**Week 8 Assignment Linear Regression Equations **

**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.

**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

**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 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.

** **

**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:

**Question**

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

**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:

**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

The number of incorrect problems on the statistics midterm is 12. So, we must find the number of pages of notes, x, so that y(x)=12.

## 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:

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).

**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**

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:

**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

**Solution:**

**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****.**

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.

**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

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