Find & interpret the y-intercept (a) if an interpretation is possible. If it’s not possible, just report the y-intercept and explain why it can not be interpreted practically Use your model to estimate the price of a car that has 100,000 miles. Is this prediction reasonable? Why or why not? Provide a brief conclusion or discussion of the results that includes one of the following: potential problems or sources of bias are the results what you expected?
Find & interpret the y-intercept (a) if an interpretation is possible. If it’s not possible, just report the y-intercept and explain why it can not be interpreted practically Use your model to estimate the price of a car that has 100,000 miles. Is this prediction reasonable? Why or why not? Provide a brief conclusion or discussion of the results that includes one of the following: potential problems or sources of bias are the results what you expected?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
- Find & interpret the y-intercept (a) if an interpretation is possible. If it’s not possible, just report the y-intercept and explain why it can not be interpreted practically
- Use your model to estimate the price of a car that has 100,000 miles. Is this prediction reasonable? Why or why not?
- Provide a brief conclusion or discussion of the results that includes one of the following:
-
- potential problems or sources of bias
- are the results what you expected?
- are there other variables that may also be useful to predict the price of a car
![**Simple Linear Regression Analysis**
**Regression Results:**
- **Dependent Variable:** Sale Price
- **Independent Variable:** Mileage
**Regression Equation:**
\[ \text{Sale Price} = 50103.948 - 0.40458624 \times \text{Mileage} \]
**Sample Size:** 30
- **Correlation Coefficient (R):** -0.51297305
- **Coefficient of Determination (R-squared):** 0.26314135
- **Estimate of Error Standard Deviation:** 9953.8887
**Parameter Estimates:**
| Parameter | Estimate | Standard Error | Alternative | Degrees of Freedom (DF) | T-Statistic | P-value |
|-----------|------------|----------------|-------------|-------------------------|--------------|---------|
| Intercept | 50103.948 | 3680.1341 | ≠ 0 | 28 | 13.614707 | <0.0001 |
| Slope | -0.40458624 | 0.12794686 | ≠ 0 | 28 | -3.1621427 | 0.0037 |
**Analysis of Variance Table for Regression Model:**
| Source | Degrees of Freedom (DF) | Sum of Squares (SS) | Mean Square (MS) | F-statistic | P-value |
|--------|-------------------------|---------------------|------------------|------------|---------|
| Model | 1 | 9.9071446e8 | 9.9071446e8 | 9.9991466 | 0.0037 |
| Error | 28 | 2.7742372e9 | 99079901 | | |
| Total | 29 | 3.7649517e9 | | | |
**Explanation:**
- The regression equation suggests that for each additional mile driven, the sale price decreases by approximately $0.40.
- The negative correlation coefficient indicates a weak negative linear relationship between mileage and sale price.
- The p-values for both the intercept and slope are less than 0.05, suggesting that both are statistically significant.
- The F-statistic and its associated p-value indicate that the model is statistically significant.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c931c20-6ffe-410f-831b-8032826b4145%2Fd3107f97-09ec-4508-b613-89da260f06c2%2Fhueadc_processed.png&w=3840&q=75)
Transcribed Image Text:**Simple Linear Regression Analysis**
**Regression Results:**
- **Dependent Variable:** Sale Price
- **Independent Variable:** Mileage
**Regression Equation:**
\[ \text{Sale Price} = 50103.948 - 0.40458624 \times \text{Mileage} \]
**Sample Size:** 30
- **Correlation Coefficient (R):** -0.51297305
- **Coefficient of Determination (R-squared):** 0.26314135
- **Estimate of Error Standard Deviation:** 9953.8887
**Parameter Estimates:**
| Parameter | Estimate | Standard Error | Alternative | Degrees of Freedom (DF) | T-Statistic | P-value |
|-----------|------------|----------------|-------------|-------------------------|--------------|---------|
| Intercept | 50103.948 | 3680.1341 | ≠ 0 | 28 | 13.614707 | <0.0001 |
| Slope | -0.40458624 | 0.12794686 | ≠ 0 | 28 | -3.1621427 | 0.0037 |
**Analysis of Variance Table for Regression Model:**
| Source | Degrees of Freedom (DF) | Sum of Squares (SS) | Mean Square (MS) | F-statistic | P-value |
|--------|-------------------------|---------------------|------------------|------------|---------|
| Model | 1 | 9.9071446e8 | 9.9071446e8 | 9.9991466 | 0.0037 |
| Error | 28 | 2.7742372e9 | 99079901 | | |
| Total | 29 | 3.7649517e9 | | | |
**Explanation:**
- The regression equation suggests that for each additional mile driven, the sale price decreases by approximately $0.40.
- The negative correlation coefficient indicates a weak negative linear relationship between mileage and sale price.
- The p-values for both the intercept and slope are less than 0.05, suggesting that both are statistically significant.
- The F-statistic and its associated p-value indicate that the model is statistically significant.
Transcribed Image Text:### Scatter Plot: Relationship Between Mileage and Sale Price
#### Description:
This scatter plot illustrates the relationship between the mileage of vehicles and their sale prices. The x-axis represents the mileage of the vehicles, ranging from 0 to 70,000 miles. The y-axis denotes the sale price, which ranges from $30,000 to $70,000.
#### Key Observations:
- The data points are scattered throughout the plot, indicating the individual sale prices for varying mileages.
- There is a visible concentration of data points in the mileage range of 10,000 to 30,000 miles and sale prices from $30,000 to $50,000.
- Higher sale prices, especially those above $60,000, tend to be associated with lower mileage.
- As mileage increases beyond 50,000 miles, there appears to be a tendency for sale prices to cluster around the lower end of the price spectrum, although some outliers exist.
#### Analysis:
This plot can be used to assess how mileage impacts the sale price of vehicles, potentially useful for buyers and sellers to make informed decisions. Generally, it is often observed that lower mileage cars are able to command higher prices, likely due to wear and tear factors.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman