The Main Idea of a Multiple Regression Analysis

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Introduction:

The main idea of a multiple regression analysis is to understand the relationship between several independent variables and a single dependent variable. (Lind, 2004) A model of the relationship is hypothesized, and estimates of the parameter values are used to develop an estimated regression equation.(abyss.uoregon.edu) The multiple regression equation used to describe the relationship is: Y' = a + b1X1 + b2X2 + b3X3 +……. + bkXk. It is used to estimate Y given selected X values and k independent variables. (Lind, 2004)
There are two components of a multiple regression analysis that are important; the coefficient of correlation (multiple R) and coefficient of determination (R²). The coefficient of correlation is the degree to which two or more independent variables are related to the dependent variable. The coefficient of determination is "the proportion of the total variation in the dependent variable that is explained by the independent variable. It can assume any value between 0 and +1.00 inclusive." (Lind, 2004) In this assignment, we are concern with the multiple R and R² of two sets data from the "Research Methods for Managerial Decisions" simulation exercise, in which we performed a multiple regression analysis on a company called Coffee Time. We needed to determine, which, produced a better multiple regression model, and how to further optimize this model. Then the team needed to answer the following scenario:
Tourism is one consideration for Coffee Time's future. A survey of 1233 visitors to Mumbai last year revealed that 110 visited a small café during their visit.
Laura claims that 10% of tourist will include a visit to a café. Use a 0.05 significance level to test her claim. Would it be wise for her to use that claim in trying to convince management to increase their advertising spending to travel agents?

Reference:

University of Oregon. Regression and correlation analysis. October 3, 2007.

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