Question
Introduction: Briefly describe your sample and your two quantitative variables, including their units of measurement. State that the purpose of your analysis is to use
Introduction: Briefly describe your sample and your two quantitative variables, including their units of measurement. State that the purpose of your analysis is to use linear regression to predict price based on mileage. - 1 points
Insert a scatter plot with mileage on the x axis and price on the y-axis. Conduct simple linear regression, with mileage as the x (independent) variable and price as the y (dependent) variable. Copy/paste your scatterplot and regression results into the report. - 2 points
Can someone help with this portion, please.
Here is what I have down.
Here is the information I created.
1 The population of interest in this project is Chevrolet Camaros. The sample has been collected on 2018 Chevrolet Camaros within 2000 miles 33709 with variables of interest are Price of cars with level of measurement as ration scale of measurement. Mileage of car as ration scale of measurement. Color of car as nominal scale of measurement. Convertible or not as nominal scale of measurement.
2 The sampling method used is simple random sampling data of 30 cars have been taken randomly from a car website.
3 Descriptive statistics for the quantitative variables Price and Mileage is given.
Price Mileage
Mean 36008.967 Mean 34801.533
Variance 1.8030605e8 Variance 6.649222e8
Stand. Dev. 13427.809 Stand. Dev. 25786.085
Stand. Error 2451.5712 Stand. Error 4707.8736
Median 30194 Median 26176.5
Range 45676 Range 108228
Min 18283 Min 9532
Max 63959 Max 117760
Q1 27385 Q1 15614
Q3 41990 Q3 42099
Sum 1080269 Sum 1044046
Total 30 Total 30
4 Histogram for both the Price and Mileage are shown below:
5 The boxplot for both the Price and the Mileage are shown below.
The Sale Price boxplot is
The Mileage boxplot shows that it is
The frequent distribution for Exterior Color variable is shown below:
Exterior Color | Frequency | Relative Frequency |
---|---|---|
Black | 9 | 0.3 |
Blue | 3 | 0.1 |
Burgundy | 1 | 0.033333333 |
Gray | 4 | 0.13333333 |
Gray/Black | 1 | 0.033333333 |
Red | 8 | 0.26666667 |
White | 2 | 0.066666667 |
White/Black | 1 | 0.033333333 |
Yellow | 1 | 0.033333333 |
Based on the pie chart, we can say that most of the people prefer the red color car with black following behind.
Sale Price Mileage Exterior Color Convertable or Not 26301 38439 Black No 30888 38654 Black No 28861 42099 Black No 21500 91844 Red Yes 22399 58458 Gray No 28957 37323 Black Yes 59943 17962 Red No 35250 20163 Black No 25345 60647 Black No 27385 22468 Gray Yes 61988 14188 Gray No 18283 117760 Black Yes 27700 14918 Blue No 28998 25440 Gray Yes 40840 12889 Black Yes 59943 17962 Red No 26617 32851 Red No 35825 33112 Gray/Black No 32897 44017 Yellow Yes 42387 19136 Red No 29500 26913 Burgundy No 28861 42099 Black Yes 44199 23966 Blue No 63959 10910 White Yes 39800 9532 Red No 35666 40389 Red No 29064 15614 Red Yes 63494 15138 Blue Yes 21429 84989 White Yes 41990 14166 White/Black Yes
Can you please be more specific on what it is you are needing? If not, is there another tutor that can look at this as well? Please.
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Adyl98
3 hours ago
Provide information for the regression analysis report or provide the entire data set.
Adyl98
3 hours ago
provide the data of the 30 cars, their price and mileage. upload the file in google drive and paste the link here.
Here is the data for the 30 cars.
Sale Price Mileage Exterior Color Convertable or Not
26301 38439 Black No
30888 38654 Black No
28861 42099 Black No
21500 91844 Red Yes
22399 58458 Gray No
28957 37323 Black Yes
59943 17962 Red No
35250 20163 Black No
25345 60647 Black No
27385 22468 Gray Yes
61988 14188 Gray No
18283 117760 Black Yes
27700 14918 Blue No
28998 25440 Gray Yes
40840 12889 Black Yes
59943 17962 Red No
26617 32851 Red No
35825 33112 Gray/Black No
32897 44017 Yellow No
Here is the second half of that question and the findings.
Question:
Find & practically interpret the correlation coefficient (r) - 4 points Find & practically interpret the coefficient of determination (R2) - 4 points Find the equation of the least-squares line. Specifically, fill in the numbers for "a" and "b" in the least-squares equation: y^=a+bx. When fitting this model, have y be price and x be mileage. - 4 points Find & practically interpret the slope (b) - 4 points 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 - 2 points Use your model to estimate the price of a car that has 100,000 miles (it's required to include this prediction in the report, whether or not it's good practice to make this prediction). Is this prediction reasonable? Why or why not? - 3 point Provide a brief conclusion or discussion of the results that includes one of the following: - 1 point 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
Findings:
Explanation:
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
I used Excel to do the regression analysis.
