Aa Aa E. 2. Multiple coefficient of determination Macroeconomics is the study of
ID: 3251784 • Letter: A
Question
Aa Aa E. 2. Multiple coefficient of determination Macroeconomics is the study of the economy as a whole. A macroeconomic variable is one that measures a characteristic of the whole economy or one of its large-scale sectors. In forecasting the sales of a product, market researchers frequently use macroeconomic variables in addition to marketing mix variables (marketing mix variables include product, price, place lor distribution], and promotion). A market researcher is analyzing an existing multiple regression model that predicts sales for different brands of digital cameras. The dependent variable is: y monthly sales of specified digital camera (in thousands of dollars) The independent variables are the following marketing mix variables x1 ratings given by a popular digital photography magazine x2 average sale price (in dollars) x3 advertising spending for the given month (in thousands of dollars) The estimated multiple regression equation using data with 37 observations is as follows: y 2,464 201x1 187x2 362x3 The regression just given yields a multiple coefficient of determination of R2 0.47 and an adjusted multiple coefficient of determination of R 0.41. The multiple coefficient of determination indicates the proportion of variability in the dependent variable that can be explained by the regression model. The researcher would like to improve upon this model by including a macroeconomic variable that may affect sales. He decides to include the following variable: x4 most recent quarterly GDP growth rate The estimated multiple regression equation with the additional independent variable is as follows: y 2,061 273x1 142x2 307x3 55x4Explanation / Answer
The multiple coefficient of determination , denoted R^2 is the ratio of the sum of square due to the regression to the total sum of square. The R^2 for the new regression is (57893/117700)= 0.49
The sum of square due to error divided by the total sum of squares is (59807/117700) = 0.51 , 1 minus this ratio is 0.49
The adjusted multiple coefficient of determination , denoted R2 a for the new regression is 0.41.
The mean square due to error divided by the total mean square is (1869/3269) = 0.57 , and 1 minus this ratio is 0.43.
In general, adding independent variables to a multiple regression model reduces the sum of square due to error . The multiple coefficient of determination increases and adjusted multiple coefficient of determination decreases.
Adding the independent variable x4 to the multiple regression model increase the multiple coefficient of determination decrease the adjusted multiple coefficient determination.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.