# research.docx - 1 MBS659 QUANTITATIVE RESEARCH FOR BUSINESS...

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1 Subscribe to view the full document. MBS659: QUANTITATIVE RESEARCH FOR BUSINESS A. What technique are you going to use? Why? We are to test the assumption of the manufacturer representative that the weight of the car (Predictor variable) is the cause of higher fuel consumption (Criterion variable). Simple liner regression will be used to test the assumption as it allows us to make predictions of the likely values of the dependent variable (fuel consumption) from known values of the independent variable (weight of the car). B. List and define the assumptions that are needed to be considered before deciding to interpret the results of your analysis. Following assumptions are needed to be considered before analysis of the results. I. A minimum requirement is to have at least 15 times more cases than IV’s i.e. with 3 IV’s - a minimum of 45 cases. II. Regression procedures assumes that the dispersion of points is linear. III. Variance of residuals are the same for all predicted scores (homoscedasticity). IV. Differences between obtained and predicted DV values should be normally distributed. V. There is no implication that an increase in weight of the car causes an increase in fuel consumption 3 Subscribe to view the full document.

C. Provide the required assurance that your data have not breached the assumptions of that technique. We need to check and test the assumptions for Number of cases, Linearity of the relationship and homoscedasticity as given in following figures. Descriptive Statistics Mean Std. Deviation N GallonsPer100Mile s 4.7847 1.66864 392 Weight in 100 lb 2.9776 .84940 392 The above Descriptive Statistics shows that there are 392 number of cases listed on the data base indicating that it has met the minimum requirement of cases; i.e. is 45 cases as mentioned in assumption 1. Linearity and homoscedasticity of the relationship 4 o 5 Subscribe to view the full document.

The above figure represents the linearity and homoscedasticity of the relationship. A line can be drawn which will represent the direction of the relationship and we can make out that line will be as close as to all the data points. In case of homoscedasticity, it will make the data take the shape of a funnel or cigar. So, from above figure we can make out that the variables do not breach homoscedasticity. Thus, the first three assumptions are met, and we can proceed with the test. The histogram and standardized residual scatter graph (Shown above) are obtained to check the assumption that the data are normally distributed. The histogram reveals that there is no definite skewness and the data are normally distributed. Similarly, the scatter plot is roughly distributed in rectangular shape and it reveals that most of the scores are concentrated in the centre along the zero point without extreme outliers. Thus, the normality assumption is not breached, and test will be continued.  • One '14

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