# Professor Proposes Essay

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Teaching Notes “The Professor Proposes” Diamond Regression Case Study 1: Scatter plot of price v carats: [pic] Interpretation: the scatter plot shows two distinct clusters; one cluster shows diamonds in the \$300 to \$500 range, and the other cluster shows diamonds in the \$2-3,000 range. Since the professor’s diamond is in the upper range, we focus on this. Use \$1800 as the cut-off point, above which you will include this data. Note: the case study material uses a \$2,000 cut-off; I used all the diamonds in the upper cluster, which contain 7 values below \$2,000. [pic] ANALYSIS OF HIGHER-PRICED DIAMONDS: 2: Regression of price v carats: (2) Select the data set that includes the higher cluster of diamonds. Select all data rows with a price of \$2,000 or higher. Use Tools > Data Analysis > Regression. Create a plot of residuals v fitted-y by checking the “residual plots” box in the Excel regression dialog menu. Examine the regression output. Answer the following questions: -What does the R-square tell you about the relationship? There is a modest relationship between carats and price (10% of the variance explained). -What does the regression coefficient for carats mean? The negative regression coefficient is surprising – perhaps higher carat diamonds are lower in price for some reason not considered in this regression. -Is this regression coefficient significant at the alpha = .01 level?: Yes. Regression output from analysis 2: [pic] [pic] (3) Again, using only the data for diamonds with a price of \$2,000 or more, the next step requires the use of dummy or indicator variables. Using the data column “certification” assign a dummy variable by grouping GIA or AGS certified together (code these as a “1”), and the remaining codes set to “0”. Run a regression using this dummy variable versus price. -What R-squared did you