With that, our correlation coefficient is -0.632. This means that there is a moderately negative relationship between mileage and sales price. Since the value is not near -1, it is neither a perfect nor a strong relationship. The coefficient of determination is 0.3996. This means that only 40% fit our regression model, and by others standard, this isn't enough. A higher coefficient of determination is general better for a data set. Using the regression analysis data, our least-squares equation is y=47,464.41-0.32916x. Our slope is -0.32916. This supports our negative relationship stated by our correlation coefficient. As price increases, our mileage decreases. Our y-intercept is 47.464.41. Y-intercept has 0 as an x-value. Therefore, this means that our y-intercept is the price of the car with 0 mileage. Substituting x as 100000, it leaves us with a price of $ 14,548.41. This means that, using the equation we established earlier, a car with 100,000 miles will have a sale price of $ 14,548.41.
Although we have an equation, the prediction isn't what we have in reality. First, we need to remember the fact that only 40% of our data fit the regression. This means that we need more data to have a more cohesive equation. Second, in reality, buying a car with 100,000 mileage is risky. Even if it is well-maintained, a car with that mileage will have a fair share of problems in the near future, and therefore isn't worth buying at all.
Potential problems with the data are the number of observations. Generally, the more observation we have, the better and generalizable our results can be. The results are somewhat what we can predict. In real life, the more mileage a car has, the lower is its value, and this is what we see with the regression. For other variables include its condition, the location on which we ought to buy, or the color of the car. Many of these are qualitative in nature.
Sale Price (y) | Mileage (x) | ||||||||||||
26301 | 38439 | SUMMARY OUTPUT | LEAST-SQUARES EQUATION | ||||||||||
30888 | 38654 | y=47464.41-0.32916x | |||||||||||
28861 | 42099 | Regression Statistics | |||||||||||
21500 | 91844 | Multiple R | 0.632111508 | Correlation Coefficient | |||||||||
22399 | 58458 | R Square | 0.399564959 | -0.632111508 | |||||||||
28957 | 37323 | Adjusted R Square | 0.37812085 | ||||||||||
59943 | 17962 | Standard Error | 10589.07787 | ||||||||||
35250 | 20163 | Observations | 30 | ||||||||||
25345 | 60647 | ||||||||||||
27385 | 22468 | ANOVA | |||||||||||
61988 | 14188 | df | SS | MS | F | Significance F | |||||||
18283 | 117760 | Regression | 1 | 2.09E+09 | 2089275349 | 18.63285 | 0.000179 | ||||||
27700 | 14918 | Residual | 28 | 3.14E+09 | 112128570.1 | ||||||||
28998 | 25440 | Total | 29 | 5.23E+09 | |||||||||
40840 | 12889 | ||||||||||||
59943 | 17962 | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||||
26617 | 32851 | Intercept | 47464.4074 | 3283.352 | 14.45608246 | 0 | 40738.77 | 54190.05 | 40738.77 | 54190.05 | |||
35825 | 33112 | X Variable 1 | -0.32916483 | 0.076256 | -4.316579044 | 0.000179 | -0.48537 | -0.17296 | -0.48537 | -0.17296 | |||
32897 | 44017 | ||||||||||||
42387 | 19136 | ||||||||||||
29500 | 26913 | ||||||||||||
28861 | 42099 | ||||||||||||
44199 | 23966 | ||||||||||||
63959 | 10910 | ||||||||||||
39800 | 9532 | ||||||||||||
35666 | 40389 | ||||||||||||
29064 | 15614 | ||||||||||||
63494 | 15138 | ||||||||||||
21429 | 84989 | ||||||||||||
41990 | 14166 |
Sale Price (y) | Mileage (x) |
26301 | 38439 |
30888 | 38654 |
28861 | 42099 |
21500 | 91844 |
22399 | 58458 |
28957 | 37323 |
59943 | 17962 |
35250 | 20163 |
25345 | 60647 |
27385 | 22468 |
61988 | 14188 |
18283 | 117760 |
27700 | 14918 |
28998 | 25440 |
40840 | 12889 |
59943 | 17962 |
26617 | 32851 |
35825 | 33112 |
32897 | 44017 |
42387 | 19136 |
29500 | 26913 |
28861 | 42099 |
44199 | 23966 |
63959 | 10910 |
39800 | 9532 |
35666 | 40389 |
29064 | 15614 |
63494 | 15138 |
21429 | 84989 |
41990 | 14166 |
LEAST-SQUARES EQUATION |
y=47464.41-0.32916x |
Correlation Coefficient |
-0.632111508 |
SUMMARY OUTPUT | |
Regression Statistics | |
Multiple R | 0.632111508 |
R Square | 0.399564959 |
Adjusted R Square | 0.37812085 |
Standard Error | 10589.07787 |
Observations | 30 |
ANOVA | |||||||||
df | SS | MS | F | Significance F | |||||
Regression | 1 | 2.09E+09 | 2089275349 | 18.63285 | 0.000179 | ||||
Residual | 28 | 3.14E+09 | 112128570.1 | ||||||
Total | 29 | 5.23E+09 | |||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||
Intercept | 47464.4074 | 3283.352 | 14.45608246 | 0 | 40738.77 | 54190.05 | 40738.77 | 54190.05 | |
X Variable 1 | -0.32916483 | 0.076256 | -4.316579044 | 0.000179 | -0.48537 | -0.17296 | -0.48537 | -0.17296 |
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