What are the independent and dependent variables? What is the y-intercept and the slope?

Select the correct answer below:

• The independent variable (x) is the amount of time Lexie works a lawn. The dependent variable (y) is the amount, in dollars, Lexie earns for a lawn.
• Lexie charges a one-time fee of $20 (this is when x=0), so the y-intercept is 20. Lexie earns $85 for each hour she works, so the slope is 85.
• The independent variable (x) is the amount, in dollars, Lexie earns for a lawn. The dependent variable (y) is the amount of time Lexie works a lawn.
• Lexie charges a one-time fee of $20 (this is when x=0), so the y-intercept is 20. Lexie earns $85 for each hour she works, so the slope is 85.
• The independent variable (x) is the amount of time Lexie works a lawn. The dependent variable (y) is the amount, in dollars, Lexie earns for a lawn.
• Lexie charges a one-time fee of $85 (this is when x=0), so the y-intercept is 85. Lexie earns $20 for each hour she works, so the slope is 20.
• The independent variable (x) is the amount, in dollars, Lexie earns for a lawn. The dependent variable (y) is the amount of time Lexie works a lawn.
• Lexie charges a one-time fee of $85 (this is when x=0), so the y-intercept is 85. Lexie earns $20 for each hour she works, so the slope is 20.

Answer

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Activity 6

Question

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

Answer

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Activity 7

Question

Olivia keeps track of the amount of time she works on homework each week and the number of problems she is able to solve. The data are shown in the table below. Which of the scatter plots below accurately records the data?

Hours working	Problems solved
1	5
2	7
3	7
4	7
5	9

 

Select the correct answer below:

Answer

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Activity 8

Question

Daniel owns a business consulting service. For each consultation, he charges $95 plus $70 per hour of work. A linear equation that expresses the total amount of money Daniel earns per consultation is y=70x+95. What are the independent and dependent variables? What is the y-intercept and the slope?

Select the correct answer below:

• The independent variable (x) is the amount, in dollars, Daniel earns for a consultation. The dependent variable (y) is the amount of time Daniel consults.
• Daniel charges a one-time fee of $95 (this is when x=0), so the y-intercept is 95. Daniel earns $70 for each hour he works, so the slope is 70.
• The independent variable (x) is the amount of time Daniel consults. The dependent variable (y) is the amount, in dollars, Daniel earns for a consultation.
• Daniel charges a one-time fee of $95 (this is when x=0), so the y-intercept is 95. Daniel earns $70 for each hour he works, so the slope is 70.
• The independent variable (x) is the amount, in dollars, Daniel earns for a consultation. The dependent variable (y) is the amount of time Daniel consults.
• Daniel charges a one-time fee of $70 (this is when x=0), so the y-intercept is 70. Daniel earns $95 for each hour he works, so the slope is 95.
• The independent variable (x) is the amount of time Daniel consults. The dependent variable (y) is the amount, in dollars, Daniel earns for a consultation.
• Daniel charges a one-time fee of $70 (this is when x=0), so the y-intercept is 70. Daniel earns $95 for each hour he works, so the slope is 95.

Answer

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Activity 9

Question

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

Select the correct answer below:

• positive linear pattern
• positive linear pattern with deviations
• negative linear pattern
• negative linear pattern with deviations
• no pattern

Answer

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Activity 10

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?

• Positive linear pattern
• Positive linear pattern with deviations
• Negative linear pattern
• Negative linear pattern with deviations
• No pattern

Answer

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Activity 11

Question

Jamie owns a house painting service. For each house, she charges $70 plus $40 per hour of work. A linear equation that expresses the total amount of money Jamie earns per house is y=70+40x. What are the independent and dependent variables? What is the y-intercept and the slope?

 

Select the correct answer below:

• The independent variable (x) is the amount, in dollars, Jamie earns for a house. The dependent variable (y) is the amount of time Jamie paints a house.
• Jamie charges a one-time fee of $40 (this is when x=0), so the y-intercept is 40. Jamie earns $70 for each hour she works, so the slope is 70.
• The independent variable (x) is the amount, in dollars, Jamie earns for a house. The dependent variable (y) is the amount of time Jamie paints a house.
• Jamie charges a one-time fee of $70 (this is when x=0), so the y-intercept is 70. Jamie earns $40 for each hour she works, so the slope is 40.
• The independent variable (x) is the amount of time Jamie paints a house. The dependent variable (y) is the amount, in dollars, Jamie earns for a house.
• Jamie charges a one-time fee of $40 (this is when x=0), so the y-intercept is 40. Jamie earns $70 for each hour she works, so the slope is 70.
• The independent variable (x) is the amount of time Jamie paints a house. The dependent variable (y) is the amount, in dollars, Jamie earns for a house.
• Jamie charges a one-time fee of $70 (this is when x=0), so the y-intercept is 70. Jamie earns $40 for each hour she works, so the slope is 40.

Answer

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Activity 12

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 aluminium measured in the soil, x, and can be modelled by the function

G(x)=16−4x.

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

Provide your answer below:

Answer

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Activity 13

Question

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

Answer

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Activity 14

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.

Provide your answer below:

Answer

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Activity 15

Question

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

Round your final answer to the nearest whole number

Answer

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Activity 16

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

 

Provide your answer below:

Answer

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Activity 17

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.

Answer

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Activity 18

Question

Amelia plays basketball for her high school. She wants to improve to play at the college level. She notices that the number of points she scores in a game goes up in response to the number of hours she practices her jump shot each week. She records the following data:

X (hours practising jump shot)	Y (points scored in a game)
5	15
7	22
9	28
10	31
11	33
12	36

 

Which scatter plot best represents Amelia’s data?

Select the correct answer below:

Answer

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Activity 19

Question

The scatter plot below shows data about the relationship between incomes and the number of years of education people have. Which of the following patterns does the scatter plot show?

Select the correct answer below:

• positive linear pattern
• positive linear pattern with deviations
• negative linear pattern
• negative linear pattern with deviations
• no pattern

Answer

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