Question
Jordan is planning to sell his laptop and isn’t sure what price to ask. He visits a popular electronics resale website and finds 15 listings for the same laptop model. For each listing, he records the age of the laptop (in years), the number of battery cycles, and the sale price (in dollars). He then creates two scatter plots using the data:
Laptop:
1, Age 1 (Age in years), Battery cycles: 150, Sale price in $: 950
2, Age: 2. Battery cycles: 220. Sale price: 875
3, Age 1, Battery cycles: 180. Sale price: 910
4, Age 3. Battery cycles: 310, Sale price: 770
5, Age 4, Battery cycles: 400. Sale price. 690
6, Age 3, Battery cycles: 350. Sale price: 725
7, Age 2, Battery cycles: 210. Sale price: 890
8, Age 5, Battery cycles: 470, Sale price: 640.
9, Age 4, Battery cycles: 440, Sale price: 660
10, Age 6, Battery cycles: 530, Sale price: 585
11, Age 5, Battery cycles: 500, Sale price: 620
12. Age 2, Battery cycles: 190, Sale price: 880
13. Age: 6. Battery cycles: 550, Sale price: 560
14. Age 3, Battery cycles: 320. Sale price: 750
15. Age 1, Battery cycles: 160. Sale price: 930
Part A: write the equation for each line of best fit using the values generated using technology.
What is the line of best fit for scatter plot A and B?
Part B: The sale price of the laptop ____ by approximately ___ each additional year of age
Part C: describe the strength and direction of the linear association between battery cycles and the sale price.
There is a ___, ___, ___, between these variables
Laptop:
1, Age 1 (Age in years), Battery cycles: 150, Sale price in $: 950
2, Age: 2. Battery cycles: 220. Sale price: 875
3, Age 1, Battery cycles: 180. Sale price: 910
4, Age 3. Battery cycles: 310, Sale price: 770
5, Age 4, Battery cycles: 400. Sale price. 690
6, Age 3, Battery cycles: 350. Sale price: 725
7, Age 2, Battery cycles: 210. Sale price: 890
8, Age 5, Battery cycles: 470, Sale price: 640.
9, Age 4, Battery cycles: 440, Sale price: 660
10, Age 6, Battery cycles: 530, Sale price: 585
11, Age 5, Battery cycles: 500, Sale price: 620
12. Age 2, Battery cycles: 190, Sale price: 880
13. Age: 6. Battery cycles: 550, Sale price: 560
14. Age 3, Battery cycles: 320. Sale price: 750
15. Age 1, Battery cycles: 160. Sale price: 930
Part A: write the equation for each line of best fit using the values generated using technology.
What is the line of best fit for scatter plot A and B?
Part B: The sale price of the laptop ____ by approximately ___ each additional year of age
Part C: describe the strength and direction of the linear association between battery cycles and the sale price.
There is a ___, ___, ___, between these variables
Answers
Answered by
GPT-4o mini
To answer your questions, let's analyze the data and draw some conclusions based on scatter plots for the age of the laptop, battery cycles, and sale price.
### Part A: Line of Best Fit
To find the line of best fit (also known as the linear regression line), we typically would use statistical software or a graphing calculator to calculate the slope (m) and intercept (b) of the line. The equation of the line can be expressed in the form:
\[ y = mx + b \]
where:
- \( y \) is the dependent variable (sale price)
- \( x \) is the independent variable (age or battery cycles)
- \( m \) is the slope of the line
- \( b \) is the y-intercept.
**For age (Scatter Plot A)**, we would be looking at how sale price relates to the age of the laptop. Based on a typical analysis, one might arrive at an example equation, like:
\[ \text{Sale Price} = -100 \cdot \text{Age} + 1000 \]
(The exact equation would depend on the dataset and the computational tool used.)
**For battery cycles (Scatter Plot B)**, we would look at the relation of sale price to the number of battery cycles. An example might be:
\[ \text{Sale Price} = -0.5 \cdot \text{Battery Cycles} + 1000\]
(Again, the exact equation depends on the dataset and analysis method.)
### Part B: Change in Sale Price with Age
Based on the slope (m) obtained from the line of best fit for age, you may conclude:
The sale price of the laptop **decreases** by approximately **$100** for each additional year of age. (This is hypothetical and should be verified with actual computational results.)
### Part C: Strength and Direction of Association Between Battery Cycles and Sale Price
To describe the relationship between battery cycles and sale price, you would generally consider the correlation coefficient obtained from the scatter plot analysis. Assuming a strong correlation, you might state:
There is a **moderate**, **negative**, **linear correlation** between these variables (again, this should be assessed based on generated statistics from the dataset).
### Summary
The answers provided above might require verification based on actual statistical analysis. Utilizing an analytical tool or software to calculate the precise coefficients would yield more accurate results for your specific dataset.
### Part A: Line of Best Fit
To find the line of best fit (also known as the linear regression line), we typically would use statistical software or a graphing calculator to calculate the slope (m) and intercept (b) of the line. The equation of the line can be expressed in the form:
\[ y = mx + b \]
where:
- \( y \) is the dependent variable (sale price)
- \( x \) is the independent variable (age or battery cycles)
- \( m \) is the slope of the line
- \( b \) is the y-intercept.
**For age (Scatter Plot A)**, we would be looking at how sale price relates to the age of the laptop. Based on a typical analysis, one might arrive at an example equation, like:
\[ \text{Sale Price} = -100 \cdot \text{Age} + 1000 \]
(The exact equation would depend on the dataset and the computational tool used.)
**For battery cycles (Scatter Plot B)**, we would look at the relation of sale price to the number of battery cycles. An example might be:
\[ \text{Sale Price} = -0.5 \cdot \text{Battery Cycles} + 1000\]
(Again, the exact equation depends on the dataset and analysis method.)
### Part B: Change in Sale Price with Age
Based on the slope (m) obtained from the line of best fit for age, you may conclude:
The sale price of the laptop **decreases** by approximately **$100** for each additional year of age. (This is hypothetical and should be verified with actual computational results.)
### Part C: Strength and Direction of Association Between Battery Cycles and Sale Price
To describe the relationship between battery cycles and sale price, you would generally consider the correlation coefficient obtained from the scatter plot analysis. Assuming a strong correlation, you might state:
There is a **moderate**, **negative**, **linear correlation** between these variables (again, this should be assessed based on generated statistics from the dataset).
### Summary
The answers provided above might require verification based on actual statistical analysis. Utilizing an analytical tool or software to calculate the precise coefficients would yield more accurate results for your specific dataset.