Stat Project 310

# Stat Project 310 - Nicholas Huang Project BUAD-310 Section...

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Nicholas Huang BUAD-310 Project BUAD-310, Section: 14880 Instructor: Robertas Gabrys April 29, 2011 Project 1. Examine the variables and their relationships to each other: a. First look at how each variable behaves on its own by creating histograms of each. Is there any apparent skewness in any of the graphs? Explain.

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Kim 2 Profit, population, outlets, and area seem to be bimodal. All of these graphs are slightly scewed to the left except for area, which is strongly scewed to the right. Commission is scewed left with a gap because there can be either a 0 or 1. b. Get the descriptive statistics for the variables and briefly explain the business insights obtained from the variables.
Kim 3 These statistics provide us with a summary of the 51 representatives’ performances. c. Now explore the linear relationship between the response variable and each of the explanatory variables individually by constructing scatterplots of all three pairs. Do you see any strong relationships? Are they linear? Explain your answer. Column n Mean Variance Std. Dev. Std. Err. Median Range Min Max Q1 Q3 PROFIT 51 1120.0392 128571.32 358.56842 50.20962 1032 1598 188 1786 878 1412 AREA 51 13.064902 49.50234 7.03579 0.9852076 11.2 34.22 6.12 40.34 7.62 15.37 POPN 51 3.7531374 1.1808249 1.0866576 0.1521625 3.887 5.447 0.297 5.744 3.423 4.468 OUTLETS 51 174.0196 933.6596 30.555843 4.278674 174 149 85 234 149 199 COMMIS 51 0.627451 0.23843138 0.48829436 0.06837489 1 1 0 1 0 1

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Kim 4 The profit vs. area scatter plot shows a moderate negative curvilinear relationship while profit vs. population has a moderate positive curvilinear relationship. Profit vs. outlets has a weak positive curvilinear relationship. These models seem to all have a curve so a log transformation would probably work. d. Find the correlation between each pair of variables. You can create a correlation matrix using stats crunch. Comment on the results. Correlation between profit and area: -0.696 Correlation between profit and population: 0.622 Correlation between profit and outlets: 0.455 As one can see from the scatter plots above, the correlations of -0.696 and 0.622 show the moderate strength of linear regressions of profit vs. area and profit vs. population respectively. Lastly, the 0.455 shows the weak strength of the line. 2. Perform a Multiple Linear Regression analysis using all the explanatory variables AND perform a residual analysis using the graphs. a. Report the statcruch output on multiple regression using all variables. Multiple linear regression results: Dependent Variable: PROFIT Independent Variable(s): AREA, POPN, OUTLETS, COMMIS Parameter estimates: Analysis of Variable Estimate Std. Err. Tstat P-value Intercept 697.42914 367.56888 1.8974108 0.0641 AREA -23.000286 8.296634 -2.772243 0.008 POPN 101.491425 61.52084 1.649708 0.1058 OUTLETS 0.8243472 1.5522463 0.53106725 0.5979 COMMIS 316.7462 68.46514 4.6263866 <0.0001
Kim 5 variance table for multiple regression model: Summary of fit:

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Stat Project 310 - Nicholas Huang Project BUAD-310 Section...

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