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310_Group_Submission (2)

# 310_Group_Submission (2) - M ul tiple Regression Project...

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Multiple Regression Project BUAD 310 10:00 T, Th Professor Gabrys 4/28/11 Team Members: Nicholaus Johnson Brett Kan Aaron Kim Eugene Kim Jason Kim Jeremy Klif David Ko Roy Kwon

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1a) Examine the variables and their relationships to each other: Profit is roughly normal, or if anything very slightly left skewed. Area is unimodal (has one peak) and is heavily right skewed (peaks are to the left of the graph). Population is unimodal and is slightly left skewed. Outlets is unimodal and is roughly normal. Commission has no apparent pattern of skewness as it is an indicator variable. 1b) Summary Statistics: Colum n Mean Variance Std. Dev. Media n Min Max PROFI T 1120.039 2 128571.32 358.56842 1032 188 1786

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AREA 13.06490 2 49.50234 7.03579 11.2 6.12 40.3 4 POPN 3.753137 4 1.1808249 1.0866576 3.887 0.29 7 5.74 4 OUTLE TS 174.0196 933.6596 30.555843 174 85 234 COMM IS 0.627451 0.2384313 8 0.4882943 6 1 0 1 This table shows the significant summary statistics like mean (average), variance (how much points of data deviate from the average), standard deviation (how much data deviates as a whole from the mean), median (the middle number), the minimum and the maximum for each of the variables. These help us obtain a rough estimate of what we should see in the data. Net profit margin has a mean of about \$1,120,039. It also has a standard deviation of \$358,568. Since this sample is roughly normal, about 95% of salespeople in this study make a profit in between \$402,000 and \$1,838,000. Also it should be noted that the minimum value for profit is \$188,000. This shows that all salespeople do make a net profit; none of them incur a loss. Area has a mean of 13,065 square miles, and a standard deviation of about 7,036 sq miles. Being heavily right skewed, most representatives cover an area between 0 and 20,000 square miles, with a few exceptions. These few representatives cover areas of up to 40,340 sq miles. Population has a mean of 3.75 million people and a standard deviation of 1.09 million people. The heavy majority of the districts hold 2-5 million people, with the smallest district holding 297,000 and the largest holding 5.74 million people. Number of outlets has a mean of 174 outlets, with a standard deviation of about 31 outlets. The districts range from having 85 to 234 outlets in them.
1c) Profit vs. area seems to have a moderately strong negatively curved linear relationship (the dots point downward along a straight line and curve up). Profit and population seems to have a somewhat strong positive linear relationship (the dots point upward along a straight line). Profit and outlets have a weak positive curved relationship (the dots point upward along a straight line). 1d) Correlation matrix:

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PROFIT AREA POPN OUTLETS AREA - 0.69585794 POPN 0.6221696 - 0.8389509 OUTLE TS 0.45451215 - 0.6405834 0.7429463 COMM IS 0.2655532 4 0.1356011 6 - 0.26944116 - 0.30914697 This correlation matrix shows the relationship between one variable and every other variable. Here we see the correlation between area and population is -.839. Since a correlation close to .9 or -.9 is considered high and may possibly cause multicollinearity, these two explanatory variables are ones we may want to watch more closely. It may also be noted that commission has fairly weak correlations (both positive and negative) with all other variables.
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