Question

7. The following data is the weight of diamond x with the US dollar price y.

x : 0.3 0.4 0.5 0.5 1.0 0.7

y : 510 1151 1343 1410 5669 2277

(a) Find the regression equation for the data points given.

(b) Determine the percentage of variation in price of diamond y that is explained by the weight x.

(c) Is it reasonable to predict the price of a 0.8-carat diamond using this model? If yes, predict it. If no, state why.

(d) Is it reasonable to predict the price of a 1.5-carat diamond using this model? If yes, predict it. If no, state why.

This is strictly to check answers.

Answer 1

Question (a)

The regression output can be found in the below image. The regression equation is

Y = 7177.021 * X+ (-2006.979)

Price in USD = 7177.021 * Weight of diamond + (-2006.979)

Question (b)

The % of variation in Price of diamond Y that is explained by Weight X is given by the R2 value

Here R2 value = 0.9363

So 93.63% of variation in Price of diamond Y is explained by Weight X

Question (c)

The model is significant since the significance F-value is 0.0015 which is very small when compared to value of 0.05 and also the p-value of Wieight of diamond X is 0.0015 whici is also very small when compared to value of 0.05. So the model can be used to predict the price

Given the weight of diamond = 0.8

So Price = 7177.021 * X+ (-2006.979)

= 7177.021 * 0.8 - 2006.979

= 3734.64

Question (d)

The model is significant since the significance F-value is 0.0015 which is very small when compared to value of 0.05 and also the p-value of Wieight of diamond X is 0.0015 whici is also very small when compared to value of 0.05. So the model can be used to predict the price

Given the weight of diamond = 1.5

So Price = 7177.021 * X+ (-2006.979)

= 7177.021 * 1.5 - 2006.979

= 8758.55