Macroeconomics is the study of the economy as a whole. A macroeconomic variable
ID: 3315848 • Letter: M
Question
Macroeconomics is the study of the economy as a whole. A macroeconomic variable is one that measuresa 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 [or 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 X2 x3 ratings given by a popular digital photography magazine average sale price (in dollars) advertising spending for the given month (in thousands of dollars) = = The estimated multiple regression equation using data with 33 observations is as follows: y = 2,364 + 210x1-193x2 357x3 The regression just given yields a coefficient of determination of R2 0.45 and an adjusted coefficient of determination of adjusted R2 0.42. The 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 =Explanation / Answer
The coefficient of determination R2 is the ratio of the SS(regression) divided by SS(Total).
R2 = 54719/116376 = 0.4702
That indicates that multiple regression equation explains 47.02%.
The sum of squares for error divided by variation in y is the unexplained variation and 1 minues this ratio is R2.
Adjusted R2 = 1 - [SSresiduals/(n-K)] / [SStotal /(n-1)]
= 1 - [61657 /(33-5) / (116376 / (33-1))]
Adjusted R2 = 1 - 2126.10344/ 3636.75 = 0.3945
In general, adding independent variables reduced the sum of square error. . The coefficient of determination increase and the adjusted coefficient of determination reduces.
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