2M2_IND3. Prices of diamond jewelry are based on the “4Cs”ofdiamonds: cut, color, clarity, and carat. A jeweler is trying toestimate the price of diamond earrings based on color, carats, andclarity. The jeweler has collected some data on 22 diamond piecesand the data is shown in Worksheet IND3. The jeweler wouldlike tobuild a multiple regression model to estimate the price of thepieces based on color, carats, and clarity.a)Prepare a scatter plotshowing the relationship betweenthe price and each of theindependent variables.b)If the jeweler wanted to build a regressionmodel using only one independent variable to predict price, whichvariable should be used?c)Why?d)How do you use the value ofSignificance F in the model with only one independent variable?e)Ifthe jeweler wanted to build a regression model using twoindependentvariables to predict price, which variable should be addedto thevariable selected in the one independent variable model?f)Why?g)Ifthe jeweler wanted to build a regression model using threeindependent variables to predict price, which variable should beaddedto the variables selectedfor the two variablemodel?h)Why?i)Based on your best model, how should the jewelerprice a diamond with a color of 2.75, a clarity of 3.00, and aweight of 0.85 carats?j)How do you use the value of Significance Fin the multiple regression model?k)Does there appear to be anymulticollinearity among the independent variables?l)How can youtell 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 | 1,625.00 |
