2. Multiple coefficient of determination Aa Aa Macroeconomics is the study of th

Question

2. Multiple coefficient of determination Aa Aa 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 [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 ymonthly sales of specified digital camera (in thousands of dollars) The independent variables are the following marketing mix variables: X1ratings given by a popular digital photography magazine x2average sale price (in dollars) X3advertising spending for the given month (in thousands of dollars) The estimated multiple regression equation using data with 42 observations is as follows y2,325 204x1 - 201x2 378x3 The regression just given yields a multiple coefficient of determination of R2 0.39 and an adjusted multiple coefficient of determination of Ra 0.38. 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: x4most recent quarterly GDP growth rate The estimated multiple regression equation with the additional independent variable is as follows: y -1,980 + 263x1 136x2 + 295x353x4 The ANOVA table for the new regression model is shown as follows: Analysis of Variance Source of Variation Regression Error Total Obtained by dividing the respective sums of squares by their corresponding degrees of freedom. For example, the total mean square of 3,676 is the total sum of squares divided by its degrees of freedom, or 150,726/41 Sum of Squares 65,105 85,621 150,726 Degrees of Mean Freedom SquareF-value P-value 16,276 2,314 3,676 4 7.03 0.0003 37

Explanation / Answer

Ans:

a) Explained Sum of Squares to the Total Sum of Squares

New R^2 is 0.4319, 43% of the variablity of digital camera sales.

b) The sum of squares due to error divided by total sum of squares is 0.5680. and then 1 minus this artio is 0.4319

c) Mean square due to error divided by total mean squarse is 0.6294 and 1 minus this value is 0.3706

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