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# (Solved) MATH225 Week 8 Assignment Linear Regression Equations

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Question

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

• 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 ofÂ \$95Â (this is whenÂ x=0), so theÂ y-intercept isÂ 95. Daniel earnsÂ \$70Â for each hour he works, so the slope isÂ 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 ofÂ \$95Â (this is whenÂ x=0), so theÂ y-intercept isÂ 95. Daniel earnsÂ \$70Â for each hour he works, so the slope isÂ 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 ofÂ \$70Â (this is whenÂ x=0), so theÂ y-intercept isÂ 70. Daniel earnsÂ \$95Â for each hour he works, so the slope isÂ 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 ofÂ \$70Â (this is whenÂ x=0), so theÂ y-intercept isÂ 70. Daniel earnsÂ \$95Â for each hour he works, so the slope isÂ 95.

Â 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?

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

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

Question

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

• 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 ofÂ \$40Â (this is whenÂ x=0), so theÂ y-intercept isÂ 40. Jamie earnsÂ \$70Â for each hour she works, so the slope isÂ 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 ofÂ \$70Â (this is whenÂ x=0), so theÂ y-intercept isÂ 70. Jamie earnsÂ \$40Â for each hour she works, so the slope isÂ 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 ofÂ \$40Â (this is whenÂ x=0), so theÂ y-intercept isÂ 40. Jamie earnsÂ \$70Â for each hour she works, so the slope isÂ 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 ofÂ \$70Â (this is whenÂ x=0), so theÂ y-intercept isÂ 70. Jamie earnsÂ \$40Â for each hour she works, so the slope isÂ 40.

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,Â G, is dependent on the percent of aluminium measured in the soil,Â x,Â and can be modelled by the function

G(x)=16âˆ’4x.

Draw the graph of the growth functionÂ by plotting itsÂ G-intercept and another point.

Question

What percent of aluminumÂ in the soil must there be for the daffodils to grow onlyÂ byÂ 5Â centimeters?

Question

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

• y(x)=30âˆ’3.5x.

Draw the graph of the functionÂ by plotting itsÂ y-intercept and another point.

Question

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

## Question

A shoeÂ designerÂ explored the relationship between the percent of defectsÂ and the percent of new machinesÂ at various production facilities throughout the state. The designer collects information fromÂ 6Â 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 defectsÂ 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

Question

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

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?

Question

The scatter plot below shows data about the relationship betweenÂ incomes and theÂ number of years of education people have.Â 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

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