Researchers studying how the price of diamonds varies according to certain attributes, including Table, Color, and Carat, collected the data shown in the table below. Use this data to analyze the relationship between the variables and develop a regression model to predict the price of a diamond based on the independent variables given. \begin{tabular}{ll} What is the correlation (r) between Carat and Price? & (round to 2 decimals) \\ What is the correlation ( r ) between Table and Price? & (round to 2 decimals) \\ What is the correlation (r) between Color and Price? & (round to 2 decimals) \end{tabular} Using only the two independent variables that are most highly correlated with Price, use Excel to perform a multiple regression analysis, and answer the following questions. What is the R-squared value. which represents the variation (unadjusted) in Price explained by the regression model? (round to 2 decimals) Whenever we use multiple independent variables in a regression, there is always some interaction between them, which effectively reduces the true power of the regression model to explain the variance in y (price). This value is reflected in the Adjust R-squared value. What is that value for this regression analysis? (round to 2 decimals) At what level is the multiple regression significant (i.e.,Sig.F)? (note: round to 3 decimals) In alphabetical order, what is the name of the first independent variable used in the regression (enter name)? and what is its coefficient? (round to 2 decimals) In alphabetical order, what is the name of the second independent variable used in the regression (enter name)? and what is its coefficient? (round to 2 decimals) What is the value of the intercept? (round to 2 decimals)