MATH 533 Week 7 Course Project Part C Regression and Correlation Analysis

MATH 533 Week 7 Course Project Part C Regression and Correlation Analysis. It is evident with the help of scatter graph trend line that there is positive relationship between Sales and calls. If number of calls increases the sales also increase and vice versa. Ans. 2 With help of Minitab, the regression equation is mentioned below as: Minitab Result Regression Analysis: Sales versus Calls The regression equation is Sales = 9.638 + 0.2018 Calls Ans. 3 Math 3 The correlation coefficient between sales and calls is calculated as 0 .871. This is positive correlation coefficient; it means there is positive relationship between sales and calls. If the number of calls are increased then sales will also be increased and vice versa. The calculated correlation shows strong positive correlation. Correlation: Sales, Calls (Appendix I)- Minitab Result Pearson correlation of Sales and Calls = 0.871 P-Value = 0.000 Ans. 4 Minitab Result: (See above scatter graph for below result) S = 2.05708 R-Sq = 75.9% R-Sq(adj) = 75.7% For the given data set, the coefficient of determination (R-sq) is 75.9%. It interprets that in the given data set, the portion of variability is 75.9% which is calculated by regression model (Kleinbaum, Kupper, Nizam & Muller, 2007). Ans .5 H0: (Null Hypothesis) – There is not significant correlation H1: (Alternate Hypothesis)- There is correlation either negative or positive. Significance Level, α = 0.05 Decision Rule: Reject H0 if the p−value0.05(significance level,alp h a) With the help of ANOVA table, it is come to know that the p-vale is (0.000). This p-value is less than significant value (.05). Thus, the null hypothesis should be rejected. It can be conclude that the regression model is valid due to overall test of significance. Minitab Result Math 4 Regression Analysis: Sales versus Calls Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 1 1307.7 1307.75 309.05 0.000 Calls 1 1307.7 1307.75 309.05 0.000 Error 98 414.7 4.23 Lack-of-Fit 58 243.7 4.20 0.98 0.530 Pure Error 40 171.0 4.27 Total 99 1722.4 Model Summary S R-sq R-sq(adj) R-sq(pred) 2.05708 75.92% 75.68% 74.85% Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 9.64 1.87 5.15 0.000 Calls 0.2018 0.0115 17.58 0.000 1.00 Regression Equation Sales = 9.64 + 0.2018 Calls Fits and Diagnostics for Unusual Observations Obs Sales Fit Resid Std Resid 13 43.000 37.883 5.117 2.52 R 27 44.000 48.374 -4.374 -2.17 R 76 52.000 45.550 6.450 3.16 R