Prices of diamond jewelry are based on the “4Cs” of diamonds: cut, color, clarit
ID: 3041766 • Letter: P
Question
Prices of diamond jewelry are based on the “4Cs” of diamonds: cut, color, clarity, and carat. A jeweler is trying to estimate the price of diamond earrings based on color, carats, and clarity. The jeweler has collected some data on 22 diamond pieces and the data is shown in Worksheet IND3. The jeweler would like to build a multiple regression model to estimate the price of the pieces based on color, carats, and clarity.
a) Prepare a scatter plot showing the relationship between the price and each of the independent variables.
b) If the jeweler wanted to build a regression model using only one independent variable to predict price, which variable should be used?
c) Why?
d) How do you use the value of Significance F in the model with only one independent variable?
e) If the jeweler wanted to build a regression model using two independent variables to predict price, which variable should be added to the variable selected in the one independent variable model?
f) Why?
g) If the jeweler wanted to build a regression model using three independent variables to predict price, which variable should be added to the variables selected for the two variable model?
h) Why?
i) Based on your best model, how should the jeweler price a diamond with a color of 2.75, a clarity of 3.00, and a weight of 0.85 carats?
j) How do you use the value of Significance F in the multiple regression model?
k) Does there appear to be any multicollinearity among the independent variables?
l) How can you tell if you have multicollinearity?
Color Clarity Carats Price 2.50 1.50 0.50 474.99 3.50 4.00 0.50 539.99 3.50 4.50 0.70 549.99 3.00 3.50 0.75 523.99 3.00 3.50 0.75 523.99 3.50 4.00 0.75 539.99 1.50 3.50 0.75 664.99 1.50 2.00 0.75 699.99 2.50 3.50 0.75 902.99 2.50 1.50 0.75 1,128.99 2.50 1.50 0.75 1,139.99 3.00 2.00 0.75 1,125.00 3.50 4.00 1.00 799.99 3.50 4.50 1.00 899.99 2.50 3.50 1.00 999.99 3.00 3.50 1.00 1,082.99 3.00 3.50 1.00 1,082.99 1.50 3.50 1.00 1,329.99 2.50 1.50 1.00 1,329.99 1.50 3.50 1.00 1,399.99 2.50 1.50 1.00 1,624.99 3.50 3.00 1.00 1,625.00Explanation / Answer
(a) the correlation matrix of these variable is given. It is difficult to show the scatter plot graph at this platform
answer b and C) The correlation of carats with Price is highest among three, so carats should be used as one independetn variables
answer d) The F-value of the and its significance is given in the following table. Since p-value of F is less than 0.01,then we can say that model is well explaining the variability in the data at 1% level of significance
answer(e) and (f) next varible which is more correlated to price is Clarity, so we add this variable with first variable carats
answer (g) and (h) off-course the colour, which is left with same principle as we choose first and second varible
answer (i)
regression model is price=3.4323color-166.2503clarity+1689.9057carats
if color=2.75, clarity=3, carats=0.85 then
price= 3.4323*2.75-166.2503*3+1689.9057*.85=947.1078
(j)since p-value of the model is less than 0.01, so we can say that model is significant at 1% level of significance
(k) and (l) the VIF is calculated for each of predictor and it is less than 10 , so we can say that there is no serious problem of multicollinearity
(l)
Analysis of Variance Source DF Sum ofSquares Mean
Square F Value Pr > F Model 1 1404166 1404166 20.20 0.0002 Error 20 1390380 69519 Corrected Total 21 2794545
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