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Staistic - Assignment Example

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Statistical Assignment 1. Scatterplot for CREDIT BALANCE vs. SIZE The relationship between the two variables, Credit Balance and the Size, is illustrated in the scatter plot below. As can be seen from the above scatter plot there exists a relationship between the two variables as with increase in the size of number of people living in a house, the credit balance also increases and vice versa…
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Download file to see previous pages The result revealed that the relationship between the two variables is best determined by linear relationship using following equation: Regression Analysis: Credit Balance($) versus Size The regression equation is Credit Balance($) = 2591 + 403 Size Predictor Coef SE Coef T P Constant 2591.4 195.1 13.29 0.000 Size 403.22 50.95 7.91 0.000 S = 620.162 R-Sq = 56.6% R-Sq(adj) = 55.7% Analysis of Variance Source DF SS MS F P Regression 1 24092210 24092210 62.64 0.000 Residual Error 48 18460853 384601 Total 49 42553062 Unusual Observations Credit Obs Size Balance($) Fit SE Fit Residual St Resid 5 2.00 1864.0 3397.9 113.7 -1533.9 -2.52R R denotes an observation with a large standardized residual. From the regression analysis above, we can see that there is a linear positive relationship between the two variables, which means as the number of people in the house increase, the credit balance also increases. Minitab results for regression indicate a factor DF, which stands for degree of freedom. The DF for a variable is calculated by one less than the number of group levels. Similarly, degree of freedom for error is calculated by subtracting number of group levels from sample size; whereas, degree of freedom for total is calculated by sample size minus 1. ...
The sum of squares (SS) are calculated using the sum of Y’s and X’s. MS is called Measure Square of the Error and is calculated by F-test in Analysis of Variance. It is a ratio of variability between groups compared to variability within the groups. If the ratio is large then the p-value would be small indicating a statistically significant result. F-test is at least 1 indicating a non-negative number. In our case it is 62.64 which considerably high thus showing a p-value less than our level of significance i.e., 0.05. Also p-value is the probability of being greater than F value or simply the area to the right of F value. . P-value of 0.000 in Analysis of Variance and 0.026 in Sequential Analysis of Variance (for Quadratic Polynomial fit) are both less than our significance level of ? = 0.05. Further, R-Square value of 56.6% suggest that the model fits well with the actual data and there is relatively a strong relationship between the two variables. 3. Coefficient of Correlation A correlation coefficient referred to as Pearson Product-Moment Correlation Coefficient is used to measure the strength of linear relationship between the two variables. The value of the coefficient is influenced by the distribution of the independent variable. Next correlation between Credit Balance and Size was determined using Pearson’s coefficient of Correlation as shown below: Correlations: Credit Balance, Size Pearson correlation of Credit Balance and Size = 0.752 P-Value = 0.000 The Pearson Correlation value of 0.752 indicated that there existed a strong relationship between the two variables since Statisticshowto.com (2009) suggests High correlation: 0.5 to 1.0 or -0.5 to -1.0 Medium correlation: 0.3 to 0.5 ...Download file to see next pagesRead More
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