I have read a report ‘Diamond carat size’ which is on website http://www.encyclopedia.com/topic/hemoglobin.aspx about changes of diamond cost by weight of diamond. There is some information about

Investigation

I have read a report ‘Diamond carat size’ which is on website http://www.encyclopedia.com/topic/hemoglobin.aspx about changes of diamond cost by weight of diamond. There is some information about that the carat weight will probably be the most important factor of diamond’s prise. In my opinion, the diamonds, which have large weight (carat), have a high price.

I considered investigating the relationship between the color of diamond and diamond’s price. I get a plot with a quite strong relationship. After that I have read an investigation ‘Birth and population trends’, which is on website http://www.stats.govt.nz/browse_for_stats/population/births/birth-population-trends.aspx about a affect of colour on the diamonds’ price. There is some information about that diamonds are range from colourless to light yellow and brown fall within the normal colour range. Within that range, colourless diamonds are the rarest, so they’re the most valuable. It is obvious relationship between the two characteristics, but, in my opinion, the colour of diamond is a minor for price of diamond.

I am going to investigate if there is a relationship between the carat of diamond and diamond’s price for the purpose of predicting the price of diamond. The explanatory variable is the carat of a diamond, measured in number of carat. The response variable is the diamond price, measured in dollars.

Initial Scatter graph

I can see that the association is positive because as the number of carat increases, the diamond price also increases, i.e. the bigger diamond to be more expensive. This is consistent with what we would expect. From the graph I can see a strong positive relationship. The scatter appears to be reasonably consistent throughout the data range with no obvious area with more points. There is a small gap between 0.9 and 1.0 carat of diamond. Reason

There are 3 possible outliers having a higher price of diamond than expected: 9739.1, 10907.4, 11205.6. It could be because these diamonds has unusual colour or good cutting. I will investigate these points more better later.

People can’t use this relationship between the carat of diamond and diamond’s price for every diamond because diamond stones in my data were collected from Singapore. So it could be use for Singapore or Asian diamonds only.

Trend

We see by the trend line that this is indeed a positive relationship – as the number of carat increases, the diamond price increases, too. The regression line of Price = 7788.7 * Carat + (-1450.02) means that for every one carat increase in diamond, the price of the diamond increases by 7788.7$. The correlation coefficient is 0.94701. There is confirmed by correlation coefficient of 0.94701, indicating that the linear relationship is strong. Most of the data points are approximately close to the regression line indicating that the relationship between the carat of diamond and diamond’s price is interpreted to be strong and liner.

The negative y-intercept of the price’s diamond when x is smaller than 0.1862 seems unrealistic as the diamonds to 0.01 carat have a price (http://www.ajediam.com/diamond_price_calculator.html). The model that I have found fits the data well and I don’t think the carat of diamonds in the lower ranges are of intercept in my investigation, so I will not change the y-intercept and look for a new linear model.

I am going to investigate whether the linear model is improved after removal of points. I have looked on the graph three unusual points, which have quite distance from the trend line. There are 3 possible outliers having a higher price of diamond than expected: 9739.1, 10907.4, 11205.6. It could be because these diamonds has unusual colour or good cutting. Reason of removing. So I can ignore these points during my investigation.

After removal of points, my liner model seems to fit the data much better. For example, the group of point from 0.45 to 0.60 carat seems closer to the trend line. Firstly, the linear model has an equation is y 7788.7 * x + -1450.02 with a correlation is 0.94701. After the removing of the points a new liner model has very the similar equation and correlation with old one: y = 7455 * x + -1317.18 with a correlation is 0.96759. The gradient of the trend line shows us that for every 1 carat of diamond increase in diamond, the price of the diamond increases by 7455$. It is a proof that there is strong relationship between the carat of diamond and diamond’s price.

Prediction

Using my linear model, which fits the data reasonably well, I can make predictions on how much a weight of the diamond (carat) will have given their price, and because of the fit I expect my predictions will be fairly accurate. For example:

If a diamond X had a carat of 0.6 we would expect the price of diamond will increase:

Y = 7788.7 * 0.6 + -1450.02= 3223.02

Based on my regression line I would predict that a diamond that a diamond would price approximately 3223.02$.Its right in the middle of my data range and I have similar values to this result. So the model appears reliable.

If a diamond X had a carat of 1.6 we would expect the price of diamond will increase:

Y=7788.7 * 1.6 + -1450.02= 11011.9

Based on my regression line I would predict that a diamond that a diamond would price approximately 11011.9$. I cannot be confident in this prediction as I do not have any diamonds more than 1.07 carat from Singapore to compare it. I found information about price of world diamonds depending by weight (carat) on the website: http://www.diamondpriceguru.com/shopping-guide/category/diamond-basics/. There is average data for diamonds from 1.5 to 1.79 carats that have average price is 11,000$. According to that I can be quite confident in my prediction.

People can use my prediction for diamond’s price based on the carat of diamond for every diamond because my equation of prediction is accurate for world diamonds.

Colour and cutting of diamonds could have effect on my prediction. Explain. Website

Improvements to model

I noticed that the data points of diamond’s price of 8,000$ and higher seem further away from the linear model and do not appear to be a good fit to the linear model. Because of this we might consider another model. I chose a quadratic model, which seems better for my data.

We see by the trend line that this is indeed a strong positive relationship. The gradient of the trend line: y = 2728 * x + 3859.9 * x^2 -159.33. The gradient of the trend line shows us that for every 1 carat increases we can expect the price of the diamond increases by 6587.9$. Most of the data points are approximately close to the regression line indicating that the relationship between the carat of diamond and diamond’s price is interpreted to be strong and liner.

My quadratic equation doesn’t have number of x, where y is negative number unlike the linear model equation. My quadratic model will have price for too small diamonds like 0.1862 and smaller. So the quadratic model for my data is more reasonable than the linear model.

Using my quadratic model, which fits the data reasonably well, I can make predictions on how much a weight of the diamond (carat) will have given their price, and because of the fit I expect my predictions will be fairly accurate. For example:

If a diamond X had a carat of 1.0 we would expect the price of diamond will increase:

y = 2728 * 1 + 3859.9 * (1)^2 -159.33

Based on my regression line I would predict that a diamond that a diamond would price approximately 6428.57$.Its in the middle of my data range and the points with price 8,000$ and bigger seem closer to the trend than on the line model. So the quadratic model appears more reliable than liner model.

If a diamond X had a carat of 1.6 we would expect the price of diamond will increase:

y = 2728 * 1.6 + 3859.9 * (1.6)^2 -159.33

Based on my regression line I would predict that a diamond that a diamond would price approximately 14086.81$. I cannot be confident in this prediction as I do not have any diamonds more than 1.07 carat from Singapore to compare it, but I can conclude that the quadratic model looks better, so I think that this prediction is probably a more reliable prediction than the liner one used earlier.

Wider Population

Colour and cutting of diamonds could have effect on my prediction. Explain. Website

Conclusion

The relationship between the carat of diamond and diamond’s price is a linear, strong and positive.

Дата добавления: 2015-11-04