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(ANSWER) MATH 225N-Week 8 Assignment: Linear Regression Equations

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Question 1

Find the graphs below which have a positive slope. Select all correct answers.

Question 2

A tennis player keeps track of the amount of time they spend practicing her tennis serve and the number of aces she gets in their match each week. The data are shown in the table below. Which of the scatter plots below accurately records the data?

Hours practicing  Aces
1 4
2 4
3 5
4 7
5 8
 

 

 

Question 3

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

 

Question 4

A student keeps track of the amount of time they study and the score they get on their 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
 

 

Question 5

Jamie owns a house painting service. For each house, they charge $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?

Answer

Answer Explanation

Correct answer:

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 they works, so the slope is 40.

The independent variable (x) is the amount of time Jamie paints a house because it is the value that changes. They may work different amounts per house, and their earnings are dependent on how many hours they work. This is why the amount, in dollars, Jamie earns for a house is the dependent variable (y).

The y-intercept is 70 (b=70). This is their one-time fee. The slope is 40 (a=40). This is the increase for each hour they work.

 

Question 6

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

 

Answer Explanation

Correct answer:

The independent variable (x) is the amount of time Ryan shovels snow. The dependent variable (y) is the amount, in dollars, Ryan earns for a driveway.

Ryan charges a one-time fee of $50 (this is when x=0), so the y-intercept is 50. Ryan earns $70 for each hour they works, so the slope is 70.

The independent variable (x) is the amount of time Ryan shovels snow because it is the value that changes. They may work different amounts per driveway, and their earnings are dependent on how many hours they work. This is why the amount, in dollars, Ryan earns for a driveway is the dependent variable (y).

The y-intercept is 50 (b=50). This is their one-time fee. The slope is 70 (a=70). This is the increase for each hour they work.

 

 

Question 7

A runner finds that the distance they run in miles, D, is dependent on the ounces of water consumed every two hours, x, and can be modeled by the function

D(x)=1.5x.

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

The function D(x)=1.5x is a linear equation, so its graph is a straight line that can be drawn by plotting 2 points and connecting them.

Its D intercept occurs when x=0, so

D(0)=0,

and (0,0) is the D-intercept.

To find another point, plug in another x value into the function D(x). For example, when x=4, we have

D(4)=1.5(4)=6.

So, (4,6) is another point on the graph of D(x).

 

Question 8

How much water should be consumed every two hours for a person to run 16 miles?

  • Round your final answer to the nearest whole number.

 

Question 9

A student keeps track of the amount of time they work on homework each week and the number of problems they can solve. The data are shown in the table below. Which of the scatter plots below accurately records the data?

Hours working  Problems solved
1 4
2 6
3 7
4 7
5 9

The values for hours working correspond to x-values, and the values for problems solved correspond to y-values. Each row of the table of data corresponds to a point (x,y) plotted in the scatter plot. For example, the first row, 1,4, corresponds to the point (1,4). Doing this for every row in the table, we find the scatter plot should have points (1,4), (2,6), (3,7), (4,7), and (5,9).

 

Question 10

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

 

Question 11

A tennis player keeps track of the amount of time they spend practicing the tennis serve and the number of aces she gets in her match each week. The data are shown in the table below. Which of the scatter plots below accurately records the data?

Hours practicing  Aces
1 2
2 3
3 4
4 6
 

 

5 7

The values for hours practicing correspond to x-values, and the values for aces correspond to y-values. Each row of the table of data corresponds to a point (x,y) plotted in the scatter plot. For example, the first row, 1,2, corresponds to the point (1,2). Doing this for every row in the table, we find the scatter plot should have points (1,2), (2,3), (3,4), (4,6), and (5,7).

 

Question 12

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

 

Question 13

A baker keeps track of the amount of time they spend baking and the number of pies they are able to bake in that time. The data are shown in the table below. Which of the scatter plots below accurately records the data?

Hours working  Pies baked
1 2
2 4
3 6
4 9
5 9

The values for hours working correspond to x-values, and the values for pies baked correspond to y-values. Each row of the table of data corresponds to a point (x,y) plotted in the scatter plot. For example, the first row, 1,2, corresponds to the point (1,2). Doing this for every row in the table, we find the scatter plot should have points (1,2), (2,4), (3,6), (4,9), and (5,9).

Question 14

Describe the relationship between the independent variable, x, and the dependent variable, y, if the correlation is positive.

 

Question 15

Which of the following patterns does the scatter plot show?

 

 

 

 

 

 

 

 

 

 

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