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 A3. 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 predictprice, which variable should be added to the one independent variable model?

f) Why?

g) If the jeweler wanted to build a regression model using three independent variables to predictprice, which variable should be added to 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 clarityof 3.00, and a weight of 0.85 carats?

j) How do you use the value of Significance F in the model with more than one independentvariable?

k) Does there appear to be any multicollinearity among the independent variables?l) How can you tell if you have multicollinearity